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Tests of general relativity (GR) can be systematically biased when our waveform models are inaccurate. We here study systematic biases in tests of general relativity induced by neglecting lensing effects for millilensed gravitational-wave signals, where the lens mass is typically in the $10^3M_\odot$--$10^5M_\odot$ range. In particular, we use a nested-sampling Bayesian parameter estimation and model selection analysis of a millilensed signal with an unlensed parameterized post-Einsteinian (ppE) recovery model. We find that the ppE model is significantly biased toward a detection of a deviation from general relativity at signal-to-noise ratios of 30 and higher, especially when the source is aligned with the lens mass (the lensing effect is pronounced) and when its total mass is low (the signal duration is long). We use a toy model and the linear signal and Laplace approximations to provide a semi-analytic explanation for the trends in the systematic errors found in the nested sampling analysis. Moreover, a Bayes factor analysis reveals that the (unlensed) ppE model is weakly favored over the (unlensed) GR model, and a fitting factor study shows there is a significant loss of signal-to-noise ratio when using the (unlensed) ppE model. This implies that although a parameter estimation study may incorrectly infer a deviation from general relativity, a residual signal-to-noise ratio test would reveal that the ppE model is not a good fit to the data. Thus, with current detectors, millilensing-induced systematic biases are unlikely to result in false positive detections of GR deviations., Comment: 25 pages, 14 figures

Massive scalar fields are promising candidates to address many unresolved problems in fundamental physics. We report the first model-agnostic Bayesian search of massive scalar fields in LIGO/Virgo/KAGRA gravitational-wave data. We find no evidence for such fields and place the most stringent upper limits on their coupling for scalar masses $\lesssim 2\times10^{-12}\,{\rm eV}$. We exemplify the strength of these bounds by applying them to massive scalar-Gauss-Bonnet gravity, finding the tightest constraints on the coupling constant to date, $\sqrt{\alpha_{\rm GB}}\lesssim 1\,{\rm km}$ for scalar masses $\lesssim 10^{-13}\,{\rm eV}$ to 90% confidence., Comment: 18 pages, 7 figures

Precise measurements of neutron star observables (such as mass and radius) allow one to constrain the equations of state for supranuclear matter and develop a stronger understanding of nuclear physics. The Neutron star Interior Composition ExploreR (NICER) tracks X-ray hotspots on rotating NSs and is able to infer precise information about the compactness of the star. Gravitational waves carry information about the tidal deformability (related to the tidal Love number) of neutron stars, which has been measured by the LIGO/Virgo/KAGRA collaboration. These two observables enjoy an approximately universal property between each other that is insensitive to the equations of state (the "universal Love-C relation"). In this paper, we focus on deriving two analytic expressions for the Love-C relations that are ready-to-use and improve upon previous analytic expressions. The first model is inspired by a Newtonian polytrope, whose perturbation to the gravitational potential can be found analytically. We extend this Newtonian model to the relativistic regime by providing a quadratic fit to the gravitational potential perturbation against stellar compactness. The second model makes use of the Tolman VII model and adopts a spectral expansion with Chebyshev polynomials, which converges faster than the Taylor expansions used in previous work. We find that the first model provides a more accurate description of the Love-C relation for realistic neutron stars than the second model, and it provides the best expression among all other analytic relations studied here in terms of describing the averaged numerical Love-C relation. These new models are not only useful in practice, but they also show the power and importance of analytic modeling of neutron stars., Comment: 11 pages, 9 figures

We study the robustness of parametrized tests of General Relativity (GR) with gravitational waves due to waveform inaccuracy. In particular, we determine the properties of the signal (signal-to-noise ratio (SNR) and source parameters) such that we are led to falsely identify a GR deviation due to neglecting spin precession or higher models in the recovery model. To characterize the statistical significance of the biases, we compute the Bayes factor between the non-GR and GR models, and the fitting factor of the non-GR model. For highly-precessing, edge-on signals, we find that mismodeling the signal leads to a significant systematic bias in the recovery of the non-GR parameter, even at an SNR of 30. However, these biased inferences are characterized by a significant loss of SNR and a weak preference for the non-GR model (over the GR model). At a higher SNR, the biased inferences display a strong preference for the non-GR model (over the GR model) and a significant loss of SNR. For edge-on signals containing asymmetric masses, at an SNR of 30, we find that excluding higher modes does not impact the ppE tests as much as excluding spin precession. Our analysis, therefore, identifies the spin-precessing and mass-asymmetric systems for which parametrized tests of GR are robust. With a toy model and using the linear signal approximation, we illustrate these regimes of bias and characterize them by obtaining bounds on the ratio of systematic to statistical error and the effective cycles incurred due to mismodeling. As a by-product of our analysis, we explicitly connect different measures and techniques commonly used to estimate systematic errors -- linear-signal approximation, Laplace approximation, fitting factor, effective cycles, and Bayes factor -- that are generally applicable to all studies of systematic uncertainties in gravitational wave parameter estimation., Comment: 51 pages, 22 figures, 5 tables

Radial mode stability is a necessary condition for the astrophysical viability of compact objects. In recent years, astrophysical models with two fluids have gain popularity, especially in their ability to model dark matter admixed neutron stars.Just as is the case of single-fluid stars, a stability criterion based on the background equations has been developed -- the critical curve for the particle numbers of the two fluids in the two-dimensional configuration space determines a one-dimensional sequence that labels the marginally stable configurations -- but its validity depends on the linear stability of radial perturbations which remains unstudied. In this paper, we establish a set of stability criteria for two perfect-fluid relativistic stars by carefully studying the radial mode perturbation equations. We prove that modes are complete, have real eigenvalues with a minimum eigenvalue (i.e. a fundamental mode), thus a configuration is stable if and only if the fundamental mode is positive. As a consequence, our work formally and rigorously proves these necessary conditions for the stability criterion based on the background equations., Comment: 29 pages, 1 figure, submitting to Physical Review D

This review is focused on tests of Einstein's theory of general relativity with gravitational waves that are detectable by ground-based interferometers and pulsar-timing experiments. Einstein's theory has been greatly constrained in the quasi-linear, quasi-stationary regime, where gravity is weak and velocities are small. Gravitational waves are allowing us to probe a complimentary, yet previously unexplored regime: the non-linear and dynamical \emph{extreme gravity regime}. Such a regime is, for example, applicable to compact binaries coalescing, where characteristic velocities can reach fifty percent the speed of light and gravitational fields are large and dynamical. This review begins with the theoretical basis and the predicted gravitational-wave observables of modified gravity theories. The review continues with a brief description of the detectors, including both gravitational-wave interferometers and pulsar-timing arrays, leading to a discussion of the data analysis formalism that is applicable for such tests. The review then discusses gravitational-wave tests using compact binary systems, and ends with a description of the first gravitational wave observations by advanced LIGO, the stochastic gravitational wave background observations by pulsar timing arrays, and the tests that can be performed with them.., Comment: Update to Living Rev.Rel. 16 (2013) 9, now with twice the content and three times the number of references! arXiv admin note: substantial text overlap with arXiv:1304.3473

Effective field theory methods allow us to modify general relativity through higher-curvature corrections to the Einstein-Hilbert action, while preserving Lorentz invariance and the number of gravitational degrees of freedom. We here construct an approximate inspiral-merger-ringdown waveform model within the cubic, parity-preserving class of effective-field-theory extensions to Einstein's theory for the gravitational waves emitted by quasi-circular binary black holes with aligned/anti-aligned spins. Using this waveform model, we first explore the detectability of non-Einsteinian effective-field-theory effects through an extended version of effective cycles to illustrate the need to include non-Einsteinian amplitude corrections. We then use this model to analyze the GW170608 event in a full Bayesian framework, and we place new improved and more robust constraints on the coupling constants of the effective field theory. Our Bayesian model selection study disfavors the non-Einsteinian theory with a (log) Bayes factor of $\log \mathcal{B}^{\text{EFT}}_{\text{GR}} = -2.81$. Our Bayesian parameter estimation study places the constraints $\bar{\alpha}_1=0.87^{+1.95}_{-1.03}$ and $ \bar{\alpha}_2=-0.35^{+4.12}_{-2.92}$ at $90\%$ confidence on the coupling parameters of the effective-field theory. These constraints are $3.5$ stronger than previous constraints, informative relative to the prior, and independent of the choice of prior on the coupling parameters of the modified theory., Comment: 18 pages, 7 figures; Comments are welcome

Dissipative tidal interactions can be used to probe the out-of-equilibrium physics of neutron stars using gravitational wave observations. In this paper, we present the first post-Newtonian (PN) corrections to the orbital dynamics of a binary system containing objects whose tidal interactions have a dissipative contribution. We derive the 1PN-accurate equations of motion in the center-of-mass frame and a generalized energy-balance law that is valid for dissipative tidal interactions. We show how mass and energy loss due to the absorption of orbital energy change the orbital dynamics and derive the next-to-leading order correction to the gravitational wave phase of a binary system in a quasi-circular orbit containing initially non-spinning components. We then use this waveform model to constrain, for the first time, the individual dissipative tidal deformabilities of each of the binary components that generated the GW170817 event using real data. We find that the GW170817 data requires $\Xi_{1} \lesssim 1121$ and $\Xi_{2} \lesssim 1692$ at 90\% confidence, where $\Xi_{1,2}$ are the individual tidal deformabilities of the primary and secondary binary components that produced the GW170817 event., Comment: 15 pages, 2 figures. Minor typos corrected

The standard cosmological model involves the assumption of isotropy and homogeneity, a principle that is generally well-motivated but is now in conflict with various anisotropies found using independent astrophysical probes. These anisotropies tend to take the form of dipoles; while some can be explained by simple kinematic effects, many others are not fully understood. Thus, generic phenomenological models are being considered, such as a dipole in the luminosity distance. We demonstrate how such a dipole could be measured using gravitational waves from binary neutron star mergers observed by six different networks of gravitational-wave detectors, ranging from upgraded LIGO detectors to anticipated next-generation ground-based observatories. We find that, for example, a network of three next-generation detectors would produce strong constraints on a dipole's amplitude ($\sim 13\%$) and location ($\sim 84$ deg$^2$) after just one year of observing. We demonstrate that the constraints scale with the number of detections, enabling projections for multiple years of observing. Our findings indicate that future observations of binary neutron star mergers would improve upon existing dipole constraints, provided that at least one next-generation detector is built. We also assess directional sensitivity of the dipole measurements by varying the dipole's location on a grid across the sky. We find that for a network of three next-generation detectors, the range of the constraints is only $\lesssim 1.2\%$ for the amplitude and $\lesssim 4\%$ for the location, indicating that the location of the dipole will not greatly impact our ability to measure its effects., Comment: 18 pages, 9 figures

The gravitational waves emitted in the ringdown phase of binary black-hole coalescence are a unique probe of strong gravity. Understanding how deviations from general relativity affect the ringdown phase of black holes, however, is extremely challenging, as it requires solving highly-coupled and sometimes higher-order partial differential equations. We here extend a novel approach, \textit{Metric pErTuRbations wIth speCtral methodS} (METRICS), to study the metric perturbations and the quasinormal mode frequencies of ringing black holes in modified gravity. We first derive the asymptotic behavior of metric perturbations at the event horizon and spatial infinity for rotating black holes beyond general relativity. We then extend the eigenvalue-perturbation theory approach of METRICS to allow us to compute the leading-order modified gravity corrections to the quasinormal-mode frequencies and metric perturbations. We apply METRICS to rotating black holes in scalar-Gauss-Bonnet gravity. Without decoupling or simplifying the linearized field equations in this theory, we compute the leading-order corrections to the quasinormal frequencies of the axial and polar perturbations of the $nlm = 022$, 021 and 033 modes of black holes of $a \leq 0.85$. The numerical accuracy of the METRICS frequencies is $\leq 10^{-5}$ for $a \leq 0.6$, $\lesssim 10^{-4}$ for $0.6 < a \leq 0.7 $, and $\lesssim 10^{-2}$ for $0.7 < a \leq 0.85 $ for all modes studied. We fit the frequencies as a polynomial in spin, whose coefficients (up to second order in spin) are consistent with those obtained in previous slow-rotating approximations. These results are the first accurate computations of the gravitational quasinormal-mode frequencies of rapidly rotating black holes (of $a \sim 0.85$) in scalar-Gauss-Bonnet gravity., Comment: Matched the published version; abstract trimmed, please refer to the PDF for the full abstract; 24 pages, 8 figures, 6 tables

After black holes collide, the remnant settles to a stationary state by emitting gravitational waves. Once non-linearities subside, these ringdown waves are dominated by exponentially-damped sinusoids, or quasinormal modes. We develop a general method using perturbative spectral expansions to calculate the quasinormal-mode frequencies and damping times in a wide class of modified gravity theories for black holes with any subextremal spin. We apply this method to scalar-Gauss-Bonnet gravity to show its accuracy, thus enabling robust ringdown tests with gravitational wave data., Comment: 5 pages, 2 figures; matched the version published by Phys. Rev. Lett

General relativity (GR) has proven to be a highly successful theory of gravity since its inception. The theory has thrivingly passed numerous experimental tests, predominantly in weak gravity, low relative speeds, and linear regimes, but also in the strong-field and very low-speed regimes with binary pulsars. Observable gravitational waves (GWs) originate from regions of spacetime where gravity is extremely strong, making them a unique tool for testing GR, in previously inaccessible regions of large curvature, relativistic speeds, and strong gravity. Since their first detection, GWs have been extensively used to test GR, but no deviations have been found so far. Given GR's tremendous success in explaining current astronomical observations and laboratory experiments, accepting any deviation from it requires a very high level of statistical confidence and consistency of the deviation across GW sources. In this paper, we compile a comprehensive list of potential causes that can lead to a false identification of a GR violation in standard tests of GR on data from current and future ground-based GW detectors. These causes include detector noise, signal overlaps, gaps in the data, detector calibration, source model inaccuracy, missing physics in the source and in the underlying environment model, source misidentification, and mismodeling of the astrophysical population. We also provide a rough estimate of when each of these causes will become important for tests of GR for different detector sensitivities. We argue that each of these causes should be thoroughly investigated, quantified, and ruled out before claiming a GR violation in GW observations., Comment: Review article; 1 figure; 1 table; comments welcome

The parametrized post-Einsteinian (ppE) framework and its variants are widely used to probe gravity through gravitational-wave tests that apply to a large class of theories beyond general relativity. However, the ppE framework is not truly theory-agnostic as it only captures certain types of deviations from general relativity: those that admit a post-Newtonian series representation in the inspiral of coalescencing compact objects. Moreover, each type of deviation in the ppE framework has to be tested separately, making the whole process computationally inefficient and expensive, possibly obscuring the theoretical interpretation of potential deviations that could be detected in the future. We here present the neural post-Einsteinian (npE) framework, an extension of the ppE formalism that overcomes the above weaknesses using deep-learning neural networks. The core of the npE framework is a variantional autoencoder that maps the discrete ppE theories into a continuous latent space in a well-organized manner. This design enables the npE framework to test many theories simultaneously and to select the theory that best describes the observation in a single parameter estimation run. The smooth extension of the ppE parametrization also allows for more general types of deviations to be searched for with the npE model. We showcase the application of the new npE framework to future tests of general relativity with the fifth observing run of the LIGO-Virgo-KAGRA collaboration. In particular, the npE framework is demonstrated to efficiently explore modifications to general relativity beyond what can be mapped by the ppE framework, including modifications coming from higher-order curvature corrections to the Einstein-Hilbert action at high post-Newtonian order, and dark-photon interactions in possibly hidden sectors of matter that do not admit a post-Newtonian representation., Comment: 30 pages, 15 figures, submitted to PRD

Accurately modeling the tidal response of neutron stars is crucial to connecting gravitational wave observations of binaries to ultra-dense nuclear physics. Most current models of the tidal response of relativistic stars either assume a static response model, or use phenomenological models inspired by Newtonian gravity. In this work, we present a general formalism for computing the linear dynamical tidal response function of relativistic, spherically symmetric stars. Our formalism incorporates stratification due to thermal and chemical imbalances, allowing one to study the effects of g modes on the tidal response function. We also describe how to incorporate sources of dissipation due to shear and bulk viscosity. To showcase the utility of our approach, we present several applications for polytropic stars in general relativity. We show how our formalism can capture the dynamical tidal resonance due to the f and g modes of inviscid stars and explore the sensitivity of the dynamical tidal response to the compactness of the star. We also compute the dissipative tidal deformability due to bulk and shear viscous dissipation assuming a simple viscous profile for the bulk and shear viscosity., Comment: Matches published version. Link to the code updated. Available at https://github.com/AbhiHegade/Dynamical-Tidal-Response-of-Polytropic-Stars

Future gravitational-wave detectors, especially the Laser Interferometer Space Antenna (LISA), will be sensitive to black hole binaries formed in astrophysical environments that promote large eccentricities and spin-induced orbital precession. Approximate models of gravitational waves that include both effects have only recently begun to be developed. The Efficient Fully Precessing Eccentric (EFPE) family is one such model, covering the inspiral stage with small-eccentricity-expanded gravitational-wave amplitudes accurate for initial time eccentricities $e < 0.3$ at 4 years before reaching an orbital frequency of 1 Hz. In this work, we extend this model to cover a larger range of initial eccentricities. The new EFPE for moderate eccentricities (EFPE_ME) model is able to accurately represent the leading-order gravitational-wave amplitudes to $e \leq 0.8$. Comparing the EFPE and the EFPE_ME models in the LISA band, however, reveals that there is no significant difference when the eccentricity at 4 years before merger, $e_0$, is less than or equal to 0.5, as radiation reaction circularizes supermassive black hole binaries too quickly. This suggests that the EFPE model may have a larger regime of validity in eccentricity space than previously thought, making it suitable for some inspiral parameter estimation with LISA data. On the other hand, for systems with $e_0 > 0.5$, the deviations between the models are significant, particularly for binaries with total masses below $10^5\, \mathrm{M}_{\odot}$. This suggests that the EFPE_ME model will be crucial to avoid systematic bias in parameter estimation with LISA in the future, once this model has been hybridized to include the merger and ringdown and the computation of the amplitudes is optimized., Comment: 23 pages, 10 figures; matches published version

The accurate observations of neutron stars have deepened our knowledge of both general relativity and the properties of nuclear physics at large densities. Relating observations to the microphysics that govern these stars can sometimes be aided by approximate universal relations. One such relation connects the ratio of the central pressure to the central energy density and the compactness of the star, and it has been found to be insensitive to realistic models for the equation of state to a $\sim 10\%$ level. In this paper, we clarify the meaning of the microscopic quantity appearing in this relation, which is reinterpreted as the average of the speed of sound squared in the interior of a star, $\langle c_s^2 \rangle\!$. The physical origin of the quasi-universality of the $\langle c_s^2 \rangle - C$ relation is then investigated. Making use of post-Minkowskian expansions, we find it to be linked to the Newtonian limit of the structure equations, as well as to the fact that the equations of state that describe NSs are relatively stiff. The same post-Minkowskian approach is also applied to the relations between $\langle c_s^2 \rangle\!$, the moment of inertia, and the tidal deformability of a neutron star, arriving at similar conclusions., Comment: 17 pages, 12 figures

Extensions to General Relativity (GR) allow the polarization of gravitational waves (GW) from astrophysical sources to suffer from amplitude and velocity birefringence, which respectively induce changes in the ellipticity and orientation of the polarization tensor. We introduce a multi-messenger approach to test this polarization behavior of GWs during their cosmological propagation using binary sources, for which the initial polarization is determined by the inclination and orientation angles of the orbital angular momentum vector with respect to the line of sight. In particular, we use spatially-resolved radio imaging of the jet from a binary neutron star (BNS) merger to constrain the orientation angle and hence the emitted polarization orientation of the GW signal at the site of the merger, and compare to that observed on Earth by GW detectors. For GW170817 we constrain the deviation from GR due to amplitude birefringence to $\kappa_A = -0.12^{+0.60}_{-0.61}$, while the velocity birefringence parameter $\kappa_V$ remains unconstrained. The inability to constrain $\kappa_V$ is due to the fact that Virgo did not detect GW170817, and measurements of the polarization orientation require information from a combination of multiple detectors with different alignments. For this reason, we also mock future BNS mergers with resolved afterglow proper motion and project that $\kappa_V$ could be constrained to a precision of $5\,$rad (corresponding to an angular shift of the GW polarization of $\delta\phi_V\approx 0.2\,$rad for a BNS at $100\,$Mpc) by a future network of third-generation ground-based GW detectors such as Cosmic Explorer and the radio High Sensitivity Array. Crucially, this velocity birefringence effect cannot be constrained with dark binary mergers as it requires polarization information at the emission time, which can be provided only by electromagnetic emission.

Parity violation in the gravitational sector is a prediction of many theories beyond general relativity. In the propagation of gravitational waves, parity violation manifests by inducing amplitude and/or velocity birefringence between right- and left-circularly polarized modes. We study how the stochastic gravitational wave background can be used to place constraints on these birefringent effects. We consider two model scenarios, one in which we allow birefringent corrections to become arbitrarily large, and a second in which we impose stringent theory priors. In the former, we place constraints on a generic birefringent gravitational-wave signal due to the current non-detection of a stochastic background from compact binary events. We find a joint constraint on birefringent parameters, $\kappa_D$ and $\kappa_z$, of $\mathcal{O}(10^{-1})$. In the latter scenario, we forecast constraints on parity violating theories resulting from observations of the future upgraded LIGO-Virgo-KAGRA network as well as proposed third-generation detectors. We find that third-generation detectors will be able to improve the constraints by at least two orders of magnitude, yielding new stringent bounds on parity violating theories. This work introduces a novel and powerful probe of gravitational parity violation with gravitational-wave data., Comment: 29 pages, 17 figures. Data is available at https://zenodo.org/doi/10.5281/zenodo.10384998 and code to regenerate figures and results is stored at https://github.com/tcallister/stochastic-birefringence

We present a novel approach, $\textit{Metric pErTuRbations wIth speCtral methodS}$ (METRICS), to calculate the gravitational metric perturbations and the quasinormal-mode frequencies of rotating black holes of any spin without decoupling the linearized field equations. We demonstrate the method by applying it to perturbations of Kerr black holes of any spin, simultaneously solving all ten linearized Einstein equations in the Regge-Wheeler gauge through purely algebraic methods and computing the fundamental (co-rotating) quadrupole mode frequency at various spins. We moreover show that the METRICS approach is accurate and precise, yielding (i) quasinormal mode frequencies that agree with Leaver's, continuous-fraction solution with a relative fractional error smaller than $10^{-5}$ for all dimensionless spins below up to 0.95, and (ii) metric perturbations that lead to Teukolsky functions that also agree with Leaver's solution with mismatches below $1\%$ for all spins below 0.9. By not requiring the decoupling or the angular separation of the linearized field equations, the METRICS approach has the potential to be straightforwardly adapted for the computation of the quasinormal-mode frequencies of rotating black holes of any spin beyond general relativity or in the presence of matter., Comment: 24 pages of main text, 12 figures, match the published version

The detection of gravitational waves resulting by the LIGO-Virgo-Kagra collaboration has inaugurated a new era in gravitational physics, providing an opportunity to test general relativity and its modifications in the strong gravity regime. One such test involves the study of the ringdown phase of gravitational waves from binary black-hole coalescence, which can be decomposed into a superposition of quasinormal modes. In general relativity, the spectra of quasinormal modes depend on the mass, spin, and charge of the final black hole, but they can be influenced by additional properties of the black hole, as well as corrections to general relativity. In this work, we employ the modified Teukolsky formalism developed in a previous study to investigate perturbations of slowly rotating black holes in a modified theory known as dynamical Chern-Simons gravity. Specifically, we derive the master equations for the $\Psi_0$ and $\Psi_4$ Weyl scalar perturbations that characterize the radiative part of gravitational perturbations, as well as for the scalar field perturbations. We employ metric reconstruction techniques to obtain explicit expressions for all relevant quantities. Finally, by leveraging the properties of spin-weighted spheroidal harmonics to eliminate the angular dependence from the evolution equations, we derive two, radial, second-order, ordinary differential equations for $\Psi_0$ and $\Psi_4$, respectively. These equations are coupled to another radial, second-order, ordinary differential equation for the scalar field perturbations. This work is the first attempt to derive a master equation for black holes in dynamical Chern-Simons gravity using curvature perturbations. The master equations can be numerically integrated to obtain the quasinormal mode spectrum of slowly rotating black holes in this theory, making progress in the study of ringdown in dynamical Chern-Simons gravity., Comment: 40 pages, 2 figures and 1 table

General relativity, though the most successful theory of gravity, has been continuously modified to resolve its incompatibility with quantum mechanics and explain the origin of dark energy or dark matter. One way to test these modified gravity theories is to study the gravitational waves emitted during the ringdown of binary mergers, which consist of quasinormal modes. In several modified gravity theories, the even- and odd-parity gravitational perturbations of non-rotating and slowly rotating black holes have different quasinormal mode frequencies, breaking the isospectrality of general relativity. For black holes with arbitrary spin in modified gravity, there were no avenues to compute quasinormal modes except numerical relativity, until recent extensions of the Teukolsky formalism. In this work, we describe how to use the modified Teukolsky formalism to study isospectrality breaking in modified gravity. We first introduce how definite-parity modes are defined through combinations of Weyl scalars in general relativity, and then, we extend this definition to modified gravity. We then use the eigenvalue perturbation method to show how the degeneracy in quasinormal mode frequencies of different parity is broken in modified gravity. To demonstrate our analysis, we also apply it to some specific modified gravity theories. Our work lays the foundation for studying isospectrality breaking of quasinormal modes in modified gravity for black holes with arbitrary spin., Comment: 29 pages

Measurements of neutron star masses, radii, and tidal deformability have direct connections to nuclear physics via the equation of state (EoS), which for the cold, catalyzed matter in neutron star cores is commonly represented as the pressure as a function of energy density. Microscopic models with exotic degrees of freedom display nontrivial structure in the speed of sound ($c_s$) in the form of first-order phase transitions and bumps, oscillations, and plateaus in the case of crossovers and higher-order phase transitions. We present a procedure based on Gaussian processes to generate an ensemble of EoSs that include nontrivial features. Using a Bayesian analysis incorporating measurements from X-ray sources, gravitational wave observations, and perturbative QCD results, we show that these features are compatible with current constraints. We investigate the possibility of a global maximum in $c_s$ that occurs within the densities realized in neutron stars -- implying a softening of the EoS and possibly an exotic phase in the core of massive stars -- and find that such a global maximum is consistent with, but not required by, current constraints., Comment: Version submitted to PRD, 31 pages, 9 figures

Photon rings are key targets for near-future space-based very-long baseline interferometry missions. The ratio of flux measured between successive light-rings is characterized by the Lyapunov exponents of the corresponding nearly-bound null geodesics. Therefore, understanding Lyapunov exponents in this environment is of crucial importance to understanding black hole observations in general, and in particular, they may offer a route for constraining modified theories of gravity. While recent work has made significant progress in describing these geodesics for Kerr, a theory-agnostic description is complicated by the fact that Lyapunov exponents are time-parameterization dependent, which necessitates care when comparing these exponents in two different theories. In this work, we present a robust numerical framework for computing and comparing the Lyapunov exponents of null geodesics in Kerr with those in an arbitrary modified theory. We then present results obtained from calculating the Lyapunov exponents for null geodesics in two particular effective theories, scalar Gauss-Bonnet gravity and dynamical Chern-Simons gravity. Using this framework, we determine accuracy lower-bounds required before a very-long baseline interferometry observation can constrain these theories., Comment: 11 pages, 5 figures, new version to reflect correction of some typos in companion paper

In some modified theories of gravity, gravitational waves can contain up to six different polarizations, which can travel at speeds different from that of light. Searches for these different polarizations in gravitational wave data are important because any detection would be clear evidence of new physics, while clear non-detections could constrain some modified theories. The first step toward searching the data for such gravitational wave content is the calculation of the amplitudes of these different polarizations. Here we present a model-independent method to obtain the different polarizations of gravitational waves directly from the metric perturbation in theories where these polarizations are allowed to travel at different speeds. We develop our calculations so that the same procedure works with either the metric perturbation itself or its trace-reversed form. Our results are in agreement with previous work in the limit that all polarization speeds are the speed of light. We demonstrate how our model-independent method can be used with two specific modified theories of gravity, suggesting its wide applicability to other theories that allow for different gravitational wave propagation speeds. We further extend the parametrized post-Einsteinian formalism to apply to such theories that travel with different speeds. Finally, we discuss how the different speeds of different polarizations may affect null stream tests of general relativity with gravitational wave observations by multiple interferometers. Differences in propagation speeds may make null streams ineffective or lead to the detection of what seem to be isolated scalar or vector modes., Comment: 13 pages; replaced with accepted version

We study the impact of out-of-equilibrium, dissipative effects on the dynamics of inspiraling neutron stars. We find that modeling dissipative processes (such as those from the stars internal effective fluid viscosity) requires that one introduce a new tidal deformability parameter--the dissipative tidal deformability--which modifies the phase of gravitational waves emitted during the inspiral phase of a neutron star binary. We show that the dissipative tidal deformability corrects the gravitational-wave phase at 4 post-Newtonian order for quasi-circular binaries. This correction receives a large finite-size enhancement by the stellar compactness, analogous to the case of the tidal deformability. Moreover, the correction is not degenerate with the time of coalescence, which also enters at 4PN order, because it contains a logarithmic frequency-dependent contribution. Using a simple Fisher analysis, we show that physically allowed values for the dissipative tidal deformability may be constrained by measurements of the phase of emitted gravitational waves to roughly the same extent as the (electric-type, quadrupolar) tidal deformability. Finally, we show that there are no out-of-equilibrium, dissipative corrections to the tidal deformability itself. We conclude that there are at least two relevant tidal deformability parameters that can be constrained with gravitational-wave phase measurements during the late inspiral of a neutron star binary: one which characterizes the adiabatic tidal response of the star, and another which characterizes the leading-order out-of-equilibrium, dissipative tidal response. These findings open a window to probe dissipative processes in the interior of neutron stars with gravitational waves., Comment: 24 pages, 1 figure. Edits in response to comments + referee report. Slight change in normalization of \bar{\Xi}. Small edits to match journal version

Although Lorentz symmetry is a staple of General Relativity (GR), there are several reasons to believe it may not hold in a more advanced theory of gravity, such as quantum gravity. Einstein-aether theory is a modified theory of gravity that breaks Lorentz symmetry by introducing a dynamical vector field called the aether. The theory has four coupling constants that characterize deviations from GR and that must be determined through observations. Although three of the four parameters have been constrained by various empirical observations and stability requirements, one, called $c_\omega$, remains essentially unconstrained. The aim of this work is to see if a constraint on $c_\omega$ can be derived from the I-Love-Q universal relations for neutron stars, which connect the neutron star moment of inertia (I), the tidal Love number (Love), and the quadrupole moment (Q) in a way that is insensitive to uncertainties in the neutron star equation-of-state. To understand if the theory can be constrained through such relations, we model slowly-rotating or weakly tidally-deformed neutron stars in Einstein-aether theory, derive their I-Love-Q relations, and study how they depend on $c_\omega$. We find that the I-Love-Q relations in Einstein-aether theory are insensitive to $c_\omega$ and that they are close to the relations in GR. This means that the I-Love-Q relations in Einstein-aether theory remain universal but cannot be used to constrain the theory. These results indicate that to constrain the theory with neutron stars, it is necessary to investigate relations involving other observables., Comment: 20 pages, 6 figures

Near-future, space-based, radio- and gravitational-wave interferometry missions will enable us to rigorously test whether the Kerr solution of general relativity accurately describes astrophysical black holes, or if it requires some kind of modification. At the same time, recent work has greatly improved our understanding of theories of gravity that modify the Einstein-Hilbert action with terms quadratic in the curvature, allowing us to calculate black hole solutions to (essentially) arbitrary order in a slow-rotation expansion. Observational constraints of such quadratic gravity theories require the calculation of observables that are robust against the expansion order of the black hole solution used. We carry out such a study here and determine the accuracy with respect to expansion order of ten observables associated with the spacetime outside a rotating black hole in two quadratic theories of gravity, dynamical-Chern-Simons and scalar-Gauss-Bonnet gravity. We find that for all but the most rapidly rotating black holes, only about the first eight terms in the spin expansion are necessary to achieve an accuracy that is better than the statistical uncertainties of current and future missions., Comment: 19 pages, 11 figures, new version added two more references

Gravitational parity violation arises in a variety of theories beyond general relativity. Gravitational waves in such theories have their propagation altered, leading to birefringence effects in both the amplitude and speed of the wave. In this work, we introduce a generalized, theory-motivated parametrization scheme to study parity violation in gravitational wave propagation. This parametrization maps to parity-violating gravity theories in a straightforward way. We find that the amplitude and velocity birefringence effects scale with an effective distance measure that depends on how the dispersion relation is modified. Furthermore, we show that this generic parametrization can be mapped to the parametrized-post-Einsteinian (ppE) formalism with convenient applications to gravitational wave observations and model-agnostic tests of general relativity. We derive a mapping to the standard ppE waveform of the gravitational wave response function, and also find a ppE waveform mapping at the level of the polarization modes, $h_+$ and $h_\times$. Finally, we show how existing constraints in the literature translate to bounds on our new parity-violating parameters and discuss avenues for future analysis., Comment: 19 pages

Out-of-equilibrium effects may play an important role in the dynamics of neutron star mergers and in heavy-ion collisions. Bemfica, Disconzi, Noronha and Kovtun (BDNK) recently derived a causal, locally well-posed, and modally stable relativistic fluid model that incorporates the effects of viscosity and heat diffusion. We study the non-relativistic limit of this fluid model and show that causality for relativistic motion restricts the transport coefficients in the non-relativistic limit. This restriction provides an upper bound on the ratio of the shear viscosity to the entropy density for fluids that can be described as relativistic within the BDNK model and can be exactly modeled using the Navier-Stokes equation in the non-relativistic limit. Furthermore, we show that the Fourier law of heat conduction must be modified by higher gradient corrections for such fluids. We also show that the non-relativistic limit of the BDNK equations of motion are never hyperbolic, in contrast to the non-relativistic limit of extended variable models, whose non-relativistic equations of motion can be hyperbolic or not depending on the scaling of the transport coefficients present in the auxiliary equations for viscous degrees of freedom., Comment: v2-matches published version in PRD

We develop a method to perform an untargeted Bayesian search for anisotropic gravitational-wave backgrounds that can efficiently and accurately reconstruct the background intensity map. Our method employs an analytic marginalization of the posterior of the spherical-harmonic components of the intensity map, without assuming the background possesses any specific angular structure. The key idea is that the likelihood function of the spherical-harmonic components is a multivariate Gaussian when the intensity map is expressed as a linear combination of the spherical-harmonic components and the noise is stationary and Gaussian. If a uniform and wide prior of these spherical-harmonic components is prescribed, the marginalized posterior and the Bayes factor can be well approximated by a high-dimensional Gaussian integral. The analytical marginalization allows us to regard the spherical-harmonic components of the intensity map of the background as free parameters, and to construct their individual marginalized posterior distribution in a reasonable time, even though many spherical-harmonic components are required. The marginalized posteriors can, in turn, be used to accurately construct the intensity map of the background. By applying our method to mock data, we show that we can recover precisely the angular structures of various simulated anisotropic backgrounds, without assuming prior knowledge of the relation between the spherical-harmonic components predicted by a given model. Our method allows us to bypass the time-consuming numerical sampling of a high-dimensional posterior, leading to a more model-independent and untargeted Bayesian measurement of the angular structures of the gravitational-wave background., Comment: Match the published version

Lorentz symmetry is a fundamental property of Einstein's theory of general relativity that one may wish to test with gravitational wave observations. Einstein-aether theory is a model that introduces Lorentz-symmetry breaking in the gravitational sector through an aether vector field, while still leading to second-order field equations. This well-posed theory passes particle physics constraints because it modifies directly only the gravitational sector, yet it predicts deviations in the inspiral and coalescence of compact objects. We here, for the first time, put this theory to the test by comparing its gravitational wave predictions directly against LIGO/Virgo gravitational wave data. We construct a waveform model for Einstein-aether theory, EA_IMRPhenomD_NRT, through modifications of the general relativity IMRPhenomD_NRTidalv2 model (used by the LIGO/VIRGO collaboration). This model constructs a reponse function that not only contains the transverse-traceless polarization, but also additional Einstein-aether (scalar and vectorial) polarizations simultaneously. We then use the many current constraints on the theory to construct non-trivial priors for the Einstein-aether coupling constants. After testing the waveform model, we conduct parameter estimation studies on two gravitational wave events: GW170817 and GW190425. We find that these data are not sufficiently informative to place constraints on the theory that are stronger than current bounds from binary pulsar, solar system and cosmological observations. This is because, although Einstein-aether modifications include additional polarizations and have been computed beyond leading post-Newtonian order, these modifications are dominated by (already-constrained) dipole effects. These difficulties make it unclear whether future gravitational wave observations will be able to improve on current constraints on Einstein-aether theory., Comment: 32 pages, 24 figures

Gravitational wave memory is a nonoscillatory correction to the gravitational wave strain predicted by general relativity, which has yet to be detected. Within general relativity, its dominant component, known as the null memory, can be understood as arising from the backreaction of the energy carried by gravitational waves, and therefore it corresponds to a direct manifestation of the nonlinearity of the theory. In this paper, we investigate the null-memory prediction in a broad class of modified gravity theories, with the aim of exploring potential lessons to be learned from future measurements of the memory effect. Based on Isaacson's approach to the leading-order field equations, we in particular compute the null memory for the most general scalar-vector-tensor theory with second-order equations of motion and vanishing field potentials. We find that the functional form of the null memory is only modified through the potential presence of additional radiative null energy sources in the theory. We subsequently generalize this result by proving a theorem that states that the simple structure of the tensor null-memory equation remains unaltered in any metric theory whose massless gravitational fields satisfy decoupled wave equations to first order in perturbation theory, which encompasses a large class of viable extensions to general relativity., Comment: 39 pages

We develop a novel technique through spectral decompositions to study the gravitational perturbations of a black hole, without needing to decouple the linearized field equations into master equations and separate their radial and angular dependence. We first spectrally decompose the metric perturbation in a Legendre and Chebyshev basis for the angular and radial sectors respectively, using input from the asymptotic behavior of the perturbation at spatial infinity and at the black hole event horizon. This spectral decomposition allows us to then transform the linearized Einstein equations (a coupled set of partial differential equations) into a linear matrix equation. By solving the linear matrix equation for its generalized eigenvalues, we can estimate the complex quasinormal frequencies of the fundamental mode and various overtones of the gravitational perturbations simultaneously and to high accuracy. We apply this technique to perturbations of a nonspinning, Schwarzschild black hole in general relativity and find the complex quasinormal frequencies of two fundamental modes and their first two overtones. We demonstrate that the technique is robust and accurate, in the Schwarzschild case leading to relative fractional errors of $\leq 10^{-10} - 10^{-8}$ for the fundamental modes, $\leq 10^{-7} - 10^{-6}$ for their first overtones, $\leq 10^{-7} - 10^{-4}$ for their second overtones. This method can be applied to any black hole spacetime, irrespective of its Petrov type, making the numerical technique extremely powerful in the study of black hole ringdown in and outside general relativity., Comment: match the published version, animation available in the source files

Gaussian processes provide a promising framework by which to extrapolate the equation of state (EoS) of cold, catalyzed matter beyond $1-2$ times nuclear saturation density. Here we discuss how to extend Gaussian processes to include nontrivial features in the speed of sound, such as bumps, kinks, and plateaus, which are predicted by nuclear models with exotic degrees of freedom. Using a fully Bayesian analysis incorporating measurements from X-ray sources, gravitational wave observations, and perturbative QCD results, we show that these features are compatible with current constraints and report on how the features affect the EoS posteriors., Comment: 10 pages, 4 figures, CSQCD IX proceedings

The post-Newtonian formalism plays an integral role in the models used to extract information from gravitational wave data, but models that incorporate this formalism are inherently approximations. Disagreement between an approximate model and nature will produce mismodeling biases in the parameters inferred from data, introducing systematic error. We here carry out a proof-of-principle study of such systematic error by considering signals produced by quasi-circular, inspiraling black hole binaries through an injection and recovery campaign. In particular, we study how unknown, but calibrated, higher-order post-Newtonian corrections to the gravitational wave phase impact systematic error in recovered parameters. As a first study, we produce injected data of non-spinning binaries as detected by a current, second-generation network of ground-based observatories and recover them with models of varying PN order in the phase. We find that the truncation of higher order (>3.5) post-Newtonian corrections to the phase can produce significant systematic error even at signal-to-noise ratios of current detector networks. We propose a method to mitigate systematic error by marginalizing over our ignorance in the waveform through the inclusion of higher-order post-Newtonian coefficients as new model parameters. We show that this method can reduce systematic error greatly at the cost of increasing statistical error., Comment: 14 pages, 7 figures, reuploaded on 10/16/24 to correct small typo

The 2021-22 High-Energy Physics Community Planning Exercise (a.k.a. ``Snowmass 2021'') was organized by the Division of Particles and Fields of the American Physical Society. Snowmass 2021 was a scientific study that provided an opportunity for the entire U.S. particle physics community, along with its international partners, to identify the most important scientific questions in High Energy Physics for the following decade, with an eye to the decade after that, and the experiments, facilities, infrastructure, and R&D needed to pursue them. This Snowmass summary report synthesizes the lessons learned and the main conclusions of the Community Planning Exercise as a whole and presents a community-informed synopsis of U.S. particle physics at the beginning of 2023. This document, along with the Snowmass reports from the various subfields, will provide input to the 2023 Particle Physics Project Prioritization Panel (P5) subpanel of the U.S. High-Energy Physics Advisory Panel (HEPAP), and will help to guide and inform the activity of the U.S. particle physics community during the next decade and beyond., Comment: 75 pages, 3 figures, 2 tables. This is the first chapter and summary of the full report of the Snowmass 2021 Workshop. This version fixes an important omission from Table 2, adds two references that were not available at the time of the original version, fixes a minor few typos, and adds a small amount of material to section 1.1.3

We study the dynamical formation of scalar monopole and dipole hair in scalar Gauss-Bonnet theory and dynamical Chern-Simons theory. We prove that the spherically-symmetric mode of the dipole hair is completely determined by the product of the mass of the spacetime and the value of the monopole hair. We then show that the dynamics of the $\ell=1$ mode of the dipole hair is intimately tied to the appearance of the event horizon during axisymmetric collapse, which results in the radiation of certain modes that could have been divergent in the future of the collapse. We confirm these analytical predictions by simulating the gravitational collapse of a rapidly rotating neutron star in the decoupling limit, both in scalar Gauss-Bonnet and dynamical Chern-Simons theory. Our results, combined with those of Ref.~\cite{R:2022cwe}, provide a clear physical picture of the dynamics of scalar monopole and dipole radiation in axisymmetric and spherical gravitational collapse in these theories., Comment: v2-matches published version in PRD

The mirror twin Higgs model is a candidate for (strongly-interacting) complex dark matter, which mirrors SM interactions with heavier quark masses. A consequence of this model are mirror neutron stars -- exotic stars made entirely of mirror matter, which are significantly smaller than neutron stars and electromagnetically dark. This makes mergers of two mirror neutron stars detectable and distinguishable in gravitational wave observations, but can we observationally distinguish between regular neutron stars and those that may contain some mirror matter? This is the question we study in this paper, focusing on two possible realizations of mirror matter coupled to standard model matter within a compact object: (i) mirror matter captured by a neutron star and (ii) mirror neutron star-neutron star coalescences. Regarding (i), we find that (non-rotating) mirror-matter-admixed neutron stars no longer have a single mass-radius sequence, but rather exist in a two-dimensional mass-radius plane. Regarding (ii), we find that binary systems with mirror neutron stars would span a much wider range of chirp masses and completely different binary Love relations, allowing merger remnants to be very light black holes. The implications of this are that gravitational wave observations with advanced LIGO and Virgo, and X-ray observations with NICER, could detect or constrain the existence of mirror matter through searches with wider model and parameter priors., Comment: 22 pages, 16 figures

We present a systematic exploration of the loss of predictivity in Einstein-scalar-Gauss-Bonnet (ESGB) gravity. We first formulate a gauge covariant method of characterizing the breakdown of the hyperbolicity of the equations of motion in the theory. With this formalism, we show that strong geodesic focusing leads to the breakdown of hyperbolicity, and the latter is unrelated to the violation of the null convergence condition. We then numerically study the hyperbolicity of the equations during gravitational collapse for two specific ESGB gravity theories: "shift symmetric Gauss-Bonnet gravity" and a version of the theory that admits "spontaneously scalarized" black holes. We devise a "phase space" model to describe the end states for a given class of initial data. Using our phase space picture, we demonstrate that the two theories we consider remain predictive (hyperbolic) for a range of GB couplings. The range of couplings, however, is small, and thus, the presence of "spontaneously scalarized" solutions requires fine-tuning of initial data. Our results, therefore, cast doubt as to whether scalarized black hole solutions can be realistically realized in Nature even if ESGB gravity happened to be the correct gravitational description., Comment: matches published version

Since the release of the 2015 Long Range Plan in Nuclear Physics, major events have occurred that reshaped our understanding of quantum chromodynamics (QCD) and nuclear matter at large densities, in and out of equilibrium. The US nuclear community has an opportunity to capitalize on advances in astrophysical observations and nuclear experiments and engage in an interdisciplinary effort in the theory of dense baryonic matter that connects low- and high-energy nuclear physics, astrophysics, gravitational waves physics, and data science, Comment: 70 pages, 3 figures, White Paper for the Long Range Plan for Nuclear Science

In general relativity, isolated black holes obey the no hair theorems, which fix the multipolar structure of their exterior spacetime. However, in modified gravity, or when the compact objects are not black holes, the exterior spacetime may have a different multipolar structure. When two black holes are in a binary, this multipolar structure determines the morphology of the dynamics of orbital and spin precession. In turn, the precession dynamics imprint onto the gravitational waves emitted by an inspiraling compact binary through specific amplitude and phase modulations. The detection and characterization of these amplitude and phase modulations can therefore lead to improved constraints on fundamental physics with gravitational waves. Recently, analytic precessing waveforms were calculated in two scenarios: (i) dynamical Chern-Simons gravity, where the no-hair theorems are violated, and (ii) deformed compact objects with generic mass quadrupole moments. In this work, we use these two examples to propose an extension of the parameterized post-Einsteinian~(ppE) framework to include precession effects. The new framework contains $2n$ ppE parameters $(\mathscr{b}^{\rm ppE}_{(m',n)}, b^{\rm ppE}_{(m',n)})$ for the waveform phase, and $2n$ ppE parameters $(\mathscr{a}^{\rm ppE}_{(m',n)}, a^{\rm ppE}_{(m',n)})$ for the waveform amplitudes. The number of ppE corrections $n$ corresponds to the minimum number of harmonics necessary to achieve a given likelihood threshold when comparing the truncated ppE waveform with the exact one, and $(m',n)$ corresponds to the harmonic numbers of the harmonics containing ppE parameters. We show explicitly how these ppE parameters map to the specific example waveforms discussed above. The proposed ppE framework can serve as a basis for future tests of general relativity with gravitational waves from precessing binaries., Comment: 24 pages, 5 figures, published version

The distance-inclination degeneracy limits gravitational-wave parameter estimation of compact binary mergers. Although the degeneracy can be partially broken by including higher-order modes or precession, these effects are suppressed in binary neutron stars. In this work, we implement a new parametrization of the tidal effects in the binary neutron-star waveform, exploiting the binary Love relations, that breaks the distance-inclination degeneracy. The binary Love relations prescribe the tidal deformability of a neutron star as a function of its source-frame mass in an equation-of-state insensitive way and, thus, allows direct measurement of the redshift of the source. If the cosmological parameters are assumed to be known, the redshift can be converted to a luminosity distance, and the distance-inclination degeneracy can thus be broken. We implement this new approach, studying a range of binary neutron-star observing scenarios using Bayesian parameter estimation on synthetic data. In the era of the third-generation detectors, for observations with signal-to-noise ratios ranging from 6 to 167, we forecast up to an $\sim70\%$ decrease in the $90\%$ credible interval of the distance and inclination and up to an $\sim50\%$ decrease in that of the source-frame component masses. For edge-on systems, our approach can result in moderate ($\sim50\%$) improvement in the measurements of distance and inclination for binaries with a signal-to-noise ratio as low as 10. This prescription can be used to better infer the source-frame masses and, hence, refine population properties of neutron stars, such as their maximum mass, impacting nuclear astrophysics. When combined with the search for electromagnetic counterpart observations, the work presented here can be used to put improved bounds on the opening angle of jets from binary neutron-star mergers., Comment: 19 pages, 13 figures, text and references updated, v2 matches version published in PRD

Cosmic Probes of Fundamental Physics take two primary forms: Very high energy particles (cosmic rays, neutrinos, and gamma rays) and gravitational waves. Already today, these probes give access to fundamental physics not available by any other means, helping elucidate the underlying theory that completes the Standard Model. The last decade has witnessed a revolution of exciting discoveries such as the detection of high-energy neutrinos and gravitational waves. The scope for major developments in the next decades is dramatic, as we detail in this report., Comment: Report of theTopical Group on Cosmic Probes of Fundamental Physics, for the U.S. decadal Particle Physics Planning Exercise (Snowmass 2021)

Given the lack of empirical evidence of weakly interacting dark matter, it is reasonable to look to other candidates such as a confining dark sector with a similar number of particles as the standard model. Twin Higgs mirror matter is one such model that is a twin of the standard model with particles masses 3--6 times heavier than the standard model that solves the hierarchy problem. This generically predicts mirror neutron stars, degenerate objects made entirely of mirror nuclear matter. We find their structure using a realistic equation of state from crust (nuclei) to core (relativistic mean-field model) and scale the particle masses using lattice QCD results. We find that mirror neutron stars have unique signatures that are detectable via gravitational waves and binary pulsars, that provides an intriguing possibility for probing dark matter., Comment: prepared for the proceedings of Quark Matter 2022. 6 pages, 1 figure

Ho\v{r}ava-Lifshitz gravity is an alternative theory to general relativity which breaks Lorentz invariance in order to achieve an ultraviolet complete and power-counting renormalizable theory of gravity. In the low energy limit, Ho\v{r}ava-Lifshitz gravity coincides with a vector-tensor theory known as khronometric gravity. The deviation of khronometric gravity from general relativity can be parametrized by three coupling constants: $\alpha$, $\beta$, and $\lambda$. Solar system experiments and gravitational wave observations impose stringent bounds on $\alpha$ and $\beta$, while $\lambda$ is still relatively unconstrained ($\lambda\lesssim 0.01$). In this paper, we study whether one can constrain this remaining parameter with neutron star observations through the universal I-Love-Q relations between the moment of inertia (I), the tidal Love number (Love), and the quadrupole moment (Q), which are insensitive to details in the nuclear matter equation of state. To do so, we perturbatively construct slowly-rotating and weakly tidally-deformed neutron stars in khronometric gravity. We find that the I-Love-Q relations are independent of $\lambda$ in the limit $(\alpha,\beta) \to 0$. Although some components of the field equations depend on $\lambda$, we show through induction and a post-Minkowskian analysis that slowly-rotating neutron stars do not depend on $\lambda$ at all. Tidally deformed neutron stars, on the other hand, are modified in khronometric gravity (though the usual Love number is not modified, as mentioned earlier), and there are potentially new, non-GR Love numbers, though their observability is unclear. These findings indicate that it may be difficult to constrain $\lambda$ with rotating/tidally-deformed neutron stars., Comment: 18 pages. Added a new Appendix, added additional explanation to Sects. II and III, and added a small clarification to Sect. V, no change to main results

The detection of gravitational waves from compact binary mergers by the LIGO/Virgo collaboration has, for the first time, allowed for tests of relativistic gravity in the strong, dynamical and nonlinear regime. Outside Einstein's relativity, spinning black holes may be different from their general relativistic counterparts, and their merger may then lead to a modified ringdown. We study the latter and, for the first time, derive a modified Teukolsky equation, i.e., a set of linear, decoupled differential equations that describe dynamical perturbations of non-Kerr black holes for the radiative Newman-Penrose scalars $\Psi_0$ and $\Psi_4$. We first focus on non-Ricci-flat, Petrov type D black hole backgrounds in modified gravity, and derive the modified Teukolsky equation through direct decoupling and through a new approach, proposed by Chandrasekhar, that uses certain gauge conditions. We then extend this analysis to non-Ricci-flat, Petrov type I black hole backgrounds in modified gravity, assuming they can be treated as a linear perturbation of Petrov type D, black hole backgrounds in GR by generalizing Chandrasekhar's approach, and derive the decoupled modified Teukolsky equation. Our work lays the foundation to study the gravitational waves emitted in the ringdown phase of black hole coalescence in modified gravity for black holes of any spin. Our work can also be extended to compute gravitational waves emitted by extreme mass-ratio binary inspirals in modified gravity., Comment: 33 pages, 2 figures, 1 table

Particular couplings between a scalar field and the Gauss-Bonnet invariant lead to spontaneous scalarization of black holes. Here we continue our work on simulating this phenomenon in the context of binary black hole systems. We consider a negative coupling for which the black-hole spin plays a major role in the scalarization process. We find two main phenomena: (i) dynamical descalarization, in which initially scalarized black holes form an unscalarized remnant, and (ii) dynamical scalarization, whereby the late merger of initially unscalarized black holes can cause scalar hair to grow. An important consequence of the latter case is that modifications to the gravitational waveform due to the scalar field may only occur post-merger, as its presence is hidden during the entirety of the inspiral. However, with a sufficiently strong coupling, we find that scalarization can occur before the remnant has even formed. We close with a discussion of observational implications for gravitational-wave tests of general relativity., Comment: 16 pages, 12 figures

Spin precession in compact binaries is intricately tuned to the multipole structure of the underlying bodies. For black holes, violations of the no-hair theorems induced by modifications to general relativity correct the precession dynamics, which in turn imprints onto the amplitude and phase modulations of the gravitational waves emitted by the binary. Recently, the spin precession equations were derived up to second order in spin for dynamical Chern-Simons gravity, a parity violating modified theory of gravity. We here solve these equations and construct, for the first time, analytic expressions for the time- and frequency-domain gravitational waves emitted in the quasi-circular inspiral of spin-precessing black hole binaries in a modified theory of gravity using the post-Newtonian approximation. Working within the small coupling approximation and using multiple scale analysis, we show that the corrections to the nutation phase enter at relative 1PN order, and the corrections to the precession angle and Thomas phase enter at relative 0PN order. Making use of the stationary phase approximation and shifted uniform asymptotics, we find that the Fourier phase of the waveform is characterized by three modifications, two due to the back-reaction of the precession dynamics onto the spin-orbit and spin-spin couplings that enter at 1.5PN and 2PN orders, and a 2PN modification due to the emission of dipole radiation. We also find that back-reaction of the precession dynamics forces the dCS corrections to the Fourier amplitude to enter at 0PN order, as opposed to 2PN order, as expected for spin-aligned binaries. Our work lays the first foundational stones to build an inspiral-merger-ringdown phenomenological model for spin-precessing binaries in a modified theory of gravity., Comment: 32 pages, 4 figures, published version