Search

We explore the use of the mass spectrum of neutron stars and black holes in gravitational-wave compact binary sources as a cosmological probe. These standard siren sources provide direct measurements of luminosity distance. In addition, features in the mass distribution, such as mass gaps or peaks, will redshift, and thus provide independent constraints on their redshift distribution. We argue that the entire mass spectrum should be utilized to provide cosmological constraints. For example, we find that the mass spectrum of LIGO--Virgo--KAGRA events introduces at least five independent mass ``features'': the upper and lower edges of the pair instability supernova (PISN) gap, the upper and lower edges of the neutron star--black hole gap, and the minimum neutron star mass. We find that although the PISN gap dominates the cosmological inference with current detectors (2G), as shown in previous work, it is the lower mass gap that will provide the most powerful constraints in the era of Cosmic Explorer and Einstein Telescope (3G). By using the full mass distribution, we demonstrate that degeneracies between mass evolution and cosmological evolution can be broken, unless an astrophysical conspiracy shifts all features of the full mass distribution simultaneously following the (non-trivial) Hubble diagram evolution. We find that this self-calibrating ``spectral siren'' method has the potential to provide precision constraints of both cosmology and the evolution of the mass distribution, with 2G achieving better than $10\%$ precision on $H(z)$ at $z\lesssim1$ within a year, and 3G reaching $\lesssim1\%$ at $z\gtrsim2$ within one month., Comment: Matches PRL published version

It is generally assumed within the standard cosmological model that initial density perturbations are Gaussian at all scales. However, primordial quantum diffusion unavoidably generates non-Gaussian, exponential tails in the distribution of inflationary perturbations. These exponential tails have direct consequences for the formation of collapsed structures in the universe, as has been studied in the context of primordial black holes. We show that these tails also affect the very-large-scale structures, making heavy clusters like "El Gordo", or large voids like the one associated with the cosmic microwave background cold spot, more probable. We compute the halo mass function and cluster abundance as a function of redshift in the presence of exponential tails. We find that quantum diffusion generically enlarges the number of heavy clusters and depletes subhalos, an effect that cannot be captured by the famed $f_{\mathrm{NL}}$ corrections. These late-universe signatures could thus be fingerprints of quantum dynamics during inflation that should be incorporated in $N$-body simulations and checked against astrophysical data., 5 pages without appendices (total 8 pages), 3 figures, matches published version in Phys. Rev. Letters

Strong gravitational lensing of gravitational waves (GWs) has been forecasted to become detectable in the upcoming observing runs. However, definitively distinguishing pairs of lensed sources from random associations is a challenging problem. We investigate the degree to which unlensed events mimic lensed ones because of the overlap of parameters due to a combination of random coincidence and errors in parameter estimation. We construct a mock catalog of lensed and unlensed events. We find that the false alarm probability (FAP) based on coincidental overlaps of the chirp mass, sky location, and coalescence phase are approximately $9\%$, $1\%$, and $10\%$ per pair, respectively. Combining all three, the overall FAP per pair is $\sim10^{-4}$. As the number of events, $N$, in the GW catalogs increases, the number of random pairs of events increases as $\sim N^2$. Meanwhile, the number of lensed events will increase linearly with $N$, implying that for sufficiently high $N$, the false alarms will always dominate over the true lensing events. This issue can be compensated for by placing higher thresholds on the lensing candidates (e.g., selecting a higher signal-to-noise ratio (SNR) threshold), which will lead to better parameter estimation and, thus, lower FAP per pair -- at the cost of dramatically decreasing the size of the lensing sample (by $\sim 1/\mbox{SNR}^3$). We show that with our simple overlap criteria for current detectors at design sensitivity, the false alarms will dominate for realistic lensing rates ($\lesssim10^{-3}$) even when selecting the highest SNR pairs. These results highlight the necessity to design alternative identification criteria beyond simple waveform and sky location overlap. Future GW detectors Cosmic Explorer and Einstein Telescope may provide sufficient improvement in parameter estimation, allowing for the conclusive detection of strong lensing of GWs., 17 pages, 14 figures. Matches the version published in Phys. Rev. D 107, 063023 (2023)

The mass-sheet degeneracy is a well-known problem in gravitational lensing which limits our capability to infer astrophysical lens properties or cosmological parameters from observations. As the number of gravitational wave observations grows, detecting lensed events will become more likely, and to assess how the mass-sheet degeneracy may affect them is crucial. Here we study both analytically and numerically how the lensed waveforms are affected by the mass-sheet degeneracy computing the amplification factor from the diffraction integral. In particular, we differentiate between the geometrical optics, wave optics and interference regimes, focusing on ground-based gravitational waves detectors. In agreement with expectations of gravitational lensing of electromagnetic radiation, we confirm how, in the geometrical optics scenario, the mass-sheet degeneracy cannot be broken with only one lensed image. However, we find that in the interference regime, and in part in the wave-optics regime, the mass-sheet degeneracy can be broken with only one lensed waveform thanks to the characteristic interference patterns of the signal. Finally, we quantify, through template matching, how well the mass-sheet degeneracy can be broken. We find that, within present GW detector sensitivities and considering signals as strong as those which have been detected so far, the mass-sheet degeneracy can lead to a $1\sigma$ uncertainty on the lens mass of $\sim 12\%$. With these values the MSD might still be a problematic issue. But in case of signals with higher signal-to-noise ratio, the uncertainty can drop to $\sim 2\%$, which is less than the current indeterminacy achieved by dynamical mass measurements., Comment: 13 pages, 8 figures. Comments are welcome

Since 2015 the gravitational-wave observations of LIGO and Virgo have transformed our understanding of compact-object binaries. In the years to come, ground-based gravitational-wave observatories such as LIGO, Virgo, and their successors will increase in sensitivity, discovering thousands of stellar-mass binaries. In the 2030s, the space-based LISA will provide gravitational-wave observations of massive black holes binaries. Between the $\sim 10$-$10^3~\mathrm{Hz}$ band of ground-based observatories and the $\sim10^{-4}$-$10^{-1}~\mathrm{Hz}$ band of LISA lies the uncharted decihertz gravitational-wave band. We propose a Decihertz Observatory to study this frequency range, and to complement observations made by other detectors. Decihertz observatories are well suited to observation of intermediate-mass ($\sim10^2$-$10^4 M_\odot$) black holes; they will be able to detect stellar-mass binaries days to years before they merge, providing early warning of nearby binary neutron star mergers and measurements of the eccentricity of binary black holes, and they will enable new tests of general relativity and the Standard Model of particle physics. Here we summarise how a Decihertz Observatory could provide unique insights into how black holes form and evolve across cosmic time, improve prospects for both multimessenger astronomy and multiband gravitational-wave astronomy, and enable new probes of gravity, particle physics and cosmology., Comment: 13 pages, 1 figure. Published in Experimental Astronomy. Summarising white paper arXiv:1908.11375

Since the very beginning of astronomy the location of objects on the sky has been a fundamental observational quantity that has been taken for granted. While precise two dimensional positional information is easy to obtain for observations in the electromagnetic spectrum, the positional accuracy of current and near future gravitational wave detectors is limited to between tens and hundreds of square degrees, which makes it extremely challenging to identify the host galaxies of gravitational wave events or to confidently detect any electromagnetic counterparts. Gravitational wave observations provide information on source properties and distances that is complementary to the information in any associated electromagnetic emission and that is very hard to obtain in any other way. Observing systems with multiple messengers thus has scientific potential much greater than the sum of its parts. A gravitational wave detector with higher angular resolution would significantly increase the prospects for finding the hosts of gravitational wave sources and triggering a multi-messenger follow-up campaign. An observatory with arcminute precision or better could be realised within the Voyage 2050 programme by creating a large baseline interferometer array in space and would have transformative scientific potential. Precise positional information of standard sirens would enable precision measurements of cosmological parameters and offer new insights on structure formation; a high angular resolution gravitational wave observatory would allow the detection of a stochastic background and resolution of the anisotropies within it; it would also allow the study of accretion processes around black holes; and it would have tremendous potential for tests of modified gravity and the discovery of physics beyond the Standard Model., 26 pages, 2 figures. White paper submitted to ESA's Voyage 2050 call on behalf of the LISA Consortium 2050 Task Force

Gravitational wave (GW) detections of binary black holes (BBHs) have shown evidence for a dearth of component black holes with masses above $\sim50M_\odot$. This is consistent with expectations of a mass gap due to the existence of pair-instability supernovae (PISN). We argue that ground-based GW detectors will be sensitive to BBHs with masses above this gap, $\gtrsim120\,M_\odot$. With no detections, two years at upgraded sensitivity (A+) would constrain the local merger rate of these BBHs on the "far side" of the PISN gap to be lower than $0.01\,\mathrm{yr}^{-1}\mathrm{Gpc}^{-3}$. Alternatively, with a few tens of events we could constrain the location of the upper edge of the gap to the percent level. We consider the potential impact of "interloper" black holes within the PISN mass gap on this measurement. Far side BBHs would also be observed by future instruments such as Cosmic Explorer (CE), Einstein Telescope (ET) and LISA, and may dominate the fraction of multi-band events. We show that by comparing observations from ground and space it is possible to constrain the merger rate history. Moreover, we find that the upper edge of the PISN mass gap leaves an imprint on the spectral shape of the stochastic background of unresolved binaries, which may be accessible with A+ sensitivity. Finally, we show that by exploiting the upper edge of the gap, these high-mass BBHs can be used as standard sirens to constrain the cosmic expansion at redshifts of $\sim0.4$, $0.8$, and~$1.5$ with LISA, LIGO-Virgo, and CE/ET, respectively. These far-side binaries would be the most massive BBHs LIGO-Virgo could detect., Matches ApJL accepted version. New analysis of the impact of a population of interloper BBHs within the PISN gap

Strong gravitational lensing of gravitational wave sources offers a novel probe of both the lens galaxy and the binary source population. In particular, the strong lensing event rate and the time delay distribution of multiply-imaged gravitational-wave binary coalescence events can be used to constrain the mass distribution of the lenses as well as the intrinsic properties of the source population. We calculate the strong lensing event rate for a range of second (2G) and third generation (3G) detectors, including Advanced LIGO/Virgo, A+, Einstein Telescope (ET), and Cosmic Explorer (CE). For 3G detectors, we find that {$\sim0.1\%$} of observed events are expected to be strongly lensed. We predict detections of {$\sim 1$} lensing pair per year with A+, and {$\sim 50$} pairs {per year} with ET/CE. These rates are highly sensitive to the characteristic galaxy velocity dispersion, $\sigma_*$, implying that observations of the rates will be a sensitive probe of lens properties. We explore using the time delay distribution between multiply-imaged gravitational-wave sources to constrain properties of the lenses. We find that 3G detectors would constrain $\sigma_*$ to {$\sim21\%$ after 5 years}. Finally, we show that the presence or absence of strong lensing {within the detected population} provides useful insights into the source redshift and mass distribution out to redshifts beyond the peak of the star formation rate, which can be used to constrain formation channels and their relation to the star formation rate and delay time distributions for these systems., Comment: 26 pages, 13 figures; Updated Equation 6 and the corresponding lensing event rates and figures. Added discussion on SIS magnification ratio in the appendix

We study the cosmological propagation of gravitational waves (GWs) beyond general relativity (GR) across homogeneous and isotropic backgrounds. We consider scenarios in which GWs interact with an additional tensor field and use a parametrized phenomenological approach that generically describes their coupled equations of motion. We analyze four distinct classes of derivative and non-derivative interactions: mass, friction, velocity, and chiral. We apply the WKB formalism to account for the cosmological evolution and obtain analytical solutions to these equations. We corroborate these results by analyzing numerically the propagation of a toy GW signal. We then proceed to use the analytical results to study the modified propagation of realistic GWs from merging compact binaries, assuming that the GW signal emitted is the same as in GR. We generically find that tensor interactions lead to copies of the originally emitted GW signal, each one with its own possibly modified dispersion relation. These copies can travel coherently and interfere with each other leading to a scrambled GW signal, or propagate decoherently and lead to echoes arriving at different times at the observer that could be misidentified as independent GW events. Depending on the type of tensor interaction, the detected GW signal may exhibit amplitude and phase distortions with respect to a GW waveform in GR, as well as birefringence effects. We discuss observational probes of these tensor interactions with both individual GW events, as well as population studies for both ground- and space-based detectors., Updated to journal version

The curvature perturbations produced during an early era of inflation are known to have quasi-Gaussian distribution functions close to their maximum, where they are well constrained by measurements of the cosmic microwave background anisotropies and of the large-scale structures. In contrast, the tails of these distributions are poorly known, although this part is the relevant one for rare, extreme objects such as primordial black holes. We show that these tails are highly non-Gaussian, and cannot be described with standard non-Gaussian expansions, that are designed to approximate the distributions close to their maximum only. Using the stochastic-$\delta N$ formalism, we develop a generic framework to compute the tails, which are found to have an exponential, rather than Gaussian, decay. These exponential tails are inevitable, and do not require any non-minimal feature as they simply result from the quantum diffusion of the inflaton field along its potential. We apply our formalism to a few relevant single-field, slow-roll inflationary potentials, where our analytical treatment is confirmed by comparison with numerical results. We discuss the implications for the expected abundance of primordial black holes in these models, and highlight that it can differ from standard results by several orders of magnitude. In particular, we find that potentials with an inflection point overproduce primordial black holes, unless slow roll is violated., Comment: 34 pages, 14 figures. Justification of the characteristic function expansion in section 2.2 amended; definition of a new scalar product in equation (2.21); figure 13 is corrected. Our results are unchanged

We consider gravitational wave (GW) sources with an associated electromagnetic (EM) counterpart, and analyze the time delay between both signals in the presence of lensing. If GWs have wavelengths comparable to the Schwarzschild radius of astrophysical lenses, they must be treated with wave optics, whereas EM waves are typically well within the approximation of geometric optics. With concrete examples, we confirm that the GW signal never arrives before its EM counterpart, if both are emitted at the same time. However, during the inspiral of a binary, peaks of the GW waveform can arrive before their EM counterpart. We stress this is only an apparent superluminality since the GW waveform is both distorted and further delayed with respect to light. In any case, measuring the multi-messenger time delay and correctly interpreting it has important implications for unveiling the distribution of lenses, testing the nature of gravity, and probing the cosmological expansion history., Comment: 8 pages, 5 figures. Accepted PRD. Updated Eq. (1)-(3) to comoving distance

The gravitational-wave astronomical revolution began in 2015 with LIGO's observation of the coalescence of two stellar-mass black holes. Over the coming decades, ground-based detectors like LIGO will extend their reach, discovering thousands of stellar-mass binaries. In the 2030s, the space-based LISA will enable gravitational-wave observations of the massive black holes in galactic centres. Between LISA and ground-based observatories lies the unexplored decihertz gravitational-wave frequency band. Here, we propose a Decihertz Observatory to cover this band, and complement observations made by other gravitational-wave observatories. The decihertz band is uniquely suited to observation of intermediate-mass ($\sim 10^2$-$10^4 M_\odot$) black holes, which may form the missing link between stellar-mass and massive black holes, offering a unique opportunity to measure their properties. Decihertz observations will be able to detect stellar-mass binaries days to years before they merge and are observed by ground-based detectors, providing early warning of nearby binary neutron star mergers, and enabling measurements of the eccentricity of binary black holes, providing revealing insights into their formation. Observing decihertz gravitational-waves also opens the possibility of testing fundamental physics in a new laboratory, permitting unique tests of general relativity and the Standard Model of particle physics. Overall, a Decihertz Observatory will answer key questions about how black holes form and evolve across cosmic time, open new avenues for multimessenger astronomy, and advance our understanding of gravitation, particle physics and cosmology., 52 pages, 5 figures, 4 tables. Submitted to Classical & Quantum Gravity. Based upon a white paper for ESA's Voyage 2050 on behalf of the LISA Consortium 2050 Task Force

Gravitational wave (GW) oscillations occur whenever there are additional tensor modes interacting with the perturbations of the metric coupled to matter. These extra modes can arise from new spin-2 fields (as in e.g. bigravity theories) or from non-trivial realisations of the cosmological principle induced by background vector fields with internal symmetries (e.g. Yang-Mills, gaugids or multi-Proca). We develop a general cosmological framework to study such novel features due to oscillations. The evolution of the two tensor modes is described by a linear system of coupled second order differential equations exhibiting friction, velocity, chirality and mass mixing. We follow appropriate schemes to obtain approximate solutions for the evolution of both modes and show the corresponding phenomenology for different mixings. Observational signatures include modulations of the wave-form, oscillations of the GW luminosity distance, anomalous GW speed and chirality. We discuss the prospects of observing these effects with present and future GW observatories such as LIGO/VIRGO and LISA., 36 pages, 9 figures. Matches JCAP version

Primordial Black Holes (PBH) arise naturally from high peaks in the curvature power spectrum of near-inflection-point single-field inflation, and could constitute today the dominant component of the dark matter in the universe. In this letter we explore the possibility that a broad spectrum of PBH is formed in models of Critical Higgs Inflation (CHI), where the near-inflection point is related to the critical value of the RGE running of both the Higgs self-coupling $\lambda(\mu)$ and its non-minimal coupling to gravity $\xi(\mu)$. We show that, for a wide range of model parameters, a half-domed-shaped peak in the matter spectrum arises at sufficiently small scales that it passes all the constraints from large scale structure observations. The predicted cosmic microwave background spectrum at large scales is in agreement with Planck 2015 data, and has a relatively large tensor-to-scalar ratio that may soon be detected by B-mode polarization experiments. Moreover, the wide peak in the power spectrum gives an approximately lognormal PBH distribution in the range of masses $0.01 - 100\,M_\odot$, which could explain the LIGO merger events, while passing all present PBH observational constraints. The stochastic background of gravitational waves coming from the unresolved black-hole-binary mergers could also be detected by LISA or PTA. Furthermore, the parameters of the CHI model are consistent, within $2\sigma$, with the measured Higgs parameters at the LHC and their running. Future measurements of the PBH mass spectrum could allow us to obtain complementary information about the Higgs couplings at energies well above the EW scale, and thus constrain new physics beyond the Standard Model., Comment: 6 pages, 3 figures. Matches PLB version

We study the role of field redefinitions in general scalar-tensor theories. In particular, we first focus on the class of field redefinitions linear in the spin-2 field and involving derivatives of the spin-0 mode, generically known as disformal transformations. We start by defining the action of a disformal transformation in the tangent space. Then, we take advantage of the great economy of means of the language of differential forms to compute the full transformation of Horndeski's theory under general disformal transformations. We obtain that Horndeski's action maps onto itself modulo a reduced set of non-Horndeski Lagrangians. These new Lagrangians are found to be invariant under disformal transformation that depend only in the first derivatives of the scalar. Moreover, these combinations of Lagrangians precisely appear when expressing in our basis the constraints of the recently proposed Extended Scalar-Tensor (EST) theories. These results allow us to classify the different orbits of scalar-tensor theories invariant under particular disformal transformations, namely the special disformal, kinetic disformal and disformal Horndeski orbits. In addition, we consider generalizations of this framework. We find that there are possible well-defined extended disformal transformations that have not been considered in the literature. However, they generically cannot link Horndeski theory with EST theories. Finally, we study further generalizations in which extra fields with different spin are included. These field redefinitions can be used to connect different gravity theories such as multi-scalar-tensor theories, generalized Proca theories and bi-gravity. We discuss how the formalism of differential forms could be useful for future developments in these lines., Comment: 23+10 pages, 1 figure and 2 tables

Multi-messenger gravitational wave (GW) astronomy has commenced with the detection of the binary neutron star merger GW170817 and its associated electromagnetic counterparts. The almost coincident observation of both signals places an exquisite bound on the GW speed $|c_g/c-1|\leq5\cdot10^{-16}$. We use this result to probe the nature of dark energy (DE), showing that a large class of scalar-tensor theories and DE models are highly disfavored. As an example we consider the covariant Galileon, a cosmologically viable, well motivated gravity theory which predicts a variable GW speed at low redshift. Our results eliminate any late-universe application of these models, as well as their Horndeski and most of their beyond Horndeski generalizations. Three alternatives (and their combinations) emerge as the only possible scalar-tensor DE models: 1) restricting Horndeski's action to its simplest terms, 2) applying a conformal transformation which preserves the causal structure and 3) compensating the different terms that modify the GW speed (to be robust, the compensation has to be independent on the background on which GWs propagate). Our conclusions extend to any other gravity theory predicting varying $c_g$ such as Einstein-Aether, Ho\v{r}ava gravity, Generalized Proca, TeVeS and other MOND-like gravities., Comment: 6 pages, 2 figures. Matches PRL version

We use a description based on differential forms to systematically explore the space of scalar-tensor theories of gravity. Within this formalism, we propose a basis for the scalar sector at the lowest order in derivatives of the field and in any number of dimensions. This minimal basis is used to construct a finite and closed set of Lagrangians describing general scalar-tensor theories invariant under Local Lorentz Transformations in a pseudo-Riemannian manifold, which contains ten physically distinct elements in four spacetime dimensions. Subsequently, we compute their corresponding equations of motion and find which combinations are at most second order in derivatives in four as well as arbitrary number of dimensions. By studying the possible exact forms (total derivatives) and algebraic relations between the basis components, we discover that there are only four Lagrangian combinations producing second order equations, which can be associated with Horndeski's theory. In this process, we identify a new second order Lagrangian, named kinetic Gauss-Bonnet, that was not previously considered in the literature. However, we show that its dynamics is already contained in Horndeski's theory. Finally, we provide a full classification of the relations between different second order theories. This allows us to clarify, for instance, the connection between different covariantizations of Galileons theory. In conclusion, our formulation affords great computational simplicity with a systematic structure. As a first step we focus on theories with second order equations of motion. However, this new formalism aims to facilitate advances towards unveiling the most general scalar-tensor theories., 28 pages, 1 figure, version published in PRD (minor changes)

Primordial black-holes (PBH) can be produced in single-field models of inflation with a quasi-inflection point in the potential. In these models, a large production of PBHs requires a deviation from the slow-roll (SR) trajectory. In turn, this SR violation can produce an exponential growth of quantum fluctuations. We study the back-reaction of these quantum modes on the inflationary dynamics using stochastic inflation in the Hamilton-Jacobi formalism. We develop a methodology to solve quantum diffusion beyond SR in terms of the statistical moments of the probability distribution. We apply these techniques to a toy model potential with a quasi-inflection point. We find that there is an enhancement of the power spectrum due to the dominance of the stochastic noise in the phase beyond SR. Moreover, non-Gaussian corrections become as well relevant with a large positive kurtosis. Altogether, this produces a significant boost of PBH production. We discuss how our results extend to other single-field models with similar dynamics. We conclude that the abundance of PBHs in this class of models should be revisited including quantum diffusion., 17+7 pages, 5 figures. Matches JCAP version