Search

We use a suite of the most recent cosmological observations to test models of dynamical dark energy motivated by quantum gravity. Specifically, we focus on hilltop quintessence scenarios, able to satisfy theoretical constraints from quantum gravity. We discuss their realisation based on axions, their supersymmetric partners, and Higgs-like string constructions. We also examine a specific parameterisation for dynamical dark energy suitable for hilltop quintessence. We then perform an analysis based on Markov Chain Monte-Carlo to assess their predictions against CMB, galaxy surveys, and supernova data. We show to what extent current data can distinguish amongst different hilltop set-ups, providing model parameter constraints that are complementary to and synergetic with theoretical bounds from quantum gravity conjectures, as well as model comparisons across the main dark energy candidates in the literature. However, all these constraints are sensitive to priors based on theoretical assumptions about viable regions of parameter space. Consequently, we discuss theoretical challenges in refining these priors, with the aim of maximizing the informative power of current and forthcoming cosmological datasets for testing dark energy scenarios in quantum gravity., Comment: 35 pages + appendices, 24 figures, 9 tables

We discuss a mechanism of primordial black hole (PBH) formation that does not require specific features in the inflationary potential, revisiting previous literature. In this mechanism, a light spectator field evolves stochastically during inflation and remains subdominant during the post-inflationary era. Even though the curvature power spectrum stays small at all scales, rare perturbations of the field probe a local maximum in its potential, leading to non-Gaussian tails in the distribution of curvature fluctuations, and to copious PBH production. For a concrete axion-like particle (ALP) scenario we analytically determine the distribution of the compaction function for perturbations, showing that it is characterized by a heavy tail, which produces an extended PBH mass distribution. We find the ALP mass and decay constant to be correlated with the PBH mass, for instance, an ALP with a mass $m_a = 5.4 \times 10^{14}$ eV and a decay constant $f_a = 4.6 \times 10^{-5} Mpl$ can lead to PBHs of mass $M_{\rm PBH} = 10^{21}$ g as the entire dark matter (DM) of the universe, and is testable in future PBH observations via lensing in the NGRST and mergers detectable in the LISA and ET Gravitational Waves (GW) detectors. We then extend our analysis to mixed ALP and PBH dark matter and Higgs-like spectator fields. We find that PBHs cluster strongly over all cosmological scales, clashing with CMB isocurvature bounds. We argue that this problem is shared by all PBH production from inflationary models that depend solely on large non-Gaussianity without a peak in the curvature power spectrum and discuss possible remedies., Comment: 30 pages + Appendices, 7 figures; comments are welcome !

The gravitational wave (GW) interferometers LISA and ET are expected to be functional in the next decade(s), possibly around the same time. They will operate over different frequency ranges, with similar integrated sensitivities to the amplitude of a stochastic GW background (SGWB). We investigate the synergies between these two detectors, in terms of a multi-band detection of a cosmological SGWB characterised by a large amplitude, and a broad frequency spectrum. By investigating various examples of SGWBs, such as those arising from cosmological phase transition, cosmic string, primordial inflation, we show that LISA and ET operating together will have the opportunity to assess more effectively the characteristics of the GW spectrum produced by the same cosmological source, but at separate frequency scales. Moreover, the two experiments in tandem can be sensitive to features of early universe cosmic expansion before big-bang nucleosynthesis (BBN), which affects the SGWB frequency profile, and which would not be possible to detect otherwise, since two different frequency ranges correspond to two different pre-BBN (or post-inflationary) epochs. Besides considering the GW spectrum, we additionally undertake a preliminary study of the sensitivity of LISA and ET to soft limits of higher order tensor correlation functions. Given that these experiments operate at different frequency bands, their synergy constitutes an ideal direct probe of squeezed limits of higher order GW correlators, which can not be measured operating with a single instrument only., Comment: 44 pages, 10 figures

We generalise Phinney's 'practical theorem' to account for modified graviton dispersion relations motivated by certain cosmological scenarios. Focusing on specific examples, we show how such modifications can induce characteristic localised distortions, bumps, in the frequency profile of the stochastic gravitational wave background emitted from distant binary sources. We concentrate on gravitational waves at nano-Hertz frequencies probed by pulsar timing arrays, and we forecast the capabilities of future experiments to accurately probe parameters controlling modified dispersion relations. Our predictions are based on properties of gravitational waves emitted in the first inspiral phase of the binary process, and do not rely on assumptions of non-linear effects occurring during the binary merging phase, Comment: 19 pages, 5 figures, 2 tables

Various scenarios of cosmic inflation enhance the amplitude of the stochastic gravitational wave background (SGWB) at frequencies detectable by the LISA detector. We develop tools for a template-based analysis of the SGWB and introduce a template databank to describe well-motivated signals from inflation, prototype their template-based searches, and forecast their reconstruction with LISA. Specifically, we classify seven templates based on their signal frequency shape, and we identify representative fundamental physics models leading to them. By running a template-based analysis, we forecast the accuracy with which LISA can reconstruct the template parameters of representative benchmark signals, with and without galactic and extragalactic foregrounds. We identify the parameter regions that can be probed by LISA within each template. Finally, we investigate how our signal reconstructions shed light on fundamental physics models of inflation: we discuss their impact for measurements of \emph{e.g.,} ~the couplings of inflationary axions to gauge fields; the graviton mass during inflation; the fluctuation seeds of primordial black holes; the consequences of excited states during inflation, and the presence of small-scale spectral features., Comment: 82 pages, 29 figures

The circular polarization of the stochastic gravitational wave background (SGWB) is a key observable for characterising the origin of the signal detected by Pulsar Timing Array (PTA) collaborations. Both the astrophysical and the cosmological SGWB can have a sizeable amount of circular polarization, due to Poisson fluctuations in the source properties for the former, and to parity violating processes in the early universe for the latter. Its measurement is challenging since PTA are blind to the circular polarization monopole, forcing us to turn to anisotropies for detection. We study the sensitivity of current and future PTA datasets to circular polarization anisotropies, focusing on realistic modelling of intrinsic and kinematic anisotropies for astrophysical and cosmological scenarios respectively. Our results indicate that the expected level of circular polarization for the astrophysical SGWB should be within the reach of near future datasets, while for cosmological SGWB circular polarization is a viable target for more advanced SKA-type experiments., Comment: 28 pages, 9 figures

Dynamical dark energy has gained renewed interest due to recent theoretical and observational developments. In the present paper, we focus on a string-motivated dark energy set-up, and perform a detailed cosmological analysis of exponential quintessence with potential $V=V_0 e^{-\lambda\phi}$, allowing for non-zero spatial curvature. We first gain some physical intuition into the full evolution of such a scenario by analysing the corresponding dynamical system. Then, we test the model using a combination of Planck CMB data, DESI BAO data, as well as recent supernovae datasets. For the model parameter $\lambda$, we obtain a preference for nonzero values: $\lambda = 0.48^{+0.28}_{-0.21},\; 0.68^{+0.31}_{-0.20},\; 0.77^{+0.18}_{-0.15}$ at 68% C.L. when combining CMB+DESI with Pantheon+, Union3 and DES-Y5 supernovae datasets respectively. We find no significant hint for spatial curvature. We discuss the implications of current cosmological results for the exponential quintessence model, and more generally for dark energy in string theory., Comment: 34 pages, 13 figures, 10 tables. Comments welcome! V2 - updated plots and added references

Recent Pulsar Timing Array (PTA) collaborations show strong evidence for a stochastic gravitational wave background (SGWB) with the characteristic Hellings-Downs inter-pulsar correlations. The signal may stem from supermassive black hole binary mergers, or early universe phenomena. The former is expected to be strongly anisotropic while primordial backgrounds are likely to be predominantly isotropic with small fluctuations. In case the observed SGWB is of cosmological origin, our relative motion with respect to the SGWB rest frame is a guaranteed source of anisotropy, leading to $\textit{O}(10^{-3})$ energy density fluctuations of the SGWB. For such cosmological SGWB, kinematic anisotropies are likely to be larger than the intrinsic anisotropies, akin to the cosmic microwave background (CMB) dipole anisotropy. We assess the sensitivity of current PTA data to the kinematic dipole anisotropy, and we also forecast at what extent the magnitude and direction of the kinematic dipole can be measured in the future with an SKA-like experiment. We also discuss how the spectral shape of the SGWB and the location of the pulsars to monitor affect the prospects of detecting the kinematic dipole with PTA. In the future, a detection of this anisotropy may even help resolve the discrepancy in the magnitude of the kinematic dipole as measured by CMB and large-scale structure observations., Comment: 29 pages, 6 figures. V2: corrected upper limit, updated forecasts

The Laser Interferometer Space Antenna (LISA) is the first scientific endeavour to detect and study gravitational waves from space. LISA will survey the sky for Gravitational Waves in the 0.1 mHz to 1 Hz frequency band which will enable the study of a vast number of objects ranging from Galactic binaries and stellar mass black holes in the Milky Way, to distant massive black-hole mergers and the expansion of the Universe. This definition study report, or Red Book, presents a summary of the very large body of work that has been undertaken on the LISA mission over the LISA definition phase., Comment: 155 pages, with executive summary and table of contents

The physics of primordial black holes can be affected by the non-Gaussian statistics of the density fluctuations that generate them. Therefore, it is important to have good theoretical control of the higher-order correlation functions for primordial curvature perturbations. By working at leading order in a $1/|\eta|$ expansion, we analytically determine the bispectrum of curvature fluctuations for single field inflationary scenarios producing primordial black holes. The bispectrum has a rich scale and shape dependence, and its features depend on the dynamics of the would-be decaying mode. We apply our analytical results to study gravitational waves induced at second order by enhanced curvature fluctuations. Their statistical properties are derived in terms of convolution integrals over wide momentum ranges, and they are sensitive on the scale and shape dependence of the curvature bispectrum we analytically computed., Comment: 14+12 pages, 5 figures. V2: Discussion improved and references added

We determine hidden conformal symmetries behind the evolution equations of black hole perturbations in a vector-tensor theory of gravity. Such hidden symmetries are valid everywhere in the exterior region of a spherically symmetric, asymptotically flat black hole geometry. They allow us to factorize second order operators controlling the black hole perturbations into a product of two commuting first order operators. As a consequence, we are able to analytically determine the most general time-dependent solutions for the black hole perturbation equations. We focus on solutions belonging to a highest weight representation of a conformal symmetry, showing that they correspond to quasi-bound states with an ingoing behaviour into the black hole horizon, and exponential decay at spatial infinity. Their time-dependence is characterized by purely imaginary frequencies, with imaginary parts separated by integer numbers, as the overtones of quasi-normal modes in General Relativity., Comment: 22 pages, no figures

We propose a cosmological dark matter production mechanism in the form of a longitudinal massive vector boson. We build upon the work of Graham et.al. including non-minimal couplings of the massive vector with gravity, developing a well motivated set-up from an effective field theory perspective. We carefully track the dynamics of vector field in passing from inflation to radiation dominated universe to show that the late time abundance of longitudinal modes -- excited initially by the quantum fluctuations during inflation -- can provide the observed dark matter abundance for sufficiently weak non-minimal coupling and wide range of vector masses $5 \times 10^{-7} \lesssim m\, [{\rm eV}] \lesssim 5 \times 10^{3}$. The final abundance of dark matter depends on two parameter, the vector mass and its non-minimal coupling with gravity. We discuss experimental venues to probe this framework, including the production of a stochastic gravitational wave background. The latter is especially interesting, as the same mechanism that generates dark matter can potentially lead to the production of gravitational waves in the LISA frequency band, through the second-order effects of large dark matter iso-curvature perturbations at small scales. We take a first step in this direction, identifying the potential information that gravitational wave experiments can provide on the parameter space of dark matter within this scenario., Comment: 25 pages plus appendices, 9 figures. Links to codes are provided in the text

Doppler anisotropies, induced by our relative motion with respect to the source rest frame, are a guaranteed property of stochastic gravitational wave backgrounds of cosmological origin. If detected by future pulsar timing array measurements, they will provide interesting information on the physics sourcing gravitational waves, which is hard or even impossible to extract from measurements of the isotropic part of the background only. We analytically determine the pulsar response function to kinematic anisotropies, including possible effects due to parity violation, to features in the frequency dependence of the isotropic part of the spectrum, as well as to the presence of extra scalar and vector polarizations. For the first time, we show how the sensitivity to different effects crucially depends on the pulsar configuration with respect to the relative motion among frames. Correspondingly, we propose examples of strategies of detection, each aimed at exploiting future measurements of kinematic anisotropies for characterizing distinct features of the cosmological gravitational wave background., Comment: 18+10 pages, 6 figures. V2: version to be published in PRD

Several pulsar timing array (PTA) collaborations recently announced the first detection of a stochastic gravitational wave (GW) background, leaving open the question of its source. We explore the possibility that it originates from cosmic inflation, a guaranteed source of primordial GW. The inflationary GW background amplitude is enhanced at PTA scales by a non-standard early cosmological evolution, driven by Dirac-Born-Infeld (DBI) scalar dynamics motivated by string theory. The resulting GW energy density has a broken power-law frequency profile, entering the PTA band with a peak amplitude consistent with the recent GW detection. After this initial DBI kination epoch, the dynamics starts a new phase mainly controlled by the scalar potential. It provides a realization of an early dark energy scenario aimed at relaxing the $H_0$ tension, and a late dark energy model which explains the current cosmological acceleration with no need of a cosmological constant. Hence our mechanism - besides providing a possible explanation for the recent PTA results - connects them with testable properties of the physics of the dark universe., Comment: v1: 18 pages, 5 figures; v2: 20 pages, 6 figures, discussions and references added; v3: 18 pages, 6 figures, discussions added, to appear in JCAP

Single field models of inflation capable to produce primordial black holes usually require a significant departure from the standard, perturbative slow-roll regime. In fact, in many of these scenarios, the size of the slow-roll parameter $|\eta|$ becomes larger than one during a short phase of inflationary evolution. In order to develop an analytical control on these systems, we explore the limit of $|\eta|$ large, and promote $1/|\eta|$ to a small quantity to be used for perturbative expansions. Formulas simplify, and we obtain analytic expressions for the two and three point functions of curvature fluctuations, which share some of the features found in realistic inflationary models generating primordial black holes. We study one-loop corrections in this framework: we discuss criteria for adsorbing ultraviolet divergences into the available parameters, leaving log-enhanced infrared contributions of controllable size., Comment: 21 pages, 3 figures. V2: Improved version, to be published in PRD

We review conceptual aspects of inflationary scenarios able to produce primordial black holes, by amplifying the size of curvature fluctuations to the level required for triggering black hole formation. We identify general mechanisms to do so, both for single and multiple field inflation. In single field inflation, the spectrum of curvature fluctuations is enhanced by pronounced gradients of background quantities controlling the cosmological dynamics, which can induce brief phases of non--slow-roll inflationary evolution. In multiple field inflation, the amplification occurs through appropriate couplings with additional sectors, characterized by tachyonic instabilities that enhance the size of their fluctuations. As representative examples, we consider axion inflation, and two-field models of inflation with rapid turns in field space. We develop our discussion in a pedagogical manner, by including some of the most relevant calculations, and by guiding the reader through the existing theoretical literature, emphasizing general themes common to several models., Comment: 58 Pages, 19 Figures + Appendices, Published version: the ambiguity in the definition of threshold, as well as its relation with the critical density is clarified in Section 2.2, some typos are corrected and references added

The anisotropies of the stochastic gravitational wave background, as produced in the early phases of cosmological evolution, can act as a key probe of the primordial universe particle content. We point out a new universal property of gravitational wave anisotropies of cosmological origin: for adiabatic initial conditions, their angular power spectrum is insensitive to the equation of state of the cosmic fluid driving the expansion before big-bang nucleosynthesis. Any deviation from this universal behaviour points to the presence of non-adiabatic sources of primordial fluctuations. Such scenarios can be tested by gravitational wave detectors operating at a frequency range which is fully complementary to CMB experiments. In this work we prove this general result, and we illustrate its consequences for a representative realisation of initial conditions based on the curvaton scenario. In the case of the simplest curvaton setup, we also find a significant cross-correlation between gravitational wave anisotropies and the CMB temperature fluctuations. There is a fourfold enhancement vis-\`{a}-vis the purely adiabatic scenario. We discuss the implications of our findings for identifying the origin of the (cosmological) gravitational wave background when, as is often the case, this cannot be determined solely on the basis of its spectral shape., Comment: 14 pages, 4 figures. Version accepted at PRD

Effective field theories (EFT) of dark energy (DE) -- built to parameterise the properties of DE in an agnostic manner -- are severely constrained by measurements of the propagation speed of gravitational waves (GW). However, GW frequencies probed by ground-based interferometers lie around the typical strong coupling scale of the EFT, and it is likely that the effective description breaks down before even reaching that scale. We discuss how this leaves the possibility that an appropriate ultraviolet completion of DE scenarios, valid at scales beyond an EFT description, can avoid present constraints on the GW speed. Instead, additional constraints in the lower frequency LISA band would be harder to escape, since the energies involved are orders of magnitude lower. By implementing a method based on GW multiband detections, we show indeed that a single joint observation of a GW150914-like event by LISA and a terrestrial interferometer would allow one to constrain the speed of light and gravitons to match to within $10^{-15}$. Multiband GW observations can therefore firmly constrain scenarios based on the EFT of DE, in a robust and unambiguous way., Comment: 11 pages, 4 figures. Updated to match the version published in JCAP

We study the response function of the Einstein Telescope to kinematic Doppler anisotropies, which represent one of the guaranteed properties of the stochastic gravitational wave background. If the frequency dependence of the stochastic background changes slope within the detector frequency band, the Doppler anisotropic contribution to the signal can not be factorized in a part depending on frequency, and a part depending on direction. For the first time, we study the detector response function to Doppler anisotropies without making any factorizable Ansatz. Moreover, we do not assume that kinematic effects are small, and we derive general formulas valid for any relative velocity among frames. We apply our findings to three well-motivated examples of background profiles: power-law, broken power-law, and models with a resonance motivated by primordial black hole scenarios. We derive the signal-to-noise ratio associated with an optimal estimator for the detection of non-factorizable kinematic anisotropies, and we study it for representative examples., Comment: v1: 19+9 pages, 11 figures; v2: 21+9 pages, 10 figures, improved version, published in Phys. Rev. D

We analytically investigate a new family of horizonless compact objects in vector-tensor theories of gravity, called ultracompact vector stars. They are sourced by a vector condensate, induced by a non-minimal coupling with gravity. They can be as compact as black holes, thanks to their internal anisotropic stress. In the spherically symmetric case their interior resembles an isothermal sphere, with a singularity that can be resolved by tuning the available integration constants. The star interior smoothly matches to an exterior Schwarzschild geometry, with no need of extra energy-momentum tensor at the star surface. We analyse the behaviour of geodesics within the star interior, where stable circular orbits are allowed, as well as trajectories crossing in both ways the star surface. We analytically study stationary deformations of the vector field and of the geometry, which break spherical symmetry, and whose features depend on the vector-tensor theory we consider. We introduce and determine the vector magnetic susceptibility as a probe of the star properties, and we analyze how the rate of rotation of the star is affected by the vector charges., Comment: 23 pages, 4 figures

Gravitational wave (GW) backgrounds of cosmological origin are expected to be nearly isotropic, with small anisotropies resembling those of the cosmic microwave background. We analyse the case of a scalar-induced GW background and clarify in the process the relation between two different approaches to calculating GW anisotropies. We focus on GW scenarios sourced by a significantly peaked scalar spectrum, which are frequently considered in the context of primordial black holes production. We show that the resulting GW anisotropies are characterised by a distinct frequency dependence. We explore the observational consequences concentrating on a GW background enhanced in the frequency band of space-based GW detectors. We study the detectability of the signal through both cross-correlations among different space-based GW detectors, and among GW and CMB experiments., Comment: 31 pages, 6 figures. Version accepted at JCAP

The Laser Interferometer Space Antenna (LISA) has the potential to reveal wonders about the fundamental theory of nature at play in the extreme gravity regime, where the gravitational interaction is both strong and dynamical. In this white paper, the Fundamental Physics Working Group of the LISA Consortium summarizes the current topics in fundamental physics where LISA observations of GWs can be expected to provide key input. We provide the briefest of reviews to then delineate avenues for future research directions and to discuss connections between this working group, other working groups and the consortium work package teams. These connections must be developed for LISA to live up to its science potential in these areas., Comment: Accepted in: Living Reviews in Relativity

Primordial gravitational waves (PGW) produced during inflation span a large range of frequencies, carrying information on the dynamics of the primordial universe. During an early scalar-tensor dominated epoch, the amplitude of the PGW spectrum can be enhanced over a wide range of frequencies. To study this phenomenon, we focus on a class of scalar-tensor theories, well motivated by high energy theories of dark energy and dark matter, where the scalar is conformally and disformally coupled to matter during the early cosmological evolution. For a conformally dominated epoch, the PGW spectrum has a flat step-like shape. More interestingly, a disformally dominated epoch is characterised by a peaked spectrum with a broken power-law profile, with slopes depending on the scalar-tensor theory considered. We introduce a graphical tool, called broken power-law sensitivity curve, as a convenient visual indicator for understanding whether a given broken power-law profile can be detected by GW experiments. We then analyse the GW spectra for a variety of representative conformal and disformal models, discussing their detectability prospects with the Einstein Telescope (ET), Laser Interferometer Space Antenna (LISA), DECi-hertz Interferometer Gravitational wave Observatory (DECIGO), and Big Bang Observer (BBO)., Comment: 40 pages, 20 figures

The Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological applications of gravitational wave observations extends well beyond these two objectives. This publication presents a summary of the state of the art in LISA cosmology, theory and methods, and identifies new opportunities to use gravitational wave observations by LISA to probe the universe.

Several pulsar-timing array (PTA) collaborations are finding tantalising hints for a stochastic gravitational wave background signal in the nano-Hertz regime. So far, though, no convincing evidence for the expected Hellings-Downs quadrupolar correlations has been found. While this issue might get fixed at the light of more accurate, forthcoming data, it is important to keep an eye open on different possibilities, and explore scenarios able to produce different types of PTA angular correlations. We point out that a stationary non-Gaussian component to the gravitational wave background can modulate the 2-point PTA overlap reduction function, adding contributions that can help in fitting the angular distribution of PTA data. We discuss possible sources for such non-Gaussian signal in terms of cosmological processes occurring after inflation ends, and we investigate further tests for this idea., Comment: 9 pages plus appendixes, 4 figures

The propagation speed of gravitational waves, $c_T$, has been tightly constrained by the binary neutron star merger GW170817 and its electromagnetic counterpart, under the assumption of a frequency-independent $c_T$. Drawing upon arguments from Effective Field Theory and quantum gravity, we discuss the possibility that modifications of General Relativity allow for transient deviations of $c_T$ from the speed of light at frequencies well below the band of current ground-based detectors. We motivate two representative Ans\"atze for $c_T(f)$, and study their impact upon the gravitational waveforms of massive black hole binary mergers detectable by the LISA mission. We forecast the constraints on $c_T(f)$ obtainable from individual systems and a population of sources, from both inspiral and a full inspiral-merger-ringdown waveform. We show that LISA will enable us to place stringent independent bounds on departures from General Relativity in unexplored low-frequency regimes, even in the absence of an electromagnetic counterpart., Comment: 38+20 pages, 22 figures. V2: Analysis improved, to be published in JCAP

One of the guaranteed features of the stochastic gravitational wave background (SGWB) is the presence of Doppler anisotropies induced by the motion of the detector with respect to the rest frame of the SGWB source. We point out that kinematic effects can be amplified if the SGWB is characterised by large tilts in its spectrum as a function of frequency, or by sizeable intrinsic anisotropies. Hence we examine the possibility to use Doppler effects as complementary probes of the SGWB frequency profile. For this purpose we work in multipole space, and we study the effect of kinematic modulation and aberration on the GW energy density parameter and on its angular power spectrum. We develop a Fisher forecast analysis and we discuss prospects for constraining parameters controlling kinematically induced anisotropies with future detector networks. As a case study, we apply our framework to a background component with constant slope in frequency, potentially detectable by a network of future ground-based interferometers. For this specific example, we show that a measurement of kinematic anisotropies with a network of Einstein Telescope and Cosmic Explorer will allow us to constrain the spectral shape with a precision of about 16$\%$. Finally, we identify cosmological and astrophysical scenarios where kinematic effects are enhanced in frequency ranges probed by current and future GW experiments., Comment: 34 pages, 9 figures. V2: analysis improved. Version to appear in JCAP

We propose a coarse-graining procedure for describing the superhorizon dynamics of inflationary tensor modes. Our aim is to formulate a stochastic description for the statistics of spin-2 modes which seed the background of gravitational waves from inflation. Using basic principles of quantum mechanics, we determine a probability density for coarse-grained tensor fields, which satisfies a stochastic Fokker-Planck equation at superhorizon scales. The corresponding noise and drift are computable, and depend on the cosmological system under consideration. Our general formulas are applied to a variety of cosmological scenarios, also considering cases seldom considered in the context of stochastic inflation, and which are important for their observational consequences. We start obtaining the expected expressions for noise and drift in pure de Sitter and power-law inflation, also including a discussion of effects of non-attractor phases. We then apply our methods to describe scenarios with a transition from inflation to standard cosmological eras of radiation and matter domination. We show how the interference between modes flowing through the cosmological horizon, and modes spontaneously produced at superhorizon scales, can affect the stochastic evolution of coarse-grained tensor quantities. In appropriate limits, we find that the corresponding spectrum of tensor modes at horizon crossing matches with the results of quantum field theory calculations, but we also highlight where differences can arise., Comment: 27 pages, 2 figures

We investigate the sensitivity of the Laser Interferometer Space Antenna (LISA) to the anisotropies of the Stochastic Gravitational Wave Background (SGWB). We first discuss the main astrophysical and cosmological sources of SGWB which are characterized by anisotropies in the GW energy density, and we build a Signal-to-Noise estimator to quantify the sensitivity of LISA to different multipoles. We then perform a Fisher matrix analysis of the prospects of detectability of anisotropic features with LISA for individual multipoles, focusing on a SGWB with a power-law frequency profile. We compute the noise angular spectrum taking into account the specific scan strategy of the LISA detector. We analyze the case of the kinematic dipole and quadrupole generated by Doppler boosting an isotropic SGWB. We find that $\beta\, \Omega_{\rm GW}\sim 2\times 10^{-11}$ is required to observe a dipolar signal with LISA. The detector response to the quadrupole has a factor $\sim 10^3 \,\beta$ relative to that of the dipole. The characterization of the anisotropies, both from a theoretical perspective and from a map-making point of view, allows us to extract information that can be used to understand the origin of the SGWB, and to discriminate among distinct superimposed SGWB sources., Comment: 48 page + appendices, 13 figures

We discuss new consistency relations for single field models of inflation capable of generating primordial black holes (PBH), and their observational implications for CMB $\mu$-space distortions. These inflationary models include a short period of non-attractor evolution: the scale-dependent profile of curvature perturbation is characterized by a pronounced dip, followed by a rapid growth leading to a peak responsible for PBH formation. We investigate the squeezed and the collapsed limits of three and four point functions of curvature perturbation around the dip, showing that they satisfy consistency relations connecting their values to the total amplification of the curvature spectrum, and to the duration of the non-attractor era. Moreover, the corresponding non-Gaussian parameters are scale-dependent in proximity of the dip, with features that again depend on the amplification of the spectrum. For typical PBH scenarios requiring an order ${\cal O}(10^7)$ enhancement of the spectrum from large towards small scales, we generally find values $f_{\rm NL}^{\rm sq}\,=\,{\cal O}(10)$ and $\tau_{\rm NL}^{\rm col}\,=\,{\cal O}(10^3)$ in a range of scales that can be probed by CMB $\mu$-space distortions. Using these consistency relations, we carefully analyze how the scale-dependence of non-Gaussian parameters leads to characteristic features in $\langle \mu T \rangle$ and $\langle \mu \mu \rangle$ correlators, providing distinctive probes of inflationary PBH scenarios that can be tested using well-understood CMB physics., Comment: 27 Pages + Appendices, 15 Figures

We propose a new method for probing inflationary models of primordial black hole (PBH) production, using only CMB physics at relatively large scales. In PBH scenarios, the primordial power spectrum profile for curvature perturbations is characterized by a pronounced dip, followed by a rapid growth towards small scales, leading to a peak responsible for PBH formation. We focus on scales around the dip that are well separated from the peak to analytically compute expressions for the curvature power spectrum and bispectrum. The size of the squeezed bispectrum is enhanced at the position of the dip, and it acquires a characteristic scale dependence that can be probed by cross-correlating CMB $\mu$-distortions and temperature fluctuations. We quantitatively study the properties of such cross-correlations and how they depend on the underlying model, discussing how they can be tested by the next generation of CMB $\mu$-distortion experiments. This method allows one to experimentally probe inflationary PBH scenarios using well-understood CMB physics, without considering non-linearities associated with PBH formation and evolution., Comment: 34 pages, 6 figures, Published version in PRD, Conclusions are extended and the discussion in Section 3 is clarified

We analyze the propagation of high-frequency gravitational waves (GW) in scalar-tensor theories of gravity, with the aim of examining properties of cosmological distances as inferred from GW measurements. By using symmetry principles, we first determine the most general structure of the GW linearized equations and of the GW energy momentum tensor, assuming that GW move with the speed of light. Modified gravity effects are encoded in a small number of parameters, and we study the conditions for ensuring graviton number conservation in our covariant set-up. We then apply our general findings to the case of GW propagating through a perturbed cosmological space-time, deriving the expressions for the GW luminosity distance $d_L^{({\rm GW})}$ and the GW angular distance $d_A^{({\rm GW})}$. We prove for the first time the validity of Etherington reciprocity law $d_L^{({\rm GW})}\,=\,(1+z)^2\,d_A^{({\rm GW})}$ for a perturbed universe within a scalar-tensor framework. We find that besides the GW luminosity distance, also the GW angular distance can be modified with respect to General Relativity. We discuss implications of this result for gravitational lensing, focussing on time-delays of lensed GW and lensed photons emitted simultaneously during a multimessenger event. We explicitly show how modified gravity effects compensate between different coefficients in the GW time-delay formula: lensed GW arrive at the same time as their lensed electromagnetic counterparts, in agreement with causality constraints., Comment: 22 pages plus technical appendixes. 3 figures. V2: version published in JCAP

Brief periods of non-slow-roll evolution during inflation can produce interesting observable consequences, as primordial black holes, or an inflationary gravitational wave spectrum enhanced at small scales. We develop a model independent, analytic approach for studying the predictions of single-field scenarios which include short phases of slow-roll violation. Our method is based on Taylor expanding the equations for cosmological fluctuations in a small quantity, which parameterizes the duration of the non-slow-roll eras. The super-horizon spectrum of perturbations is described by few effective parameters, and is characterized by a pronounced dip followed by a rapid growth in its amplitude, as typically found in numerical and analytical studies. The dip position $k_{\rm dip}/k_*$ and the maximal enhancement $\Pi_{\rm max}$ of the spectrum towards small scales are found to be related by the law $k_{\rm dip}/k_*\propto \Pi_{\rm max}^{-1/4}$, and we determine the proportionality constant. For a single epoch of slow-roll violation we confirm previous studies, finding that the steepest slope of the spectrum well after the dip has spectral index $n-1\,=\,4$. On the other hand, with multiple phases of slow-roll violation, the slope of the spectrum is generally enhanced. For example, when two epochs of slow-roll violation take place, separated by a phase of quasi-de Sitter expansion, we find that the spectral index can reach the value $n-1\,=\,8$. This phenomenon indicates that the slope of the spectrum keeps memory of the history of non-slow-roll phases occurred during inflation., Comment: 37 pages, 11 figures. V2: References added, small improvements made. Accepted for publication in PRD. V3: One reference added

We consider theories containing scalar fields interacting with vector or with tensor degrees of freedom, equipped with symmetries that prevent the propagation of linearized scalar excitations around solutions of the equations of motion. We first study the implications of such symmetries for building vector theories that break Abelian gauge invariance without necessarily exciting longitudinal scalar fluctuations in flat space. We then examine scalar-tensor theories in curved space, and relate the symmetries we consider with a non-linear realization of broken space-time symmetries acting on scalar modes. We determine sufficient conditions on the space-time geometry to avoid the propagation of scalar fluctuations. We analyze linearized perturbations around spherically symmetric black holes, proving the absence of scalar excitations, and pointing out modifications in the dynamics of spin-2 fluctuations with respect to Einstein gravity. We then study consequences of this set-up for the dark energy problem, determining scalar constraints on cosmological configurations that can lead to self-accelerating universes whose expansion is insensitive to the value of the bare cosmological constant., Comment: 27 pages. References added, to appear in PRD

Sourced gravitational waves in chromonatural inflation (CNI) can give rise to a chiral spectrum of tensor fluctuations that is considerably enhanced relative to the vacuum fluctuations. If the field content of CNI acts purely as a spectator (SCNI), the inflationary sector can be consistent with current data making SCNI very appealing in view of future observations. We investigate the prospects of embedding SCNI in string theory, in the framework of K\"ahler inflation in type IIB large volume string compactifications, with a spectator sector associated with gaugino condensation on multiply magnetised D7-branes. We first introduce a generalised field theory framework that describes non-trivial multifield inflation coupled to gauge fields of the form generically arising in supergravity and string theory. We then use these results to study numerically and analytically both the background evolution and the dynamics of cosmological perturbations. We show that a successful inflationary background evolution with a large enhancement of the gravitational wave spectrum and a controllable backreaction from the amplified tensor fluctuations can be achieved by considering suitable values of three parameters present in our scenario: the magnetic flux, the degree of the condensing gauge group and the wrapping number of the D7-brane. On the other hand, the required values for these quantities may present a challenge for its successful realisation within string theory. We also discuss these challenges and the model from the viewpoint of the weak gravity conjecture., Comment: 43 pages, 21 figures. References updated, typos corrected

Luminosity distance estimates from electromagnetic and gravitational wave sources are generally different in models of dynamical dark energy and gravity beyond the standard cosmological scenario. We show that this leaves a unique imprint on the angular power-spectrum of fluctuations of the luminosity distance of gravitational-wave observations which tracks inhomogeneities in the dark energy field. Exploiting the synergy in supernovae and gravitational wave distance measurements, we build a joint estimator that directly probes dark energy fluctuations, providing a conclusive evidence for their existence in case of detection. Moreover, such measurement would also allow to probe the running of the Planck mass. We discuss experimental requirements to detect these signals., Comment: 9 pages, 2 figures. Matching published version

Given the recent advances in gravitational-wave detection technologies, the detection and characterisation of gravitational-wave backgrounds (GWBs) with the Laser Interferometer Space Antenna (LISA) is a real possibility. To assess the abilities of the LISA satellite network to reconstruct anisotropies of different angular scales and in different directions on the sky, we develop a map-maker based on an optimal quadratic estimator. The resulting maps are maximum likelihood representations of the GWB intensity on the sky integrated over a broad range of frequencies. We test the algorithm by reconstructing known input maps with different input distributions and over different frequency ranges. We find that, in an optimal scenario of well understood noise and high frequency, high SNR signals, the maximum scales LISA may probe are $\ell_{\rm max} \lesssim 15$. The map-maker also allows to test the directional dependence of LISA noise, providing insight on the directional sky sensitivity we may expect., Comment: Corresponding author: Arianna I. Renzini, as a part of their PhD thesis. 13 pages, 9 figures

Characterizing the physical properties of the stochastic gravitational waves background (SGWB) is a key step towards identifying the nature of its possible origin. We focus our analysis on SGWB anisotropies. The existence of a non-trivial primordial scalar-tensor-tensor (STT) correlation in the squeezed configuration may be inferred from the effect that a long wavelength scalar mode has on the gravitational wave power spectrum: an anisotropic contribution. Crucially, such contribution is correlated with temperature anisotropies in the cosmic microwave background (CMB). We show that, for inflationary models that generate suitably large STT non-Gaussianities, cross-correlating the CMB with the stochastic background of gravitational waves is a very effective probe of early universe physics. The resulting signal can be a smoking-gun for primordial SGWB anisotropies., Comment: 6 pages, 2 figures. Version matching the published manuscript

The detection of gravitational waves (GWs) propagating through cosmic structures can provide invaluable information on the geometry and content of our Universe, as well as on the fundamental theory of gravity. In order to test possible departures from General Relativity, it is essential to analyse, in a modified gravity setting, how GWs propagate through a perturbed cosmological space-time. Working within the framework of geometrical optics, we develop tools to address this topic for a broad class of scalar-tensor theories, including scenarios with non-minimal, derivative couplings between scalar and tensor modes. We determine the corresponding evolution equations for the GW amplitude and polarization tensor. The former satisfies a generalised evolution equation that includes possible effects due to a variation of the effective Planck scale; the latter can fail to be parallely transported along GW geodesics unless certain conditions are satisfied. We apply our general formulas to specific scalar-tensor theories with unit tensor speed, and then focus on GW propagation on a perturbed space-time. We determine corrections to standard formulas for the GW luminosity distance and for the evolution of the polarization tensor, which depend both on modified gravity and on the effects of cosmological perturbations. Our results can constitute a starting point to disentangle among degeneracies from different sectors that can influence GW propagation through cosmological space-times., Comment: 42 pages. V2: Improved discussion, in particular on gauge conditions, and references added. Results unchanged. V3: Updated version to be published in JCAP

The possibility that primordial black holes constitute a fraction of dark matter motivates a detailed study of possible mechanisms for their production. Black holes can form by the collapse of primordial curvature fluctuations, if the amplitude of their small scale spectrum gets amplified by several orders of magnitude with respect to CMB scales. Such enhancement can for example occur in single-field inflation that exhibit a transient non-attractor phase: in this work, we make a detailed investigation of the shape of the curvature spectrum in this scenario. We make use of an analytical approach based on a gradient expansion of curvature perturbations, which allows us to follow the changes in slope of the spectrum during its way from large to small scales. After encountering a dip in its amplitude, the spectrum can acquire steep slopes with a spectral index up to $n_s-1\,=\,8$, to then relax to a more gentle growth with $n_s-1\,\lesssim\,3$ towards its peak, in agreement with the results found in previous literature. For scales following the peak associated with the presence of the non-attractor phase, the spectrum amplitude then mildly decays, during a transitional stage from non-attractor back to attractor evolution. Our analysis indicates that this gradient approach offers a transparent understanding of the contributions controlling the slope of the curvature spectrum. As an application of our findings, we characterise the slope in frequency of a stochastic gravitational wave background generated at second order from curvature fluctuations, using the more accurate information we gained on the shape of curvature power spectrum., Comment: 61 pages, 17 figures, v3, Accepted to JCAP, discussion in section 2 is revised and improved, New appendix (Appendix A) added to generalize the evolution of curvature perturbation on super-horizon scales with arbitrary boundary conditions. Results did not change

Parity violating interactions in the early Universe can source a stochastic gravitational wave background (SGWB) with a net circular polarization. In this paper, we study possible ways to search for circular polarization of the SGWB with interferometers. Planar detectors are unable to measure the net circular polarization of an isotropic SGWB. We discuss the possibility of using the dipolar anisotropy kinematically induced by the motion of the solar system with respect to the cosmic reference frame to measure the net circular polarization of the SGWB with planar detectors. We apply this approach to LISA, re-assessing previous analyses by means of a more detailed computation and using the most recent instrument specifications, and to the Einstein Telescope (ET), estimating for the first time its sensitivity to circular polarization. We find that both LISA and ET, despite operating at different frequencies, could detect net circular polarization with a signal-to-noise ratio of order one in a SGWB with amplitude $h^2 \Omega_\text{GW} \simeq 10^{-11}$. We also investigate the case of a network of ground based detectors. We present fully analytical, covariant formulas for the detector overlap functions in the presence of circular polarization. Our formulas do not rely on particular choices of reference frame, and can be applied to interferometers with arbitrary angles among their arms., Comment: 33 pages + appendices, 6 figures

We introduce the concept of stationary graviton non-Gaussianity (nG), an observable that can be probed in terms of 3-point correlation functions of a stochastic gravitational wave (GW) background. When evaluated in momentum space, stationary nG corresponds to folded bispectra of graviton nG. We determine 3-point overlap functions for testing stationary nG with pulsar timing array GW experiments, and we obtain the corresponding optimal signal-to-noise ratio. For the first time, we consider 3-point overlap functions including scalar graviton polarizations (which can be motivated in theories of modified gravity); moreover, we also calculate 3-point overlap functions for correlating pulsar timing array with ground based GW detectors. The value of the optimal signal-to-noise ratio depends on the number and position of monitored pulsars. We build geometrical quantities characterizing how such ratio depends on the pulsar system under consideration, and we evaluate these geometrical parameters using data from the IPTA collaboration. We quantitatively show how monitoring a large number of pulsars can increase the signal-to-noise ratio associated with measurements of stationary graviton nG., Comment: 25 pages,13 figures

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., Comment: 26 pages, 2 figures. White paper submitted to ESA's Voyage 2050 call on behalf of the LISA Consortium 2050 Task Force

We investigate possible signatures of quantum gravity which could be tested with current and future gravitational-wave (GW) observations. In particular, we analyze how quantum gravity can influence the GW luminosity distance, the time dependence of the effective Planck mass and the instrumental strain noise of interferometers. Using both model-dependent and model-independent formulae, we show that these quantities can encode a non-perturbative effect typical of all quantum-gravity theories, namely the way the dimension of spacetime changes with the probed scale. Effects associated with such dimensional flow might be tested with GW observations and constrained significantly in theories with a microscopically discrete spacetime geometry, more strongly than from propagation-speed constraints. Making use of public LIGO data as well as of a simulated higher-redshift LISA source, we impose the first, respectively, actual and mock constraints on quantum-gravity parameters affecting the GW luminosity distance and discuss specific theoretical examples. If also the Newtonian potential is modified but light geodesics are not, then solar-system bounds may be stronger than GW ones. Yet, for some theories GW astronomy can give unique information not available from solar-system tests., Comment: 1+59 pages, 5 figures, 5 tables. v2: introduction expanded, minor corrections

We present a set of tools to assess the capabilities of LISA to detect and reconstruct the spectral shape and amplitude of a stochastic gravitational wave background (SGWB). We first provide the LISA power-law sensitivity curve and binned power-law sensitivity curves, based on the latest updates on the LISA design. These curves are useful to make a qualitative assessment of the detection and reconstruction prospects of a SGWB. For a quantitative reconstruction of a SGWB with arbitrary power spectrum shape, we propose a novel data analysis technique: by means of an automatized adaptive procedure, we conveniently split the LISA sensitivity band into frequency bins, and fit the data inside each bin with a power law signal plus a model of the instrumental noise. We apply the procedure to SGWB signals with a variety of representative frequency profiles, and prove that LISA can reconstruct their spectral shape. Our procedure, implemented in the code SGWBinner, is suitable for homogeneous and isotropic SGWBs detectable at LISA, and it is also expected to work for other gravitational wave observatories., Comment: 40 pages, 22 figures

Evidence for the presence of extra fields during inflation may be found in the anisotropies of the scalar and tensor spectra across a vast range of scales. Indeed, beyond the single-field slow-roll paradigm, a long tensor mode can modulate the power spectrum inducing a sizable quadrupolar anisotropy. We investigate how this dynamics plays out for the tensor two-point correlator. The resulting quadrupole stores information on squeezed tensor non-Gaussianities, specifically those sourced by the extra field content and responsible for the breaking of so-called consistency relations. We underscore the potential of anisotropies as a probe of new physics: testable at CMB scales through the detection of B-modes, they are accessible at smaller scales via interferometers and pulsar timing arrays., Comment: 7 pages, 2 figure

Dimensional flow, the scale dependence of the dimensionality of spacetime, is a feature shared by many theories of quantum gravity (QG). We present the first study of the consequences of QG dimensional flow for the luminosity distance scaling of gravitational waves in the frequency ranges of LIGO and LISA. We find generic modifications with respect to the standard general-relativistic scaling, largely independent of specific QG proposals. We constrain these effects using two examples of multimessenger standard sirens, the binary neutron-star merger GW170817 and a simulated supermassive black-hole merger event detectable with LISA. We apply these constraints to various QG candidates, finding that the quantum geometries of group field theory, spin foams and loop quantum gravity can give rise to observable signals in the gravitational-wave spin-2 sector. Our results complement and improve GW propagation-speed bounds on modified dispersion relations. Under more model-dependent assumptions, we also show that bounds on quantum geometry can be strengthened by solar-system tests., Comment: 6 pages, 1 figure. v2: discussion improved; v3: references updated

The physics of black holes can suggest new ways to test the existence of axions. Much work has been done so far to analyse the phenomenon of superradiance associated with axions in the ergoregion surrounding rotating black holes. In this work, we instead investigate how Chern-Simons axion couplings of the form $\phi \,F\,\tilde F$ and $\phi \,R\,\tilde R$, well motivated by particle physics and string theory, can induce long range profiles for light axion fields around charged black holes, with or without spin. We extend known solutions describing axion hairs around spherically symmetric, asymptotically flat dyonic black hole configurations, charged under $U(1)$ gauge symmetries, by including non-minimal couplings with gravity. The axion acquires a profile controlled by the black hole conserved charges, and we analytically determine how it influences the black hole horizon and its properties. We find a Smarr formula applying to our configurations. We then generalise known solutions describing axion hairs around slowly rotating black hole configurations with charge. To make contact with phenomenology, we briefly study how long range axion profiles induce polarised deflection of light rays, and the properties of ISCOs for the black hole configurations we investigate.

We investigate primordial tensor non-Gaussianity in single field inflation, during a phase of non-attractor evolution when the spectrum of primordial tensor modes can be enhanced to a level detectable at interferometer scales. Making use of a tensor duality we introduced in arXiv:1808.10475, we analytically compute the full bispectrum of primordial tensor fluctuations during the non-attractor era. During this epoch the shape of the tensor bispectrum is enhanced in the squeezed limit, its amplitude can be amplified with respect to slow-roll models, and tensor non-Gaussianity can exhibit a scale dependence distinctive of our set-up. We prove that our results do not depend on the frame used for the calculations. Squeezed tensor non-Gaussianity induces a characteristic quadrupolar anisotropy on the power spectrum of the stochastic background of primordial tensor perturbations. As a step to make contact with gravitational wave experiments, we discuss the response function of a ground based Michelson interferometer to a gravitational wave background with such a feature., Comment: 34 pages, 4 figures