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We study the evolution of eccentric, equatorial extreme-mass-ratio inspirals (EMRIs) immersed in the accretion disks of active galactic nuclei. We find that single gravitational-wave observations from these systems could provide measurements with ~ 10 % relative precision of, simultaneously, the disk viscosity and mass accretion rate of the central supermassive black hole. This is possible when the EMRI transitions, within the observation time, from supersonic to subsonic motion relative to the disk gas, for eccentricities e > ~ 0.025-0.1. The estimate of the accretion rate would assist in the identification of the EMRI's host galaxy, or the observation of a direct electromagnetic counterpart, improving the chances of using these sources as cosmological sirens. Our work highlights the rich phenomenology of binary evolution in astrophysical environments and the need to improve the modelling and analysis of these systems for future gravitational-wave astronomy., Comment: 12 pages + 3 pages in Appendix, 8 figures

Our current understanding is that an environment - mainly consisting of gas or stars - is required to bring massive black hole binaries (MBHBs) with total redshifted mass $M_z\sim[10^{4},10^7]~{\rm M}_\odot$ to the LISA band from parsec separation. Even in the gravitational wave (GW) dominated final inspiral, realistic environments can non-negligibly speed up or slow down the binary evolution, or leave residual, measurable eccentricity in the LISA band. Despite this fact, most of the literature does not consider environmental effects or orbital eccentricity in modelling GWs from near-equal mass MBHBs. Considering either a circular MBHB embedded in a circumbinary disc or a vacuum eccentric binary, we explore if ignoring either secular gas effects (migration and accretion) or eccentric corrections to the GW waveform can mimic a failure of General Relativity (GR). We use inspiral-only aligned-spin 3.5 post-Newtonian waveforms, a complete LISA response model, and Bayesian inference to perform a parameterized test of GR. For a four-year LISA observation of an MBHB with $M_z=10^{5}~{\rm M}_\odot$, primary-to-secondary mass ratio $q=8$, and component BHs' dimensionless spins $\chi_{1,2}=0.9$ at redshift $z=1$, even a moderate gas-disc imprint (Eddington ratio ${\rm f}_{\rm Edd}\sim0.1$) or low initial eccentricity ($e_0\sim10^{-2.5}$) causes a false violation of GR in several PN orders. However, correctly modelling either effect can mitigate systematics while avoiding significant biases in vacuum circular systems. The adoption of LISA makes it urgent to consider gas imprints and eccentricity in waveform models to ensure accurate inference for MBHBs., Comment: 11 pages, 8 figures. Accepted by MNRAS

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

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome., Comment: 239 pages, 11 figures, white paper from the LISA Consortium Waveform Working Group, invited for submission to Living Reviews in Relativity, updated with comments from community

We develop a relativistic perturbation theory for scalar clouds around rotating black holes. We first introduce a relativistic product and corresponding orthogonality relation between modes, extending a recent result for gravitational perturbations. We then derive the analog of time-dependent perturbation theory in quantum mechanics, and apply it to calculate self-gravitational frequency shifts. This approach supersedes the non-relativistic "gravitational atom" approximation, brings close agreement with numerical relativity, and has practical applications for gravitational-wave astronomy., Comment: 7+4 pages, 2+1 figures. v2: improved derivation of the main result, including two new appendices, and other minor changes. matches version accepted for publication in PRL

We introduce a bilinear form for Weyl scalar perturbations of Kerr. The form is symmetric and conserved, and we show that, when combined with a suitable renormalization prescription involving complex r integration contours, quasinormal modes are orthogonal in the bilinear form for different (l, m, n). These properties are apparently not evident consequences of standard properties for the radial and angular solutions to the decoupled Teukolsky relations and rely on the Petrov type D character of Kerr and its t-$\phi$ reflection isometry. We show that quasinormal mode excitation coefficients are given precisely by the projection with respect to our bilinear form. These properties can make our bilinear form useful to set up a framework for nonlinear quasinormal mode coupling in Kerr. We also provide a general discussion on conserved local currents and their associated local symmetry operators for metric and Weyl perturbations, identifying a collection containing an increasing number of derivatives., Comment: 14+11 pages, 2 figures. v3: fixed typos in Eq. (55) compared to the version accepted to PRD

Gravitational-wave observations of extreme mass ratio inspirals (EMRIs) offer the opportunity to probe the environments of active galactic nuclei (AGN) through the torques that accretion disks induce on the binary. Within a Bayesian framework, we study how well such environmental effects can be measured using gravitational wave observations from the Laser Interferometer Space Antenna (LISA). We focus on the torque induced by planetary-type migration on quasicircular inspirals, and use different prescriptions for geometrically thin and radiatively efficient disks. We find that LISA could detect migration for a wide range of disk viscosities and accretion rates, for both $\alpha$ and $\beta$ disk prescriptions. For a typical EMRI with masses $50M_\odot+10^6M_\odot$, we find that LISA could distinguish between migration in $\alpha$ and $\beta$ disks and measure the torque amplitude with $\sim 20\%$ relative precision. Provided an accurate torque model, we also show how to turn gravitational-wave measurements of the torque into constraints on the disk properties. Furthermore, we show that, if an electromagnetic counterpart is identified, the multimessenger observations of the AGN EMRI system will yield direct measurements of the disk viscosity. Finally, we investigate the impact of neglecting environmental effects in the analysis of the gravitational-wave signal, finding 3$\sigma$ biases in the primary mass and spin, and showing that ignoring such effects can lead to false detection of a deviation from general relativity. This work demonstrates the scientific potential of gravitational observations as probes of accretion-disk physics, accessible so far through electromagnetic observations only.

Black-hole superradiance has been used to place very strong bounds on a variety of models of ultralight bosons such as axions, new light scalars, and dark photons. It is common lore to believe that superradiance bounds are broadly model independent and therefore pretty robust. In this work we show however that superradiance bounds on dark photons can be challenged by simple, compelling extensions of the minimal model. In particular, if the dark photon populates a larger dark sector and couples to dark fermions playing the role of dark matter, then superradiance bounds can easily be circumvented, depending on the mass and (dark) charge of the dark matter., Comment: 10+3 pages, 4 figures

Binaries of relatively massive black holes like GW190521 have been proposed to form in dense gas environments, such as the disks of Active Galactic Nuclei (AGNs), and they might be associated with transient electromagnetic counterparts. The interactions of this putative environment with the binary could leave a significant imprint at the low gravitational wave frequencies observable with the Laser Interferometer Space Antenna (LISA). We show that LISA will be able to detect up to ten GW190521-like black hole binaries, with sky position errors $\lesssim1$ deg$^2$. Moreover, it will measure directly various effects due to the orbital motion around the supermassive black hole at the center of the AGN, especially the Doppler modulation and the Shapiro time delay. Thanks to a careful treatment of their frequency domain signal, we were able to perform the full parameter estimation of Doppler and Shapiro-modulated binaries as seen by LISA. We find that the Doppler and Shapiro effects will allow for measuring the AGN parameters (radius and inclination of the orbit around the AGN, central black hole mass) with up to percent-level precision. Properly modeling these low-frequency environmental effects is crucial to determine the binary formation history, as well as to avoid biases in the reconstruction of the source parameters and in tests of general relativity with gravitational waves., Comment: 13+4 pages, 7+1 figures v3: corrected typo in Fig 5

The polarization of photons emitted by astrophysical sources might be altered as they travel through a dark matter medium composed of ultra light axion-like particles (ALPs). In particular, the coherent oscillations of the ALP background in the galactic halo induce a periodic change on the polarization of the electromagnetic radiation emitted by local sources such as pulsars. Building up on previous works, we develop a new, more robust, analysis based on the generalised Lomb-Scargle periodogram to search for this periodic signal in the emission of the Crab supernova remnant observed by the QUIJOTE MFI instrument and 20 galactic pulsars from the Parkes Pulsar Timing Array (PPTA) project. We also carefully take into account the stochastic nature of the axion field, an effect often overlooked in previous works. This refined analysis leads to the strongest limits on the axion-photon coupling for a wide range of dark matter masses spanning $10^{-23}\text{ eV}\lesssim m_a\lesssim10^{-19} \text{ eV}$. Finally, we survey possible optimal targets and the potential sensitivity to axionic dark-matter in this mass range that could be achieved using pulsar polarimetry in the future., Comment: 31 pages, 10 figures, 2 tables v4: Formatting error in reference corrected

Gravitational-wave observations of black hole ringdowns are commonly used to characterize binary merger remnants and to test general relativity. These analyses assume linear black hole perturbation theory, in particular that the ringdown can be described in terms of quasinormal modes even for times approaching the merger. Here we investigate a nonlinear effect during the ringdown, namely how a mode excited at early times can excite additional modes as it is absorbed by the black hole. This is a third-order secular effect: the change in the black-hole mass causes a shift in the mode spectrum, so that the original mode is projected onto the new ones. Using nonlinear simulations, we study the ringdown of a spherically-symmetric scalar field around an asymptotically anti-de Sitter black hole, and we find that this "absorption-induced mode excitation" (AIME) is the dominant nonlinear effect. We show that this effect takes place well within the nonadiabatic regime, so we can analytically estimate it using a sudden mass-change approximation. Adapting our estimation technique to asymptotically-flat Schwarzschild black holes, we expect AIME to play a role in the analysis and interpretation of current and future gravitational wave observations., Comment: 15+4 pages, 9+4 figures

Motivated by electromagnetic-field confinement due to plasma near accreting black holes, we continue our exploration of the linear dynamics of an electromagnetic field propagating in curved spacetime in the presence of plasma by including three effects that were neglected in our previous analysis: collisions in the plasma, thermal corrections, and the angular momentum of the background black-hole spacetime. We show that: (i) the plasma-driven long-lived modes survive in a collisional plasma except when the collision timescale is unrealistically small; (ii) thermal effects, which might be relevant for accretion disks around black holes, do not affect the axial long-lived modes; (iii) in the case of a spinning black hole the plasma-driven modes become superradiantly unstable at the linear level; (iv) the polar sector in the small-frequency regime admits a reflection point due to the resonant properties of the plasma. Dissipative effects such as absorption, formation of plasma waves, and nonlinear dynamics play a crucial role in the vicinity of this resonant point., Comment: 14 pages, 5 figures

We investigate the linear dynamics of an electromagnetic field propagating in curved spacetime in the presence of plasma. The dynamical equations are generically more involved and richer than the effective Proca equation adopted as a model in previous work. We discuss the general equations and focus on the case of a cold plasma in the background of a spherically-symmetric black hole, showing that the system admits plasma-driven, quasibound electromagnetic states that are prone to become superradiantly unstable when the black hole rotates. The quasibound states are different from those of the Proca equation and have some similarities with the case of a massive scalar field, suggesting that the linear instability can be strongly suppressed compared to previous estimates. Our framework provides the first step towards a full understanding of the plasma-photon interactions around astrophysical black holes., Comment: 11 pages, 4 figures. Matches the published version

GW190521 is the compact binary with the largest masses observed to date, with at least one in the pair-instability gap. This event has also been claimed to be associated with an optical flare observed by the Zwicky Transient Facility in an Active Galactic Nucleus (AGN), possibly due to the post-merger motion of the merger remnant in the AGN gaseous disk. We show that the Laser Interferometer Space Antenna (LISA) will detect up to ten of such gas-rich black hole binaries months to years before their detection by LIGO/Virgo-like interferometers, localizing them in the sky within $\approx1$ deg$^2$. LISA will also measure directly deviations from purely vacuum and stationary waveforms, arising from gas accretion, dynamical friction, and orbital motion around the AGN's massive black hole (acceleration, strong lensing, and Doppler modulation). LISA will therefore be crucial to alert and point electromagnetic telescopes ahead of time on this novel class of gas-rich sources, to gain direct insight on their physics, and to disentangle environmental effects from corrections to General Relativity that may also appear in the waveforms at low frequencies., Comment: 6 pages, 4 figures. Matches published version

We study the evolution and gravitational wave emission of white dwarf -- black hole accreting binaries with a semi-analytical model. These systems will evolve across the mHz gravitational wave frequency band and potentially be detected by the Laser Interferometer Space Antenna (LISA). We identify new universal relations for this class of binaries, which relate the component masses to the gravitational wave frequency and its first derivative. Combined with the high precision measurements possible with LISA, these relations could allow us to infer the component masses and the luminosity distance of the source. LISA has therefore the potential to detect and characterize a virtually unexplored binary population., Comment: 8 pages, 3 figures, 2 tables. v2: corrected typo in label of fig. 3

We consider the possibility that, in the semiclassical Einstein equation for cosmological spacetimes, gravity is sourced by the amount of stress-energy that is above that of the instantaneous ground state. For this possibility to be consistent, the Bianchi identities must continue to hold. This is nontrivial because it means that the ground state expectation value of the stress-energy tensor must be covariantly conserved in spite of the fact that the ground state is generally a different state at different times. We prove that this consistency condition does hold. As a consequence, we find that the vacuum stress-energy which is above the instantaneous ground state does not renormalize the cosmological constant, as long as the instantaneous ground states and the instantaneous adiabatic vacua exist., Comment: 15 pages, 1 figure. Accepted to PRD

We study the impact of gas accretion on the orbital evolution of black-hole binaries initially at large separation in the band of the planned Laser Interferometer Space Antenna (LISA). We focus on two sources: (i)~stellar-origin black-hole binaries~(SOBHBs) that can migrate from the LISA band to the band of ground-based gravitational-wave observatories within weeks/months; and (ii) intermediate-mass black-hole binaries~(IMBHBs) in the LISA band only. Because of the large number of observable gravitational-wave cycles, the phase evolution of these systems needs to be modeled to great accuracy to avoid biasing the estimation of the source parameters. Accretion affects the gravitational-wave phase at negative ($-4$) post-Newtonian order, and is therefore dominant for binaries at large separations. If accretion takes place at the Eddington or at super-Eddington rate, it will leave a detectable imprint on the dynamics of SOBHBs. In optimistic astrophysical scenarios, a multiwavelength strategy with LISA and a ground-based interferometer can detect about $10$ (a few) SOBHB events for which the accretion rate can be measured at $50\%$ ($10\%$) level. In all cases the sky position can be identified within much less than $0.4\,{\rm deg}^2$ uncertainty. Likewise, accretion at $\gtrsim 10\%$ ($\gtrsim 100\%$) of the Eddington rate can be measured in IMBHBs up to redshift $z\approx 0.1$ ($z\approx 0.5$), and the position of these sources can be identified within less than $0.01\,{\rm deg}^2$ uncertainty. Altogether, a detection of SOBHBs or IMBHBs would allow for targeted searches of electromagnetic counterparts to black-hole mergers in gas-rich environments with future X-ray detectors (such as Athena) and radio observatories (such as SKA)., Comment: 14 pages, 8 figures; v2: references and comments added to match the final version published in ApJ

We analyse the impact of various boundary conditions on the (minisuperspace) Lorentzian gravitational path integral. In particular we assess the implications for the Hartle-Hawking no-boundary wavefunction. It was shown recently that when this proposal is defined as a sum over compact metrics, problems arise with the stability of fluctuations. These difficulties can be overcome by an especially simple implementation of the no-boundary idea: namely to take the Einstein-Hilbert action at face value while adding no boundary term. This prescription simultaneously imposes an initial Neumann boundary condition for the scale factor of the universe and, for a Bianchi IX spacetime, Dirichlet conditions for the anisotropies. Another way to implement the no-boundary wavefunction is to use Robin boundary conditions. A sub-class of Robin conditions allows one to specify the Hubble rate on the boundary hypersurface, and we highlight the surprising aspect that specifying the final Hubble rate (rather than the final size of the universe) significantly alters the off-shell structure of the path integral. The conclusion of our investigations is that all current working examples of the no-boundary wavefunction force one to abandon the notion of a sum over compact and regular geometries, and point to the importance of an initial Euclidean momentum., Comment: 38 pages, 6 figures. v3: corrects an error in Eq. (42)

We study the propagation of light in the presence of a parity-violating coupling between photons and axion-like particles (ALPs). Naively, this interaction could lead to a split of light rays into two separate beams of different polarization chirality and with different refraction angles. However, by using the eikonal method we explicitly show that this is not the case and that ALP clumps do not produce any spatial birefringence. This happens due to non-trivial variations of the photon's frequency and wavevector, which absorb time-derivatives and gradients of the ALP field. We argue that these variations represent a new way to probe the ALP-photon couping with precision frequency measurements., Comment: 5 pages

We derive novel constraints on millicharged dark matter and ultralight axion-like particles using pulsar timing and fast radio burst observations. Millicharged dark matter affects the dispersion measure of the time of arrival of radio pulses in a way analogous to free electrons. Light pseudo-scalar dark matter, on the other hand, causes the polarization angle of radio signals to oscillate. We show that current and future data can set strong constraints in both cases. For dark matter particles of charge $\epsilon e$, these constraints are ${\epsilon}/{m_{\rm milli}} \lesssim 10^{-8}{\rm eV}^{-1}$, for masses $m_{\rm milli}\gtrsim 10^{-6}\,$eV. For axion-like particles, the analysis of signals from pulsars yields constraints in the axial coupling of the order of $g/m_a\lesssim 10^{-13} {\rm GeV}^{-1}/(10^{-22}{\rm eV})$. Both bounds scale as $(\rho/\rho_{\rm dm})^{1/2}$ if the energy density $\rho$ of the components is a fraction of the total dark matter energy density $\rho_{\rm dm}$. We do a detailed study of both effects using data from two samples of pulsars in the galaxy and in globular clusters, as well as data from FRB 121102 and PSR J0437$-$4715. We show that in both cases actual pulsar data constrain a new region of the parameter space for these models, and will improve with future pulsar-timing observations., Comment: 6 pages, 2 figures; v3: to appear on PRD

It is generically believed that higher-order curvature corrections to the Einstein-Hilbert action might cure the curvature singularities that plague general relativity. Here we consider Einstein-scalar-Gauss-Bonnet gravity, the only four-dimensional, ghost-free theory with quadratic curvature terms. For any choice of the coupling function and of the scalar potential, we show that the theory does not allow for bouncing solutions in the flat and open Friedmann universe. For the case of a closed universe, using a reverse-engineering method, we explicitly provide a bouncing solution which is nevertheless linearly unstable in the scalar gravitational sector. Moreover, we show that the expanding, singularity-free, early-time cosmologies allowed in the theory are unstable. These results rely only on analyticity and finiteness of cosmological variables at early times., Comment: 9 pages, 4 figures; references and discussion added; further minor revision, accepted to PRD

Theoretical arguments and cosmological observations suggest that Einstein's theory of general relativity needs to be modified at high energies. One of the best motivated higher-curvature extensions of general relativity is Einstein-scalar-Gauss-Bonnet gravity, in which a scalar field is coupled to quadratic curvature invariants. This theory is inspired by an effective string-theory model and its predictions dramatically differ from Einstein's theory in high-curvature regions - such as the interior of black holes and the early universe - where it aims at resolving curvature singularities. In this work we derive cosmological solutions in Einstein-scalar-Gauss-Bonnet gravity for quadratic and for exponential coupling functions, and for any spatial curvature. We discuss already known solutions and find new nonsingular, inflationary, and bouncing solutions. We study the linear stability of these solutions and the absence of ghosts, finding that all the aforementioned solutions are unstable against tensor perturbations. We then introduce a simple, quadratic potential for the scalar field. In some cases the presence of a mass term cures the tensor instability. The proposed model is therefore a viable and attractive candidate for inflation, and one in which the scalar field is naturally provided by the gravitational sector., Comment: Master thesis, 118 pages, 84 figures