arXiv subjects

Filippo Vernizzi

Publications and source records attributed to Filippo Vernizzi.

At least 19 recordsLinked to original sources

arXiv2025

Nonlinear Relativistic Tidal Response of Neutron Stars

We investigate the nonlinear tidal response of relativistic neutron stars by computing the fully relativistic, static, quadratic Love numbers. Using both the worldline effective field theory for extended gravitating bodies and second-order perturbations of relativistic stellar models, we derive the nonlinear tidal deformation induced by an external gravito-electric tidal field to quadratic order. Through a suitable matching procedure, we provide for the first time the leading nonlinear tidal corrections to the conservative dynamics and gravitational-wave signal of binary systems. Quadratic Love numbers are enhanced more than the linear ones in the small-compactness limit. Because of this, despite entering the gravitational-wave phase at 8th post-Newtonian (PN) order, the leading quadratic Love number can be as important as the next-to-next-to-leading order linear tidal correction, which enters at 7th PN order, and is larger than the subleading point-particle contribution entering at 4th PN order. In particular, quadratic Love numbers can be as large as ~10% of the linear Love numbers in the late inspiral phase. Our approach provides a framework to also compute the (subleading) nonlinear effects induced by magnetic tidal fields and higher multipole moments, and sets the foundations for incorporating nonlinear tidal effects in high-precision gravitational-wave modeling.

gr-qc↗

arXiv2024

Vanishing of Quadratic Love Numbers of Schwarzschild Black Holes

The induced conservative tidal response of self-gravitating objects in general relativity is parametrized in terms of a set of coefficients, which are commonly referred to as Love numbers. For asymptotically-flat black holes in four spacetime dimensions, the Love numbers are notoriously zero in the static regime. In this work, we show that this result continues to hold upon inclusion of nonlinearities in the theory for Schwarzschild black holes. We first solve the quadratic Einstein equations in the static limit to all orders in the multipolar expansion, including both even and odd perturbations. We show that the second-order solutions take simple analytic expressions, generically expressible in the form of finite polynomials. We then define the quadratic Love numbers at the level of the point-particle effective field theory. By performing the matching with the full solution in general relativity, we show that quadratic Love number coefficients are zero to all orders in the derivative expansion, like the linear ones.

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arXiv2024

Constraints on dark energy and modified gravity from the BOSS Full-Shape and DESI BAO data

We constrain dark energy and modified gravity within the effective field theory of dark energy framework using the full-shape BOSS galaxy power spectrum, combined with Planck cosmic microwave background (CMB) data and recent baryon acoustic oscillations (BAO) measurements from DESI. Specifically, we focus on a varying braiding parameter $\alpha_{\rm B}$, a running of the ``effective'' Planck mass $\alpha_{\rm M}$, and a constant dark energy equation of state $w$. The analysis is performed with two of these parameters at a time, including all the other standard cosmological parameters and marginalizing over bias and nuisance parameters. The full-shape galaxy power spectrum is modeled using the effective field theory of large-scale structure up to 1-loop order in perturbation theory. We find that the CMB data is most sensitive to $\alpha_{\rm B}$, and that adding large-scale structure information only slightly changes the parameter constraints. However, the large-scale structure data significantly improve the bounds on $\alpha_{\rm M}$ and $w$ by a factor of two. This improvement is driven by background information contained in the BAO, which breaks the degeneracy with $H_0$ in the CMB. We confirm this by comparing the BOSS full-shape information with BOSS BAO, finding no significant differences. This is likely to change with future high-precision full-shape data from Euclid and DESI however, to which the pipeline developed here is immediately applicable.

astro-ph.CO↗

arXiv2024

The Memory of Primordial Gravitational Waves

Primordial gravitational waves, after they enter the horizon and decay away, leave a residual displacement in test particles: a memory, in analogy with gravitational waves generated by astrophysical sources. The late-time distance between test particles is related to the one at early times by $\xi^i_{\rm late} = \frac{a_{\rm late}}{a_{\rm early}} (\delta^i_j -\frac12 \bar h^i_j)\xi^j_{\rm early}$. Therefore, the deformation of an initial spherical shell does not depend on the cosmological evolution, but only on the primordial value $\bar h^i_{j}$ of the gravitational wave. The memory is thus related to the adiabatic tensor mode that maps the unperturbed FLRW geometries at early and late times; this is analogous to the relation between memory in Minkowski spacetime and the BMS group. The primordial memory is also connected to the consistency relations of cosmological correlators, as the flat-space memory is related to the soft theorems for gravitational wave emission. We comment on the signature of the effect on the CMB $B$-modes and on the large-scale structure. There is also a primordial memory effect that is subleading in the spatial gradients of the wave: it is encoded in the rotation of free-falling gyroscopes.

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arXiv2023

Vanishing of Nonlinear Tidal Love Numbers of Schwarzschild Black Holes

It is well known that asymptotically flat Schwarzschild black holes in general relativity in four spacetime dimensions have vanishing induced linear tidal response. We extend this result beyond linear order for the polar sector, by solving the static nonlinear Einstein equations for the perturbations of the Schwarzschild metric and computing the quadratic corrections to the electric-type tidal Love numbers. After explicitly performing the matching with the point-particle effective theory at leading order in the derivative expansion, we show that the Love number couplings remain zero at higher order in perturbation theory.

gr-qc↗

arXiv2023

Angular momentum balance in gravitational two-body scattering: Flux, memory, and supertranslation invariance

Two puzzles continue to plague our understanding of angular momentum balance in the context of gravitational two-body scattering. First, because the standard definition of the Bondi angular momentum $J$ is subject to a supertranslation ambiguity, it has been shown that when the corresponding flux $F_J$ is expanded in powers of Newton's constant $G$, it can start at either $O(G^2)$ or $O(G^3)$ depending on the choice of frame. This naturally raises the question as to whether the $O(G^2)$ part of the flux is physically meaningful. The second puzzle concerns a set of new methods for computing the flux that were recently developed using quantum field theory. Somewhat surprisingly, it was found that they generally do not agree with the standard formula for $F_J$, except in the binary's center-of-mass frame. In this paper, we show that the resolution to both of these puzzles lies in the careful interpretation of $J$: Generically, the Bondi angular momentum $J$ is \emph{not} equal to the mechanical angular momentum $\mathcal{J}$ of the binary, which is the actual quantity of interest. Rather, it is the sum of $\mathcal{J}$ and an extra piece involving the shear of the gravitational field. By separating these contributions, we obtain a new balance law, accurate to all orders in $G$, that equates the total loss in mechanical angular momentum $Δ_\mathcal{J}$ to the sum of a radiative term, which always starts at $O(G^3)$, and a static term, which always starts at $O(G^2)$. We show that each of these terms is invariant under supertranslations, and we find that $Δ_\mathcal{J}$ matches the result from quantum field theory at least up to $O(G^2)$ in all Bondi frames. The connection between our results and other proposals for supertranslation-invariant definitions of the angular momentum is also discussed.

gr-qc↗

arXiv2023

$k$-evolution: a relativistic N-body code for clustering dark energy

We introduce $k$-evolution, a relativistic $N$-body code based on $\textit{gevolution}$, which includes clustering dark energy among its cosmological components. To describe dark energy, we use the effective field theory approach. In particular, we focus on $k$-essence with a speed of sound much smaller than unity but we lay down the basis to extend the code to other dark energy and modified gravity models. We develop the formalism including dark energy non-linearities but, as a first step, we implement the equations in the code after dropping non-linear self-coupling in the $k$-essence field. In this simplified setup, we compare $k$-evolution simulations with those of $\texttt{CLASS}$ and $\textit{gevolution}$ 1.2, showing the effect of dark matter and gravitational non-linearities on the power spectrum of dark matter, of dark energy and of the gravitational potential. Moreover, we compare $k$-evolution to Newtonian $N$-body simulations with back-scaled initial conditions and study how dark energy clustering affects massive halos.

astro-ph.CO↗

arXiv2023

Constraints on modified gravity from the BOSS galaxy survey

We develop a pipeline to set new constraints on scale-independent modified gravity, from the galaxy power spectrum in redshift space of BOSS DR12. The latter is modelled using the effective field theory of large-scale structure up to 1-loop order in perturbation theory. We test our pipeline on synthetic and simulated data, to assess systematic biases on the inferred cosmological parameters due to marginalization and theoretical errors, and we apply it to the normal branch of the DGP model with a $Λ$CDM background. When applied to synthetic data and cosmological simulations, we observe biased posteriors due to the strong degeneracy between the nDGP parameter $Ω_{\rm rc}$ and the primordial amplitude of fluctuations $A_s$. Fixing the latter to the Planck central value, we obtain a posterior distribution with $Ω_{\rm rc}\lesssim 0.65$ at 95$\%$ C.L., under the assumption of a flat prior on $\log_{10} Ω_{\rm rc}$. This upper bound, however, depends strongly on the prior on $Ω_{\rm rc}$. To alleviate this effect, we provide an upper bound based on the Bayes factor between the nDGP model and $Λ$CDM model, which gives $Ω_{\rm rc}\lesssim 0.2$ at 95$\%$ C.L..

astro-ph.CO↗

arXiv2022

Through the lens of Sgr A$^*$: identifying and resolving strongly lensed Continuous Gravitational Waves beyond the Einstein radius

Lensed gravitational waves will offer new means to probe the distribution of matter in the universe, complementary to electromagnetic signals. Lensed continuous gravitational waves provide new challenges and opportunities beyond those of transient compact binary coalescence. Here we consider continuous gravitational waves emitted by isolated neutron stars and lensed by Sgr A$^*$, the supermassive black hole at the center of our galaxy, a system observable by the next generation of gravitational wave detectors. We analyze the signatures of this system in detail, addressing parameter estimation and model selection. Future detectors can distinguish lensed continuous waves and measure their parameters with precision $\sim 1 - 10\%$ for sources within $2-4$ Einstein radii of Sgr A$^*$, depending on the source distance, thanks to the relative motion of the observer-lens-source system. The chances of observing strongly-lensed neutron stars increase by one order of magnitude relative to previous estimates, thanks to the possibility of detecting lensed systems at several Einstein radii. Multiple images can be resolved with an angular accuracy $\sim 10$mas, comparable to the best optical telescopes. Image localization probes deviations from axial symmetry and the existence of companions to Sgr A$^*$ in regions complementary to stellar orbits and black hole imaging. Our methods and many of our results extend to other lenses (e.g. galactic substructure) and sources (e.g. long-lived inspiralling binaries), rendering lensed continuous gravitational waves into versatile probes of astrophysics and fundamental physics.

gr-qc↗

arXiv2022

Gravitational Bremsstrahlung with tidal effects in the post-Minkowskian expansion

We compute the mass and current quadrupole tidal corrections to the four-momentum and energy flux radiated during the scattering of two spinless bodies, at leading order in $G$ and at all orders in the velocities, using the effective field theory worldline approach. In particular, we derive the conserved stress-energy tensor linearly coupled to gravity generated by the two bodies, including tidal fields, and the waveform in direct space. The integral is solved using scattering amplitude techniques. We show that our expressions are consistent with existing results up to the next-to-next-to-leading order in the post-Newtonian expansion.

hep-th↗

arXiv2022

Gravitational bremsstrahlung from spinning binaries in the post-Minkowskian expansion

We present a novel calculation of the four-momentum that is radiated into gravitational waves during the scattering of two arbitrarily spinning bodies. Our result, which is accurate to leading order in $G$, to quadratic order in the spins, and to all orders in the velocity, is derived by using a Routhian-based worldline effective field theory formalism in concert with a battery of analytic techniques for evaluating loop integrals. While nonspinning binaries radiate momentum only along the direction of their relative velocity, we show that the inclusion of spins generically allows for momentum loss in all three spatial directions. We also verify that our expression for the radiated energy agrees with the overlapping terms from state-of-the-art calculations in post-Newtonian theory.

hep-th↗

arXiv2022

Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity

We compute the four-momentum radiated during the scattering of two spinless bodies, at leading order in the Newton's contant $G$ and at all orders in the velocities, using the Effective Field Theory worldline approach. Following \cite{Mougiakakos:2021ckm}, we derive the conserved stress-energy tensor linearly coupled to gravity generated by localized sources, at leading and next-to-leading order in $G$, and from that the classical probability amplitude of graviton emission. The total emitted momentum is obtained by phase-space integration of the graviton momentum weighted by the modulo squared of the radiation amplitude. We recast this as a two-loop integral that we solve using techniques borrowed from particle physics, such as reverse unitarity, reduction to master integrals by integration-by-parts identities and canonical differential equations. The emitted momentum agrees with recent results obtained by other methods. Our approach provides an alternative way of directly computing radiated observables in the post-Minkowskian expansion without going through the classical limit of scattering amplitudes.

hep-th↗

arXiv2022

New Horizons for Fundamental Physics with LISA

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.

gr-qc↗

arXiv2021

The Large Scale Structure Bootstrap: perturbation theory and bias expansion from symmetries

We investigate the role played by symmetries in the perturbative expansion of the large-scale structure. In particular, we establish which of the coefficients of the perturbation theory kernels are dictated by symmetries and which not. Up to third order in perturbations, for the dark matter density contrast (and for the dark matter velocity) only three coefficients are not fixed by symmetries and depend on the particular cosmology. For generic biased tracers, where number/mass and momentum conservation cannot be imposed in general, this number rises to seven in agreement with other bias expansions discussed in the literature. A crucial role in our analysis is provided by extended Galilean invariance, which follows from diffeomorphism invariance in the non-relativistic limit. We identify a full hierarchy of extended Galilean invariance constraints, which fix the analytic structure of the perturbation theory kernels as the sums of an increasing number of external momenta vanish. Our approach is especially relevant for non-standard models that respect the same symmetries as $Λ$CDM and where perturbation theory at higher orders has not been exhaustively explored, such as dark energy and modified gravity scenarios. In this context, our results can be used to systematically extend the bias expansion to higher orders and set up model independent analyses.

astro-ph.CO↗

arXiv2021

Comparison of different approaches to the quasi-static approximation in Horndeski models

A quasi-static approximation (QSA) for modified gravity can be applied in a number of ways. We consider three different analytical formulations based on applying this approximation to: (1) the field equations; (2) the equations for the two metric potentials; (3) the use of the attractor solution derived within the Equation of State (EoS) approach. We assess the veracity of these implementations on the effective gravitational constant ($μ$) and the slip parameter ($η$), within the framework of Horndeski models. In particular, for a set of models we compare cosmological observables, i.e., the matter power spectrum and the CMB temperature and lensing angular power spectra, computed using the QSA, with exact numerical solutions. To do that, we use a newly developed branch of the CLASS code: QSA_class. All three approaches agree exactly on very small scales. Typically, we find that, except for $f(R)$ models where all the three approaches lead to the same result, the quasi-static approximations differ from the numerical calculations on large scales ($k \lesssim 3 - 4 \times 10^{-3}\,h\,{\rm Mpc}^{-1}$). Cosmological observables are reproduced to within 1% up to scales ${\rm K} = k/H_0$ of the order of a few and $\ell>5$ for the approaches based on the field equations and on the EoS, and we also do not find any appreciable difference if we use the scale-dependent expressions for $μ$ and $η$ with respect to the value on small scales, showing that the formalism and the conclusions are reliable and robust, fixing the range of applicability of the formalism. We discuss why the expressions derived from the equations for the potentials have limited applicability. Our results are in agreement with previous analytical estimates and show that the QSA is a reliable tool and can be used for comparison with current and future observations to constrain models beyond $Λ$CDM.

astro-ph.CO↗

arXiv2021

Gravitational Bremsstrahlung in the Post-Minkowskian Effective Field Theory

We study the gravitational radiation emitted during the scattering of two spinless bodies in the post-Minkowskian Effective Field Theory approach. We derive the conserved stress-energy tensor linearly coupled to gravity and the classical probability amplitude of graviton emission at leading and next-to-leading order in the Newton's constant $G$. The amplitude can be expressed in compact form as one-dimensional integrals over a Feynman parameter involving Bessel functions. We use it to recover the leading-order radiated angular momentum expression. Upon expanding it in the relative velocity between the two bodies $v$, we compute the total four-momentum radiated into gravitational waves at leading-order in $G$ and up to an order $v^8$, finding agreement with what was recently computed using scattering amplitude methods. Our results also allow us to investigate the zero frequency limit of the emitted energy spectrum.

gr-qc↗

arXiv2020

Consistency relations for large-scale structure in modified gravity and the matter bispectrum

We study perturbation theory for large-scale structure in the most general scalar-tensor theories propagating a single scalar degree of freedom, which include Horndeski theories and beyond. We model the parameter space using the effective field theory of dark energy. For Horndeski theories, the gravitational field and fluid equations are invariant under a combination of time-dependent transformations of the coordinates and fields. This symmetry allows one to construct a physical adiabatic mode which fixes the perturbation-theory kernels in the squeezed limit and ensures that the well-known consistency relations for large-scale structure, originally derived in general relativity, hold in modified gravity as well. For theories beyond Horndeski, instead, one generally cannot construct such an adiabatic mode. Because of this, the perturbation-theory kernels are modified in the squeezed limit and the consistency relations for large-scale structure do not hold. We show, however, that the modification of the squeezed limit depends only on the linear theory. We investigate the observational consequences of this violation by computing the matter bispectrum. In the squeezed limit, the largest effect is expected when considering the cross-correlation between different tracers. Moreover, the individual contributions to the 1-loop matter power spectrum do not cancel in the infrared limit of the momentum integral, modifying the power spectrum on non-linear scales.

astro-ph.CO↗

arXiv2020

Dark-Energy Instabilities induced by Gravitational Waves

We point out that dark-energy perturbations may become unstable in the presence of a gravitational wave of sufficiently large amplitude. We study this effect for the cubic Horndeski operator (braiding), proportional to $α_{\rm B}$. The scalar that describes dark-energy fluctuations features ghost and/or gradient instabilities for gravitational-wave amplitudes that are produced by typical binary systems. Taking into account the populations of binary systems, we conclude that the instability is triggered in the whole Universe for $|α_{\rm B} |\gtrsim 10^{-2}$, i.e. when the modification of gravity is sizeable. The instability is triggered by massive black-hole binaries down to frequencies corresponding to $10^{10}$ km: the instability is thus robust, unless new physics enters on even longer wavelengths. The fate of the instability and the subsequent time-evolution of the system depend on the UV completion, so that the theory may end up in a state very different from the original one. The same kind of instability is present in beyond-Horndeski theories for $|α_{\rm H}| \gtrsim 10^{-20}$. In conclusion, the only dark-energy theories with sizeable cosmological effects that avoid these problems are $k$-essence models, with a possible conformal coupling with matter.

gr-qc↗