13 research outputs found
Gravitational Wave Decay: Implications for cosmological scalar-tensor theories
The recent discovery that gravitational waves and light travel with the same speed, with an error below , has greatly constrained the parameter space of infrared modifications of gravity.
In this thesis we study the phenomenology of gravitational-wave propagation in modifications of gravity relevant for dark energy with an additional scalar degree of freedom. Of particular interest are Horndeski and Beyond Horndeski models surviving after the event GW170817.
Here the dark energy field is responsible for the spontaneous breaking of Lorentz invariance on cosmological scales. This implies that gravitons can experience new dispersion phenomena and in particular they can decay into dark energy fluctuations .
First, we study the perturbative decay channels and in Beyond Horndeski models. The first process is found to be large and thus incompatible with recent gravitational-wave observations. This provides a very stringent constraint for the particular coefficient of the Effective Field Theory of Dark Energy or, in the covariant language, on quartic Beyond Horndeski operators. We then study how the same coupling affects at loop level the propagation of gravitons. It is found that the new contribution modifies the dispersion relation in a way that is incompatible with current observations, giving bounds of the same magnitude as the decay.
Next, we improve our analysis of the decay by taking into account the large occupation number of gravitons and dark energy fluctuations in realistic situations. When the operators (cubic Horndeski) and are present, we show that the gravitational wave acts as a classical background for and affects its dynamics, with growing exponentially. In the regime of small gravitational-wave amplitude, we compute analytically the produced and the change in the gravitational wave. For the operator , self-interactions are of the same order as the resonance and affect the growth in a way that cannot be described analytically. For the operator , in some regimes self-interactions remain under control and our analysis improves the bounds from the perturbative decay, ruling out quartic Beyond Horndeski operators from having any relevance for cosmological applications.
Finally, we show that in the regime of large amplitude for the gravitational wave becomes unstable. If takes values relevant for cosmological applications, we conclude that dark energy fluctuations feature ghost and gradient instabilities in presence of gravitational waves of typical binary systems. Taking into account the populations of binary systems, we find that the instability is triggered in the whole Universe. The fate of the instability and the subsequent time-evolution of the system depends on the UV completion, so that the theory may end up in a state very different from the original one. In conclusion, the only dark-energy theories with sizeable cosmological effects that avoid these problems are -essence models, with a possible conformal coupling with matter
Weakly Lensed Gravitational Waves: Probing Cosmic Structures with Wave-Optics Features
Every signal propagating through the universe is at least weakly lensed by
the intervening gravitational field. In some situations, wave-optics phenomena
(diffraction, interference) can be observed as frequency-dependent modulations
of the waveform of gravitational waves (GWs). We will denote these signatures
as Wave-Optics Features (WOFs) and analyze them in detail. Our framework can
efficiently and accurately compute WOF in the single-image regime, of which
weak lensing is a limit. The phenomenology of WOF is rich and offers valuable
information: the dense cusps of individual halos appear as peaks in Green's
function for lensing. If resolved, these features probe the number, effective
masses, spatial distribution and inner profiles of substructures. High
signal-to-noise GW signals reveal WOFs well beyond the Einstein radius, leading
to a fair probability of observation by upcoming detectors such as LISA.
Potential applications of WOF include reconstruction of the lens' projected
density, delensing standard sirens and inferring large-scale structure
morphology and the halo mass function. Because WOF are sourced by light halos
with negligible baryonic content, their detection (or lack thereof) holds
promise to test dark matter scenarios.Comment: 26 pages, 12 figure
Beyond Perturbation Theory in Inflation
Inflationary perturbations are approximately Gaussian and deviations from
Gaussianity are usually calculated using in-in perturbation theory. This
method, however, fails for unlikely events on the tail of the probability
distribution: in this regime non-Gaussianities are important and perturbation
theory breaks down for .
In this paper we show that this regime is amenable to a semiclassical
treatment, . In this limit the wavefunction of the Universe can be
calculated in saddle-point, corresponding to a resummation of all the
tree-level Witten diagrams. The saddle can be found by solving numerically the
classical (Euclidean) non-linear equations of motion, with prescribed boundary
conditions. We apply these ideas to a model with an inflaton self-interaction
. Numerical and analytical methods show that the
tail of the probability distribution of goes as
, with a clear non-perturbative dependence on
the coupling. Our results are relevant for the calculation of the abundance of
primordial black holes.Comment: 37 pages, 14 figures. Matches JCAP versio
Gravitational radiation from a particle plunging into a Schwarzschild black hole: frequency-domain and semi-relativistic analyses
We revisit the classic problem of gravitational wave emission by a test
particle plunging into a Schwarzschild black hole both in the frequency-domain
Regge-Wheeler-Zerilli formalism and in the semi-relativistic approximation. We
use, and generalize, a transformation due to Nakamura, Sasaki and Shibata to
improve the fall-off of the source term of the Zerilli function. The faster
decay improves the numerical convergence of quantities of interest, such as the
energy radiated at spatial infinity through gravitational waves. As a test of
the method, we study the gravitational radiation produced by test particles
that plunge into the black hole with impact parameters close to the threshold
for scattering. We recover and expand upon previous results that were obtained
using the Sasaki-Nakamura equation. In particular, we study the relative
contributions to the total energy radiated due to waves of axial and polar
parity, and uncover an universal behavior in the waveforms at late times. We
complement our study with a semi-relativistic analysis of the problem, and we
compare the two approaches. The generalized Nakamura-Sasaki-Shibata
transformation presented here is a simple and practical alternative for the
analysis of gravitational-wave emission by unbound orbits in the Schwarzschild
spacetime using the frequency-domain Regge-Wheeler-Zerilli formalism.Comment: 16 pages, 10 figure
Gravitational wave lensing as a probe of halo properties and dark matter
Just like light, gravitational waves (GWs) are deflected and magnified by
gravitational fields as they propagate through the Universe. However, their low
frequency, phase coherence and feeble coupling to matter allow for distinct
lensing phenomena, such as diffraction and central images, that are challenging
to observe through electromagnetic sources. Here we explore how these phenomena
can be used to probe features of gravitational lenses. We focus on two variants
of the singular isothermal sphere, with 1) a variable slope of the matter
density and 2) a central core. We describe the imprints of these features in
the wave- and geometric-optics regimes, including the prospect of detecting
central images. We forecast the capacity of LISA and advanced LIGO to study
strongly lensed signals and measure the projected lens mass, impact parameter
and slope or core size. A broad range of lens masses allows all parameters to
be measured with precision up to , despite large
degeneracies. Thanks to wave-optics corrections, all parameters can be
measured, even when no central image forms. Although GWs are sensitive to
projected quantities, we compute the probability distribution of lens redshift,
virial mass and projection scale given a cosmology. As an application, we
consider the prospect of constraining self-interacting and ultra-light dark
matter, showing the regions of parameter space accessible to strongly-lensed
GWs. The distinct GW signatures will enable novel probes of fundamental physics
and astrophysics, including the properties of dark matter and the central
regions of galactic halos.Comment: 43 pages, 27 figures. Matches PRD versio
Lensing of gravitational waves: efficient wave-optics methods and validation with symmetric lenses
Gravitational wave (GW) astronomy offers the potential to probe the
wave-optics regime of gravitational lensing. Wave optics (WO) effects are
relevant at low frequencies, when the wavelength is comparable to the
characteristic lensing time delay multiplied by the speed of light, and are
thus often negligible for electromagnetic signals. Accurate predictions require
computing the conditionally convergent diffraction integral, which involves
highly oscillatory integrands and is numerically difficult. We develop and
implement several methods to compute lensing predictions in the WO regime valid
for general gravitational lenses. First, we derive approximations for high and
low frequencies, obtaining explicit expressions for several analytic lens
models. Next, we discuss two numerical methods suitable in the intermediate
frequency range: 1) Regularized contour flow yields accurate answers in a
fraction of a second for a broad range of frequencies. 2) Complex deformation
is slower, but requires no knowledge of solutions to the geometric lens
equation. Both methods are independent and complement each other. We verify
sub-percent accuracy for several lens models, which should be sufficient for
applications to GW astronomy in the near future. Apart from modelling lensed
GWs, our method will also be applicable to the study of plasma lensing of radio
waves and tests of gravity.Comment: 21 pages, 9 figures. Matches PRD versio
Resonant decay of gravitational waves into dark energy
We study the decay of gravitational waves into dark energy fluctuations \u3c0, taking into account the large occupation numbers. We describe dark energy using the effective field theory approach, in the context of generalized scalar-tensor theories. When the m33 (cubic Horndeski) and 3c m42 (beyond Horndeski) operators are present, the gravitational wave acts as a classical background for \u3c0 and modifies its dynamics. In particular, \u3c0 fluctuations are described by a Mathieu equation and feature instability bands that grow exponentially. Focusing on the regime of small gravitational-wave amplitude, corresponding to narrow resonance, we calculate analytically the produced \u3c0, its energy and the change of the gravitational-wave signal. The resonance is affected by \u3c0 self-interactions in a way that we cannot describe analytically. This effect is very relevant for the operator m33 and it limits the instability. In the case of the 3c m42 operator self-interactions can be neglected, at least in some regimes. The modification of the gravitational-wave signal is observable for 3
7 10-20 64 \u3b1H 64 10-17 with a LIGO/Virgo-like interferometer and for 10-16 64 \u3b1H 64 10-10 with a LISA-like one
Dark-Energy Instabilities induced by Gravitational Waves
International audienceWe 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 αB. 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 |αB |≳ 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 1010 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 |αH| ≳ 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
Gravitational Wave Decay into Dark Energy
International audienceWe study the decay of gravitational waves into dark energy fluctuations π, through the processes γ → ππ and γ → γ π, made possible by the spontaneous breaking of Lorentz invariance. Within the EFT of Dark Energy (or Horndeski/beyond Horndeski theories) the first process is large for the operator ½ ˜ m42(t) δ g00 ( (3)R + δ Kμν δ Kμν −δ K2 ), so that the recent observations force ˜ m4 = 0 (or equivalently 0αH=). This constraint, together with the requirement that gravitational waves travel at the speed of light, rules out all quartic and quintic GLPV theories. Additionally, we study how the same couplings affect the propagation of gravitons at loop order. The operator proportional to ˜ m42 generates a calculable, non-Lorentz invariant higher-derivative correction to the graviton propagation. The modification of the dispersion relation provides a bound on ˜ m42 comparable to the one of the decay. Conversely, operators up to cubic Horndeski do not generate sizeable \hbox{higher-derivative corrections.
Non-perturbative Wavefunction of the Universe in Inflation with (Resonant) Features
International audienceWe study the statistics of scalar perturbations in models of inflation with small and rapid oscillations in the inflaton potential (resonant non-Gaussianity). We do so by deriving the wavefunction non-perturbatively in , but at first order in the amplitude of the oscillations. The expression of the wavefunction of the universe (WFU) is explicit and does not require solving partial differential equations. One finds qualitative deviations from perturbation theory for , where is the number of oscillations per Hubble time. Notably, the WFU exhibits distinct behaviours for negative and positive values of (troughs and peaks respectively). While corrections for remain relatively small, of the order of the oscillation amplitude, positive yields substantial effects, growing exponentially as in the limit of large . This indicates that even minute oscillations give large effects on the tail of the distribution