11 research outputs found
Beyond Perturbation Theory in Cosmology
Over many years, our current understanding of the Universe has been extremely relied on perturbation theory (PT) both theoretically and experimentally. There are, however, many situations in cosmology in which the analysis beyond PT is required. In this thesis we study three examples: the resonant decay of gravitational waves (GWs), the dark energy (DE) instabilities induced by GWs, and the tail of the primordial field distribution function. The first two cases are within the context of the Effective Field Theory (EFT) of DE, whereas the last one is within inflation.
We first review the construction of the EFT of DE, which is the most general Lagrangian for the scalar and tensor perturbations around the flat FLRW metric. Specifically, this EFT can be mapped to the covariant theories, known as Horndeski and Beyond Horndeski theories. We then study the implications on the dark energy theories coming from the fact that GWs travel with the speed at LIGO/Virgo frequencies. After that, we consider the perturbative decay of GWs into DE fluctuations () due to the operator. This process is kinematically allowed by the spontaneous breaking of Lorentz invariance. Therefore, having no perturbative decay of gravitons together with at LIGO/Virgo, rules out all quartic and quintic beyond Horndeski theories.
As the first non-perturbative regime in this thesis, we study the decay of GWs into DE fluctuations , taking into account the large occupation numbers of gravitons. When the (cubic Horndeski) and (beyond Horndeski) operators are present, the GW acts as a classical background for and modifies its dynamics. In particular, fluctuations are described by a Mathieu equation and feature instability bands that grow exponentially. In the regime of small GW amplitude which corresponds to narrow resonance, we calculate analytically the produced , its energy and the change of the GW signal. Eventually, the resonance is affected by self-interactions in a way that we cannot describe analytically. The fact that self-couplings coming from the operator become quickly comparable with the resonant term affects the growth of so that the bound on remains inconclusive. However, in the case of the operator self-interactions can be neglected at least in some regimes. Therefore, our resonant analysis improves the perturbative bounds on , ruling out quartic Beyond Horndeski operators.
In the second non-perturbative regime we show that may become unstable in the presence of a GW background with sufficiently large amplitude. We find that dark-energy fluctuations feature ghost and/or gradient instabilities for GW 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 , i.e. when the modification of gravity is sizable. 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. In conclusion, the only dark-energy theories with sizable cosmological effects that avoid these problems are -essence models, with a possible conformal coupling with matter.
In the second part of the thesis we consider physics of 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 . We then 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
Quasinormal Modes from EFT of Black Hole Perturbations with Timelike Scalar Profile
The Effective Field Theory (EFT) of perturbations on an arbitrary background
geometry with a timelike scalar profile was recently constructed in the context
of scalar-tensor theories. In this paper, we use this EFT to study quasinormal
frequencies of odd-parity perturbations on a static and spherically symmetric
black hole background. Keeping a set of operators that can accommodate
shift-symmetric quadratic higher-order scalar-tensor theories, we demonstrate
the computation for two examples of hairy black holes, of which one is the
stealth Schwarzschild solution and the other is the Hayward metric accompanied
by a non-trivial scalar field. We emphasize that this is the first
phenomenological application of the EFT, opening a new possibility to test
general relativity and modified gravity theories in the strong gravity regime.Comment: 33 pages, 4 figures, 2 tables. Matches JCAP versio
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
Non-perturbative Wavefunction of the Universe in Inflation with (Resonant) Features
We 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.Comment: 56 pages, 10 figures. Matches JHEP 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
Effective Field Theory of Black Hole Perturbations with Timelike Scalar Profile: Formulation
We formulate the Effective Field Theory (EFT) of perturbations within
scalar-tensor theories on an inhomogeneous background. The EFT is constructed
while keeping a background of a scalar field to be , which
spontaneously breaks the time diffeomorphism. We find a set of consistency
relations that are imposed by the invariance of the EFT under the 3d spatial
diffeomorphism. This EFT can be generically applied to any inhomogeneous
background metric as long as the scalar profile is everywhere timelike. For
completeness, we report a dictionary between our EFT parameters to those of
Horndernski theories. Finally, we compute background equations for a class of
spherically symmetric, static black hole backgrounds, including a stealth
Schwarzschild-de Sitter solution.Comment: 31 page
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
Non-perturbative wavefunction of the universe in inflation with (resonant) features
We 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 Ψ[ζ(x)] non-perturbatively in ζ, 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 |ζ| ≳ α⁻², where α ≫ 1 is the number of oscillations per Hubble time. Notably, the WFU exhibits distinct behaviours for negative and positive values of ζ (troughs and peaks respectively). While corrections for ζ < 0 remain relatively small, of the order of the oscillation amplitude, positive ζ yields substantial effects, growing exponentially as eπα/2 in the limit of large ζ. This indicates that even minute oscillations give large effects on the tail of the distribution.ISSN:1126-6708ISSN:1029-847
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
Effective Field Theory of Black Hole Perturbations in Vector-Tensor Gravity
We formulate the effective field theory (EFT) of vector-tensor gravity for
perturbations around an arbitrary background with a vector
profile, which can be applied to study black hole perturbations. The vector
profile spontaneously breaks both the time diffeomorphism and the
symmetry, leaving their combination and the spatial diffeomorphism as the
residual symmetries in the unitary gauge. We derive two sets of consistency
relations which guarantee the residual symmetries of the EFT. Also, we provide
the dictionary between our EFT coefficients and those of generalized Proca (GP)
theories, which enables us to identify a simple subclass of the EFT that
includes the GP theories as a special case. For this subclass, we consider the
stealth Schwarzschild(-de Sitter) background solution with a constant temporal
component of the vector field and study the decoupling limit of the
longitudinal mode of the vector field, explicitly showing that the strong
coupling problem arises due to vanishing sound speeds. This is in sharp
contrast to the case of gauged ghost condensate, in which perturbations are
weakly coupled thanks to certain higher-derivative terms, i.e., the scordatura
terms. This implies that, in order to consistently describe this type of
stealth solutions within the EFT, the scordatura terms must necessarily be
taken into account in addition to those already included in the simple
subclass.Comment: 33 page