[Show abstract][Hide abstract] ABSTRACT: We explore the phenomenological consequences of general late-time
modifications of gravity in the quasi-static approximation, in the case where
baryons and cold dark matter have distinct couplings to the gravitational
sector. Assuming spectroscopic and photometric surveys with configuration
parameters similar to those of the Euclid mission, we derive constraints on our
effective description from three observables: the galaxy power spectrum in
redshift space, tomographic weak-lensing shear power spectrum and the
correlation spectrum between the integrated Sachs-Wolfe effect and the galaxy
distribution. In particular, with $\Lambda$CDM as fiducial model and a specific
choice for the time dependence of our effective functions, we perform a Fisher
matrix analysis and find that the unmarginalized $68\%$ CL errors on the three
parameters describing the modifications of gravity are of order
$\sigma\sim10^{-3}$. We also consider two other fiducial models. A nonminimal
coupling of CDM enhances the effects of modified gravity and reduces the above
statistical errors accordingly. In all cases, we find that the parameters are
highly degenerate, which prevents the inversion of the Fisher matrices.
Although all three observational probes are complementary in breaking some of
the degeneracies, the ISW-galaxy correlation stands out as a promising probe to
constrain the modifications of gravity.
[Show abstract][Hide abstract] ABSTRACT: Canonical models of single-field, slow-roll inflation do not lead to
appreciable non-Gaussianity, unless derivative interactions of the inflaton
become uncontrollably large. We propose a novel slow-roll scenario where scalar
perturbations propagate at a subluminal speed, leading to sizeable equilateral
non-Gaussianity, $f^{\rm equil}_{\rm NL}\propto 1/c_s^4$, largely insensitive
to the ultraviolet physics. The model is based on a low-energy effective theory
characterized by weakly broken invariance under internal galileon
transformations, $\phi\to\phi+b_\mu x^\mu$, which protects the properties of
perturbations from large quantum corrections. This provides the unique
alternative to models such as DBI inflation in generating strongly
subluminal/non-Gaussian scalar perturbations.
[Show abstract][Hide abstract] ABSTRACT: We introduce a new class of scalar-tensor theories of gravity that extend Horndeski, or "generalized Galileon," models. Despite possessing equations of motion of higher order in derivatives, we show that the true propagating degrees of freedom obey well-behaved second-order equations and are thus free from Ostrogradski instabilities, in contrast to standard lore. Remarkably, the covariant versions of the original Galileon Lagrangians-obtained by direct replacement of derivatives with covariant derivatives-belong to this class of theories. These extensions of Horndeski theories exhibit an uncommon, interesting phenomenology: The scalar degree of freedom affects the speed of sound of matter, even when the latter is minimally coupled to gravity.
[Show abstract][Hide abstract] ABSTRACT: Effective theories of a scalar $\phi$ invariant under the internal
\textit{galileon symmetry} $\phi\to\phi+b_\mu x^\mu$ have been extensively
studied due to their special theoretical and phenomenological properties. In
this paper, we introduce the notion of \textit{weakly broken galileon
invariance}, which characterizes the unique class of couplings of such theories
to gravity that maximally retain their defining symmetry. The curved-space
remnant of the galileon's quantum properties allows to construct (quasi) de
Sitter backgrounds largely insensitive to loop corrections. We exploit this
fact to build novel cosmological models with interesting phenomenology,
relevant for both inflation and late-time acceleration of the universe.
Journal of Cosmology and Astroparticle Physics 04/2015; 2015(09). DOI:10.1088/1475-7516/2015/09/007 · 5.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present a unifying treatment of dark energy and modified gravity that
allows distinct conformal-disformal couplings of matter species to the
gravitational sector. In this very general approach, we derive the conditions
to avoid ghost and gradient instabilities. We compute the equations of motion
for background quantities and linear perturbations. We illustrate our formalism
with two simple scenarios, where either cold dark matter or a relativistic
fluid is nonminimally coupled. This extends previous studies of coupled dark
energy to a much broader spectrum of gravitational theories.
Journal of Cosmology and Astroparticle Physics 04/2015; 2015(08). DOI:10.1088/1475-7516/2015/08/054 · 5.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We review and extend a novel approach that we introduced recently, to
describe general dark energy or scalar-tensor models. Our approach relies on an
ADM formulation based on the hypersurfaces where the underlying scalar field is
uniform. The advantage of this approach is that it can describe in the same
language and in a minimal way a vast number of existing models, such as
quintessence models, $F(R)$ theories, scalar tensor theories, their Horndeski
extensions and beyond. It also naturally includes Horava-Lifshitz theories. As
summarized in this review, our approach provides a unified treatment of the
linear cosmological perturbations about a FLRW universe, obtained by a
systematic expansion of our general action up to quadratic order. This shows
that the behaviour of these linear perturbations is generically characterized
by five time-dependent functions. We derive the full equations of motion in the
Newtonian gauge, and obtain in particular the equation of state for dark energy
perturbations, in the Horndeski case, in terms of these functions. Our unifying
description thus provides the simplest and most systematic way to confront
theoretical models with current and future cosmological observations.
International Journal of Modern Physics D 11/2014; 23(13). DOI:10.1142/S021827181443010X · 1.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We have recently proposed a new class of gravitational scalar-tensor theories
free from ghost instabilities. As they generalize Horndeski theories, or
"generalized" galileons, we call them G$^3$. These theories possess a simple
formulation when the time hypersurfaces are chosen to coincide with the uniform
scalar field hypersurfaces. We confirm that they do not suffer from
Ostrogradski instabilities by presenting the details of the Hamiltonian
formulation. We examine the coupling between these theories and matter.
Moreover, we investigate how they transform under a disformal redefinition of
the metric. Remarkably, these theories are preserved by disformal
transformations, which also allow subfamilies of G$^3$ to be mapped into
Horndeski theories.
Journal of Cosmology and Astroparticle Physics 08/2014; 2015(02). DOI:10.1088/1475-7516/2015/02/018 · 5.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We show that the prediction for the primordial tensor power spectrum cannot
be modified at leading order in derivatives. Indeed, one can always set to
unity the speed of propagation of gravitational waves during inflation by a
suitable disformal transformation of the metric, while a conformal one can make
the Planck mass time-independent. Therefore, the tensor-to-scalar ratio
unambiguously fixes the energy scale of inflation. Using the Effective Field
Theory of Inflation, we check that predictions are independent of the choice of
frame, as expected. The first corrections to the standard prediction come from
two parity violating operators with three derivatives. Also the correlator
$\langle\gamma\gamma\gamma\rangle$ is standard and only receives higher
derivative corrections. These results hold also in multifield models of
inflation and in alternatives to inflation and make the connection between a
(quasi) scale-invariant tensor spectrum and inflation completely robust.
[Show abstract][Hide abstract] ABSTRACT: We introduce a new class of scalar-tensor theories that extend Horndeski, or
"generalized galileon", models. Despite possessing equations of motion of
higher order in derivatives, we show that the true propagating degrees of
freedom obey well-behaved second-order equations and are thus free from
Ostrogradski instabilities, in contrast to the standard lore. Remarkably, the
covariant versions of the original galileon Lagrangians-obtained by direct
replacement of derivatives with covariant derivatives-belong to this class of
theories. These extensions of Horndeski theories exhibit an uncommon,
interesting phenomenology: the scalar degree of freedom affects the speed of
sound of matter, even when the latter is minimally coupled to gravity.
[Show abstract][Hide abstract] ABSTRACT: We compute the full cosmic microwave background temperature bispectrum generated by nonlinearities after single-field inflation. By integrating the photon temperature at second order along a perturbed geodesic in Newtonian gauge, we derive an expression for the observed temperature fluctuations that, for the first time, clarifies the separation of the gravitational lensing and time-delay effects from the purely second-order contributions. We then use the second-order Boltzmann code CosmoLib2nd to calculate these contributions and their bispectrum. Including the perturbations in the photon path, the numerically computed bispectrum exactly matches the expected squeezed limit. Moreover, the analytic squeezed-limit formula reproduces well the signal-to-noise ratio and shape of the full bispectrum, potentially facilitating the subtraction of the bias induced by second-order effects. For a cosmic-variance limited experiment with lmax=2000, the bias on a local signal is fNLloc=0.73 negligible for equilateral and orthogonal signals. The signal-to-noise ratio is unity at lmax̃3000, suggesting that second-order effects may hopefully be measured in the future.
Physical Review D 12/2013; 89(2). DOI:10.1103/PhysRevD.89.021302 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The recently derived consistency relations for Large Scale Structure do not
hold if the Equivalence Principle (EP) is violated. We show it explicitly in a
toy model with two fluids, one of which is coupled to a fifth force. We explore
the limits that galaxy surveys can set on EP violation looking at the squeezed
limit of the 3-point function involving two populations of objects. We find
that one can explore EP violations of order 10^{-3} - 10^{-4} on cosmological
scales. Chameleon models are already very constrained by the requirement of
screening within the Solar System and only a very tiny region of the parameter
space can be explored with this method. We show that no violation of the
consistency relations is expected in Galileon models.
Journal of Cosmology and Astroparticle Physics 12/2013; 2014(06). DOI:10.1088/1475-7516/2014/06/009 · 5.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We generalize the recently derived single-field consistency relations of
Large Scale Structure in two directions. First, we treat the effect of the long
modes (with momentum q) on the short ones (with momentum k) non-perturbatively,
by writing resummed consistency relations which do not require k/q \delta_q <<
1. These relations do not make any assumptions on the short-scales physics and
are extended to include (an arbitrary number of) multiple long modes, internal
lines with soft momenta and soft loops. We do several checks of these relations
in perturbation theory and we verify that the effect of soft modes always
cancels out in equal-time correlators. Second, we write the relations directly
in redshift space, without assuming the single-stream approximation: not only
the long mode affects the short scales as a homogeneous gravitational field,
but it also displaces them by its velocity along the line-of-sight. Redshift
space consistency relations still vanish when short modes are taken at equal
time: an observation of a signal in the squeezed limit would point towards
multifield inflation or a violation of the equivalence principle.
Journal of Cosmology and Astroparticle Physics 11/2013; 2014(02). DOI:10.1088/1475-7516/2014/02/051 · 5.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We derive consistency relations for the late universe (CDM and \Lambda CDM):
relations between an n-point function of the density contrast \delta and an
(n+1)-point function in the limit in which one of the (n+1) momenta becomes
much smaller than the others. These are based on the observation that a long
mode, in single-field models of inflation, reduces to a diffeomorphism since
its freezing during inflation all the way until the late universe, even when
the long mode is inside the horizon (but out of the sound horizon). These
results are derived in Newtonian gauge, at first and second order in the small
momentum q of the long mode and they are valid non-perturbatively in the
short-scale \delta. In the non-relativistic limit our results match with
(Kehagias and Riotto '12) and (Peloso and Pietroni '12). These relations are a
consequence of diffeomorphism invariance; they are not satisfied in the
presence of extra degrees of freedom during inflation or violation of the
Equivalence Principle (extra forces) in the late universe.
Journal of Cosmology and Astroparticle Physics 09/2013; 2013(12). DOI:10.1088/1475-7516/2013/12/025 · 5.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The effective field theory of cosmological perturbations stems from
considering a cosmological background solution as a state displaying
spontaneous breaking of time translations and (adiabatic) perturbations as the
related Nambu-Goldstone modes. With this insight, one can systematically
develop a theory for the cosmological perturbations during inflation and, with
minor modifications, also describe in full generality the gravitational
interactions of dark energy, which are relevant for late-time cosmology. The
formalism displays a unique set of Lagrangian operators containing an
increasing number of cosmological perturbations and derivatives. We give an
introductory description of the unitary gauge formalism for theories with
broken gauge symmetry---that allows to write down the most general
Lagrangian---and of the Stueckelberg "trick"---that allows to recover gauge
invariance and to make the scalar field explicit. We show how to apply this
formalism to gravity and cosmology and we reproduce the detailed analysis of
the action in the ADM variables. We also review some basic applications to
inflation and dark energy.
[Show abstract][Hide abstract] ABSTRACT: We propose a minimal description of single field dark energy/modified gravity
within the effective field theory formalism for cosmological perturbations,
which encompasses most existing models. We start from a generic Lagrangian
given as an arbitrary function of the lapse and of the extrinsic and intrinsic
curvature tensors of the time hypersurfaces in unitary gauge, i.e. choosing as
time slicing the uniform scalar field hypersurfaces. Focusing on linear
perturbations, we identify seven Lagrangian operators that lead to equations of
motion containing at most two (space or time) derivatives, the background
evolution being determined by the time dependent coefficients of only three of
these operators. We then establish a dictionary that translates any existing or
future model whose Lagrangian can be written in the above form into our
parametrized framework. As an illustration, we study Horndeski's-or generalized
Galileon-theories and show that they can be described, up to linear order, by
only six of the seven operators mentioned above. This implies, remarkably, that
the dynamics of linear perturbations can be more general than that of Horndeski
while remaining second order. Finally, in order to make the link with
observations, we provide the entire set of linear perturbation equations in
Newtonian gauge, the effective Newton constant in the quasi-static
approximation and the ratio of the two gravitational potentials, in terms of
the time-dependent coefficients of our Lagrangian.
Journal of Cosmology and Astroparticle Physics 04/2013; 2013(08). DOI:10.1088/1475-7516/2013/08/025 · 5.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We compute the cosmic microwave background temperature bispectrum generated by nonlinearities at recombination on all scales. We use CosmoLib2nd, a numerical Boltzmann code at second order to compute cosmic microwave background bispectra on the full sky. We consistently include all effects except gravitational lensing, which can be added to our result using standard methods. The bispectrum is peaked on squeezed triangles and agrees with the analytic approximation in the squeezed limit at the few percent level for all the scales where this is applicable. On smaller scales, we recover previous results on perturbed recombination. For cosmic-variance limited data to l_{max}=2000, its signal-to-noise ratio is S/N=0.47, corresponding to f_{NL}^{eff}=-2.79, and will bias a local signal by f_{NL}^{loc}≃0.82.
[Show abstract][Hide abstract] ABSTRACT: We use the so-called eikonal approximation, recently introduced in the context of cosmological perturbation theory, to compute power spectra for multicomponent fluids. We demonstrate that, at any given order in standard perturbation theory, multipoint power spectra do not depend on the large-scale adiabatic modes. Moreover, we employ perturbation theories to decipher how nonadiabatic modes, such as a relative velocity between two different components, damp the small-scale matter power spectrum, a mechanism recently described in the literature. In particular, we do an explicit calculation at one-loop order of this effect. While the one-loop result eventually breaks down, we show how the damping effect can be fully captured by the help of the eikonal approximation. A relative velocity not only induces mode damping but also creates large-scale anisotropic modulations of the matter power spectrum amplitude. We illustrate this for the Local Group environment.
[Show abstract][Hide abstract] ABSTRACT: We compute the cosmic microwave background temperature bispectrum generated
by nonlinearities at recombination on all scales. We use CosmoLib$2^{\rm nd}$,
a numerical Boltzmann code at second-order to compute CMB bispectra on the full
sky. We consistently include all effects except gravitational lensing, which
can be added to our result using standard methods. The bispectrum is peaked on
squeezed triangles and agrees with the analytic approximation in the squeezed
limit at the few per cent level for all the scales where this is applicable. On
smaller scales, we recover previous results on perturbed recombination. For
cosmic-variance limited data to $l_{\rm max} =2000$, its signal-to-noise is
$S/N=0.47$ and will bias a local signal by $f_{\rm NL}^{\rm loc}\simeq 0.82$.
[Show abstract][Hide abstract] ABSTRACT: We propose a universal description of dark energy and modified gravity that
includes all single-field models. By extending a formalism previously applied
to inflation, we consider the metric universally coupled to matter fields and
we write in terms of it the most general unitary gauge action consistent with
the residual unbroken symmetries of spatial diffeomorphisms. Our action is
particularly suited for cosmological perturbation theory: the background
evolution depends on only three operators. All other operators start at least
at quadratic order in the perturbations and their effects can be studied
independently and systematically. In particular, we focus on the properties of
a few operators which appear in non-minimally coupled scalar-tensor gravity and
galileon theories. In this context, we study the mixing between gravity and the
scalar degree of freedom. We assess the quantum and classical stability, derive
the speed of sound of fluctuations and the renormalization of the Newton
constant. The scalar can always be de-mixed from gravity at quadratic order in
the perturbations, but not necessarily through a conformal rescaling of the
metric. We show how to express covariant field-operators in our formalism and
give several explicit examples of dark energy and modified gravity models in
our language. Finally, we discuss the relation with the covariant EFT methods
recently appeared in the literature.
Journal of Cosmology and Astroparticle Physics 09/2012; 1302(2013):032. DOI:10.1088/1475-7516/2013/02/032 · 6.04 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Euclid is a European Space Agency medium class mission selected for launch in
2019 within the Cosmic Vision 2015-2025 programme. The main goal of Euclid is
to understand the origin of the accelerated expansion of the Universe. Euclid
will explore the expansion history of the Universe and the evolution of cosmic
structures by measuring shapes and redshifts of galaxies as well as the
distribution of clusters of galaxies over a large fraction of the sky. Although
the main driver for Euclid is the nature of dark energy, Euclid science covers
a vast range of topics, from cosmology to galaxy evolution to planetary
research. In this review we focus on cosmology and fundamental physics, with a
strong emphasis on science beyond the current standard models. We discuss five
broad topics: dark energy and modified gravity, dark matter, initial
conditions, basic assumptions and questions of methodology in the data
analysis. This review has been planned and carried out within Euclid's Theory
Working Group and is meant to provide a guide to the scientific themes that
will underlie the activity of the group during the preparation of the Euclid
mission.
Living Reviews in Relativity 06/2012; 16(1). DOI:10.12942/lrr-2013-6 · 19.25 Impact Factor