arXiv subjects

Filippo Vernizzi

Publications and source records attributed to Filippo Vernizzi.

At least 73 records · Page 4Linked to original sources

arXiv2011

The CMB bispectrum in the squeezed limit

The CMB bispectrum generated by second-order effects at recombination can be calculated analytically when one of the three modes has a wavelength much longer than the other two and is outside the horizon at recombination. This was pointed out in \cite{Creminelli:2004pv} and here we correct their results. We derive a simple formula for the bispectrum, $f_{NL}^{loc} = - (1/6+ \cos 2 θ) \cdot (1- 1/2 \cdot d \ln (l_S^2 C_{S})/d \ln l_S)$, where $C_S$ is the short scale spectrum and $θ$ the relative orientation between the long and the short modes. This formula is exact and takes into account all effects at recombination, including recombination-lensing, but neglects all late-time effects such as ISW-lensing. The induced bispectrum in the squeezed limit is small and will negligibly contaminate the Planck search for a local primordial signal: this will be biased only by $f_{NL}^{loc}\approx-0.4$. The above analytic formula includes the primordial non-Gaussianity of any single-field model. It also represents a consistency check for second-order Boltzmann codes: we find substantial agreement with the CMBquick code.

astro-ph.CO↗

arXiv2011

Cosmological structure formation with clustering quintessence

We study large-scale structure formation in the presence of a quintessence component with zero speed of sound in the framework of Eulerian Perturbation Theory. Due to the absence of pressure gradients, quintessence and dark matter are comoving and can be studied as a unique fluid in terms of the total energy density contrast and the common velocity. In this description the clustering of quintessence enhances the linear term proportional to the velocity divergence in the continuity equation by a factor (1+w) Omega_Q / Omega_m. This is responsible for a rapid evolution of the growth rate at low redshifts, and modifies the standard relation between the velocity divergence and the growth factor. For the total fluid, the solutions for the linear growth function and growth rate can be written in integral forms and admit simple fitting formulae, as in the LambdaCDM case. At second order in perturbation theory, we derive an explicit expression for the kernels F_2 and G_2. They receive modifications of the order of the ratio between quintessence and total energy density perturbations, which affect the corresponding tree-level bispectra. We finally compute the cumulative signal-to-noise in the power spectrum, bispectrum and reduced bispectrum, expected for departures from a LambdaCDM cosmology both in the clustering and smooth quintessence scenarios. The reduced bispectrum, in particular, receives sensible modifications only in the clustering case and can potentially be used to detect or rule out the model.

astro-ph.CO↗

arXiv2010

A geometrical approach to nonlinear perturbations in relativistic cosmology

We give a pedagogical review of a covariant and fully non-perturbative approach to study nonlinear perturbations in cosmology. In the first part, devoted to cosmological fluids, we define a nonlinear extension of the uniform-density curvature perturbation and derive its evolution equation. In the second part, we focus our attention on multiple scalar fields and present a nonlinear description in terms of adiabatic and entropy perturbations. In both cases, we show how the formalism presented here enables one to easily obtain equations up to second, third and higher orders.

astro-ph.CO↗

arXiv2010

Spherical collapse in quintessence models with zero speed of sound

We study the spherical collapse model in the presence of quintessence with negligible speed of sound. This case is particularly motivated for w<-1 as it is required by stability. As pressure gradients are negligible, quintessence follows dark matter during the collapse. The spherical overdensity behaves as a separate closed FLRW universe, so that its evolution can be studied exactly. We derive the critical overdensity for collapse and we use the extended Press-Schechter theory to study how the clustering of quintessence affects the dark matter mass function. The effect is dominated by the modification of the linear dark matter growth function. A larger effect occurs on the total mass function, which includes the quintessence overdensities. Indeed, here quintessence constitutes a third component of virialized objects, together with baryons and dark matter, and contributes to the total halo mass by a fraction ~ (1+w) Omega_Q / Omega_m. This gives a distinctive modification of the total mass function at low redshift.

astro-ph.CO↗

arXiv2010

Full-sky lensing shear at second order

We compute the reduced cosmic shear up to second order in the gravitational potential without relying on the small angle or thin-lens approximation. This is obtained by solving the Sachs equation which describes the deformation of the infinitesimal cross-section of light bundle in the optical limit, and maps galaxy intrinsic shapes into their angular images. The calculation is done in the Poisson gauge without a specific matter content, including vector and tensor perturbations generated at second order and taking account of the inhomogeneities of a fixed redshift source plane. Our final result is expressed in terms of spin-2 operators on the sphere and is valid on the full sky. Beside the well known lens-lens and Born corrections that dominate on small angular scales, we find new non-linear couplings. These are a purely general relativistic intrinsic contribution, a coupling between the gravitational potential at the source with the lens, couplings between the time delay with the lens, couplings between two photon deflections, as well as non-linear couplings due to the second-order vector and tensor components. The inhomogeneity in the redshift of the source induces a coupling between the photon redshift with the lens. All these corrections become important on large angular scales and should thus be included when computing higher-order observables such as the bispectrum, in full or partially full-sky surveys.

astro-ph.CO↗

arXiv2009

Sachs-Wolfe at second order: the CMB bispectrum on large angular scales

We calculate the Cosmic Microwave Background anisotropy bispectrum on large angular scales in the absence of primordial non-Gaussianities, assuming exact matter dominance and extending at second order the classic Sachs-Wolfe result δT/T=Φ/3. The calculation is done in Poisson gauge. Besides intrinsic contributions calculated at last scattering, one must consider integrated effects. These are associated to lensing, and to the time dependence of the potentials (Rees-Sciama) and of the vector and tensor components of the metric generated at second order. The bispectrum is explicitly computed in the flat-sky approximation. It scales as l^(-4) in the scale invariant limit and the shape dependence of its various contributions is represented in 3d plots. Although all the contributions to the bispectrum are parametrically of the same order, the full bispectrum is dominated by lensing. In the squeezed limit it corresponds to f_NL^local = -1/6 - cos(2 θ), where θis the angle between the short and the long modes; the angle dependent contribution comes from lensing. In the equilateral limit it corresponds to f_NL^equil ~ 3.13.

astro-ph.CO↗

arXiv2009

Inflationary trispectrum from graviton exchange

We compute the connected four-point correlation function of the primordial curvature perturbation generated during inflation with standard kinetic terms, where the correlation is established via exchange of a graviton between two pairs of scalar fluctuations. Any such correlation yields a contribution to the scalar trispectrum of the order of the tensor to scalar ratio r. This contribution is numerically one order of magnitude larger than the one previously calculated on the basis of scalar perturbations interacting at a point and satisfies a simple relation in the limit where the momentum of the graviton which is exchanged becomes much smaller than the external momenta. We conclude that the total non-linearity parameter generated by single-field models of slow-roll inflation is at maximum tauNL ~ r.

astro-ph↗

arXiv2009

Non-Gaussianities from ekpyrotic collapse with multiple fields

We compute the non-Gaussianity of the curvature perturbation generated by ekpyrotic collapse with multiple fields. The transition from the multi-field scaling solution to a single-field dominated regime converts initial isocurvature field perturbations to an almost scale-invariant comoving curvature perturbation. In the specific model of two fields, $ϕ_1$ and $ϕ_2$, with exponential potentials, $-V_i \exp (-c_i ϕ_i)$, we calculate the bispectrum of the resulting curvature perturbation. We find that the non-Gaussianity is dominated by non-linear evolution on super-Hubble scales and hence is of the local form. The non-linear parameter of the curvature perturbation is given by $f_{NL} = 5 c_j^2 /12$, where $c_j$ is the exponent of the potential for the field which becomes sub-dominant at late times. Since $c_j^2$ must be large, in order to generate an almost scale invariant spectrum, the non-Gaussianity is inevitably large. By combining the present observational constraints on $f_{\rm NL}$ and the scalar spectral index, the specific model studied in this paper is thus ruled out by current observational data.

hep-th↗

arXiv2009

The Effective Theory of Quintessence: the w<-1 Side Unveiled

We study generic single-field dark energy models, by a parametrization of the most general theory of their perturbations around a given background, including higher derivative terms. In appropriate limits this approach reproduces standard quintessence, k-essence and ghost condensation. We find no general pathology associated to an equation of state w_Q < -1 or in crossing the phantom divide w_Q = -1. Stability requires that the w_Q < -1 side of dark energy behaves, on cosmological scales, as a k-essence fluid with a virtually zero speed of sound. This implies that one should set the speed of sound to zero when comparing with data models with w_Q < -1 or crossing the phantom divide. We summarize the theoretical and stability constraints on the quintessential plane (1+w_Q) vs. speed of sound squared.

astro-ph↗

arXiv2008

Non-linear isocurvature perturbations and non-Gaussianities

We study non-linear primordial adiabatic and isocurvature perturbations and their non-Gaussianity. After giving a general formulation in the context of an extended delta N-formalism, we analyse in detail two illustrative examples. The first is a mixed curvaton-inflaton scenario in which fluctuations of both the inflaton and a curvaton (a light isocurvature field during inflation) contribute to the primordial density perturbation. The second example is that of double inflation involving two decoupled massive scalar fields during inflation. In the mixed curvaton-inflaton scenario we find that the bispectrum of primordial isocurvature perturbations may be large and comparable to the bispectrum of adiabatic curvature perturbations.

astro-ph↗

arXiv2008

Nonlinear perturbations of cosmological scalar fields

We present a covariant formalism for studying nonlinear perturbations of scalar fields. In particular, we consider the case of two scalar fields and introduce the notion of adiabatic and isocurvature covectors. We obtain differential equations governing the evolution of these two covectors, as well as the evolution equation for the covector associated with the curvature perturbation. The form of these equations is very close to the analogous equations obtained in the linear theory, but our equations are fully nonlinear and exact. As an application of our formalism, we expand these equations at second order in the perturbations. On large scales, we obtain a closed system of coupled scalar equations giving the evolution of the second-order adiabatic and entropy perturbations in terms of the first-order perturbations. These equations in general contain a nonlocal term which, however, rapidly decays in an expanding universe.

astro-ph↗

arXiv2008

Action approach to cosmological perturbations: the 2nd order metric in matter dominance

We study nonlinear cosmological perturbations during the post-inflationary evolution, using the equivalence between a perfect barotropic fluid and a derivatively coupled scalar field with Lagrangian [-(\partial ϕ)^2]^[(1+w)/2w]. Since this Lagrangian is just a special case of k-inflation, this approach is analogous to the one employed in the study of non-Gaussianities from inflation. We use this method to derive the second order metric during matter dominance in the comoving gauge directly as function of the primordial inflationary perturbation ζ. Going to Poisson gauge, we recover the metric previously derived in the literature.

astro-ph↗

arXiv2007

Covariant generalization of cosmological perturbation theory

We present an approach to cosmological perturbations based on a covariant perturbative expansion between two worldlines in the real inhomogeneous universe. As an application, at an arbitrary order we define an exact scalar quantity which describes the inhomogeneities in the number of e-folds on uniform density hypersurfaces and which is conserved on all scales for a barotropic ideal fluid. We derive a compact form for its conservation equation at all orders and assign it a simple physical interpretation. To make a comparison with the standard perturbation theory, we develop a method to construct gauge-invariant quantities in a coordinate system at arbitrary order, which we apply to derive the form of the n-th order perturbation in the number of e-folds on uniform density hypersurfaces and its exact evolution equation. On large scales, this provides the gauge-invariant expression for the curvature perturbation on uniform density hypersurfaces and its evolution equation at any order.

gr-qc↗

arXiv2006

Non-Gaussianities in two-field inflation

We study the bispectrum of the curvature perturbation on uniform energy density hypersurfaces in models of inflation with two scalar fields evolving simultaneously. In the case of a separable potential, it is possible to compute the curvature perturbation up to second order in the perturbations, generated on large scales due to the presence of non-adiabatic perturbations, by employing the $δN$-formalism, in the slow-roll approximation. In this case, we provide an analytic formula for the nonlinear parameter $f_{NL}$. We apply this formula to double inflation with two massive fields, showing that it does not generate significant non-Gaussianity; the nonlinear parameter at the end of inflation is slow-roll suppressed. Finally, we develop a numerical method for generic two-field models of inflation, which allows us to go beyond the slow-roll approximation and confirms our analytic results for double inflation.

astro-ph↗

arXiv2006

Nonlinear perturbations for dissipative and interacting relativistic fluids

We develop a covariant formalism to study nonlinear perturbations of dissipative and interacting relativistic fluids. We derive nonlinear evolution equations for various covectors defined as linear combinations of the spatial gradients of the local number of e-folds and of some scalar quantities characterizing the fluid, such as the energy density or the particle number density. For interacting fluids we decompose perturbations into adiabatic and entropy components and derive their coupled evolution equations, recovering and extending the results obtained in the context of the linear theory. For non-dissipative and noninteracting fluids, these evolution equations reduce to the conservation equations that we have obtained in recent works. We also illustrate geometrically the meaning of the covectors that we have introduced.

astro-ph↗

arXiv2006

Conserved non-linear quantities in cosmology

We give a detailed and improved presentation of our recently proposed formalism for non-linear perturbations in cosmology, based on a covariant and fully non-perturbative approach. We work, in particular, with a covector combining the gradients of the energy density and of the local number of e-folds to obtain a non-linear generalization of the familiar linear uniform density perturbation. We show that this covector obeys a remarkably simple conservation equation which is exact, fully non-linear and valid at all scales. We relate explicitly our approach to the coordinate-based formalisms for linear perturbations and for second-order perturbations. We also consider other quantities, which are conserved on sufficiently large scales for adiabatic perturbations, and discuss the issue of gauge invariance.

astro-ph↗

arXiv2005

Evolution of non-linear cosmological perturbations

We define fully non-perturbative generalizations of the uniform density and comoving curvature perturbations, which are known, in the linear theory, to be conserved on sufficiently large scales for adiabatic perturbations. Our non-linear generalizations are defined geometrically, independently of any coordinate system. We give the equations governing their evolution on all scales. Also, in order to make contact with previous works on first and second order perturbations, we introduce a coordinate system and show that previous results can be recovered, on large scales, in a remarkably simple way, after restricting our definitions to first and second orders in a perturbative expansion.

astro-ph↗

arXiv2005

Generating cosmological perturbations with mass variations

We study the possibility that large scale cosmological perturbations have been generated during the domination and decay of a massive particle species whose mass depends on the expectation value of a light scalar field. We discuss the constraints that must be imposed on the field in order to remain light and on the annihilation cross section and decay rate of the massive particles in order for the mechanism to be efficient. We compute the resulting curvature perturbations after the mass domination, recovering the results of Dvali, Gruzinov, and Zaldarriaga in the limit of total domination. By comparing the amplitude of perturbations generated by the mass domination to those originally present from inflation, we conclude that this mechanism can be the primary source of perturbations only if inflation does not rely on slow-roll conditions.

astro-ph↗