arXiv subjects

Francis Bernardeau

Publications and source records attributed to Francis Bernardeau.

At least 73 records · Page 4Linked to original sources

arXiv2011

The y-sky: diffuse spectral distortions of the cosmic microwave background

The non-linear evolution of the energy density of the radiation is shown to induce spectral distortions of the cosmic microwave background both at recombination and during the reionization era. This distortion has the same spectral signature as the one produced by the re-scattering of photons by non-relativistic hot electrons, the thermal Sunyaev-Zeldovich effect, whose amplitude is quantified by a Compton y parameter. A diffuse y-sky is then expected to emerge from mode couplings in the non-linear evolution of the cosmological perturbations and to superimpose to the point source contributions of galaxy clusters. The equations describing the evolution of the y field and a hierarchy governing its angular multipoles are derived from the second order Boltzmann equation. These equations are then integrated numerically to obtain the first predicted power spectrum of the diffuse y-sky. It is found to be a remarkable tracer of the reionization history of the Universe.

astro-ph.CO↗

arXiv2011

Cosmological Large-scale Structures beyond Linear Theory in Modified Gravity

We consider the effect of modified gravity on the growth of large-scale structures at second order in perturbation theory. We show that modified gravity models changing the linear growth rate of fluctuations are also bound to change, although mildly, the mode coupling amplitude in the density and reduced velocity fields. We present explicit formulae which describe this effect. We then focus on models of modified gravity involving a scalar field coupled to matter, in particular chameleons and dilatons, where it is shown that there exists a transition scale around which the existence of an extra scalar degree of freedom induces significant changes in the coupling properties of the cosmic fields. We obtain the amplitude of this effect for realistic dilaton models at the tree-order level for the bispectrum, finding them to be comparable in amplitude to those obtained in the DGP model.

astro-ph.CO↗

arXiv2010

CMB spectra and bispectra calculations: making the flat-sky approximation rigorous

This article constructs flat-sky approximations in a controlled way in the context of the cosmic microwave background observations for the computation of both spectra and bispectra. For angular spectra, it is explicitly shown that there exists a whole family of flat-sky approximations of similar accuracy for which the expression and amplitude of next to leading order terms can be explicitly computed. It is noted that in this context two limiting cases can be encountered for which the expressions can be further simplified. They correspond to cases where either the sources are localized in a narrow region (thin-shell approximation) or are slowly varying over a large distance (which leads to the so-called Limber approximation). Applying this to the calculation of the spectra it is shown that, as long as the late integrated Sachs-Wolfe contribution is neglected, the flat-sky approximation at leading order is accurate at 1% level for any multipole. Generalization of this construction scheme to the bispectra led to the introduction of an alternative description of the bispectra for which the flat-sky approximation is well controlled. This is not the case for the usual description of the bispectrum in terms of reduced bispectrum for which a flat-sky approximation is proposed but the next-to-leading order terms of which remain obscure.

astro-ph.CO↗

arXiv2010

Mode coupling evolution in arbitrary inflationary backgrounds

The evolution of high order correlation functions of a test scalar field in arbitrary inflationary backgrounds is computed. Whenever possible, exact results are derived from quantum field theory calculations. Taking advantage of the fact that such calculations can be mapped, for super-horizon scales, into those of a classical system, we express the expected correlation functions in terms of classical quantities, power spectra, Green functions, that can be easily computed in the long-wavelength limit. Explicit results are presented that extend those already known for a de Sitter background. In particular the expressions of the late time amplitude of bispectrum and trispectrum, as well as the whole high-order correlation structure, are given in terms of the expansion factor behavior. When compared to the case of a de Sitter background, power law inflation and chaotic inflation induced by a massive field are found to induce high order correlation functions the amplitudes of which are amplified by almost one order of magnitude. These results indicate that the dependence of the related non-Gaussian parameters - such as f_NL - on the wave-modes is at percent level.

astro-ph.CO↗

arXiv2010

Merging and fragmentation in the Burgers dynamics

We explore the noiseless Burgers dynamics in the inviscid limit, the so-called ``adhesion model'' in cosmology, in a regime where (almost) all the fluid particles are embedded within point-like massive halos. Following previous works, we focus our investigations on a ``geometrical'' model, where the matter evolution within the shock manifold is defined from a geometrical construction. This hypothesis is at variance with the assumption that the usual continuity equation holds but, in the inviscid limit, both models agree in the regular regions. Taking advantage of the formulation of the dynamics of this ``geometrical model'' in terms of Legendre transforms and convex hulls, we study the evolution with time of the distribution of matter and the associated partitions of the Lagrangian and Eulerian spaces. We describe how the halo mass distribution derives from a triangulation in Lagrangian space, while the dual Voronoi-like tessellation in Eulerian space gives the boundaries of empty regions with shock nodes at their vertices. We then emphasize that this dynamics actually leads to halo fragmentations for space dimensions greater or equal to 2 (for the inviscid limit studied in this article). This is most easily seen from the properties of the Lagrangian-space triangulation and we illustrate this process in the two-dimensional (2D) case. In particular, we explain how point-like halos only merge through three-body collisions while two-body collisions always give rise to two new massive shock nodes (in 2D). This generalizes to higher dimensions and we briefly illustrate the three-dimensional (3D) case. This leads to a specific picture for the continuous formation of massive halos through successive halo fragmentations and mergings.

astro-ph.CO↗

arXiv2010

The cosmic microwave background bispectrum from the non-linear evolution of the cosmological perturbations

This article presents the first computation of the complete bispectrum of the cosmic microwave background temperature anisotropies arising from the evolution of all cosmic fluids up to second order, including neutrinos. Gravitational couplings, electron density fluctuations and the second order Boltzmann equation are fully taken into account. Comparison to limiting cases that appeared previously in the literature are provided. These are regimes for which analytical insights can be given. The final results are expressed in terms of equivalent fNL for different configurations. It is found that for moments up to lmax=2000, the signal generated by non-linear effects is equivalent to fNL~5 for both local-type and equilateral-type primordial non-Gaussianity.

astro-ph.CO↗

arXiv2010

Multi-Point Propagators for Non-Gaussian Initial Conditions

We show here how Renormalized Perturbation Theory (RPT) calculations applied to the quasi-linear growth of the large-scale structure can be carried on in presence of primordial non-Gaussian (PNG) initial conditions. It is explicitly demonstrated that the series reordering scheme proposed in Bernardeau, Crocce and Scoccimarro (2008) is preserved for non-Gaussian initial conditions. This scheme applies to the power spectrum and higher order spectra and is based on a reorganization of the contributing terms into sum of products of multi-point propagators. In case of PNG new contributing terms appear, the importance of which is discussed in the context of current PNG models. The properties of the building blocks of such resummation schemes, the multi-point propagators, are then investigated. It is first remarked that their expressions are left unchanged at one-loop order irrespectively of statistical properties of the initial field. We furthermore show that the high-momemtum limit of each of these propagators can be explicitly computed even for arbitrary initial conditions. They are found to be damped by an exponential cutoff whose expression is directly related to the moment generating function of the one-dimensional displacement field. This extends what had been established for multi-point propagators for Gaussian initial conditions. Numerical forms of the cut-off are shown for the so-called local model of PNG.

astro-ph.CO↗

arXiv2010

Gravity and non-gravity mediated couplings in multiple-field inflation

Mechanisms for the generation of primordial non-Gaussian metric fluctuations in the context of multiple-field inflation are reviewed. As long as kinetic terms remain canonical, it appears that nonlinear couplings inducing non-gaussianities can be split into two types. The extension of the one-field results to multiple degrees of freedom leads to gravity mediated couplings that are ubiquitous but generally modest. Multiple-field inflation offers however the possibility of generating non-gravity mediated coupling in isocurvature directions that can eventually induce large non-Gaussianities in the metric fluctuations. The robustness of the predictions of such models is eventually examined in view of a case study derived from a high-energy physics construction.

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

Eulerian and Lagrangian propagators for the adhesion model (Burgers dynamics)

Motivated by theoretical studies of gravitational clustering in the Universe, we compute propagators (response functions) in the adhesion model. This model, which is able to reproduce the skeleton of the cosmic web and includes nonlinear effects in both Eulerian and Lagrangian frameworks, also corresponds to the Burgers equation of hydrodynamics. Focusing on the one-dimensional case with power-law initial conditions, we obtain exact results for Eulerian and Lagrangian propagators. We find that Eulerian propagators can be expressed in terms of the one-point velocity probability distribution and show a strong decay at late times and high wavenumbers, interpreted as a "sweeping effect" but not a genuine damping of small-scale structures. By contrast, Lagrangian propagators can be written in terms of the shock mass function -- which would correspond to the halo mass function in cosmology -- and saturate to a constant value at late times. Moreover, they show a power-law dependence on scale or wavenumber which depends on the initial power-spectrum index and is directly related to the low-mass tail of the shock mass function. These results strongly suggest that Lagrangian propagators are much more sensitive probes of nonlinear structures in the underlying density field and of relaxation processes than their Eulerian counterparts.

astro-ph.CO↗

arXiv2008

Multi-Point Propagators in Cosmological Gravitational Instability

We introduce the concept of multi-point propagators between linear cosmic fields and their nonlinear counterparts in the context of cosmological perturbation theory. Such functions express how a non-linearly evolved Fourier mode depends on the full ensemble of modes in the initial density field. We identify and resum the dominant diagrams in the large-$k$ limit, showing explicitly that multi-point propagators decay into the nonlinear regime at the same rate as the two-point propagator. These analytic results generalize the large-$k$ limit behavior of the two-point propagator to arbitrary order. We measure the three-point propagator as a function of triangle shape in numerical simulations and confirm the results of our high-$k$ resummation. We show that any $n-$point spectrum can be reconstructed from multi-point propagators, which leads to a physical connection between nonlinear corrections to the power spectrum at small scales and higher-order correlations at large scales. As a first application of these results, we calculate the reduced bispectrum at one-loop in renormalized perturbation theory and show that we can predict the decrease in its dependence on triangle shape at redshift zero, when standard perturbation theory is least successful.

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arXiv2008

Cosmic microwave background bispectrum on small angular scales

This article investigates the non-linear evolution of cosmological perturbations on sub-Hubble scales in order to evaluate the unavoidable deviations from Gaussianity that arise from the non-linear dynamics. It shows that the dominant contribution to modes coupling in the cosmic microwave background temperature anisotropies on small angular scales is driven by the sub-Hubble non-linear evolution of the dark matter component. The perturbation equations, involving in particular the first moments of the Boltzmann equation for the photons, are integrated up to second order in perturbations. An analytical analysis of the solutions gives a physical understanding of the result as well as an estimation of its order of magnitude. This allows to quantify the expected deviation from Gaussianity of the cosmic microwave background temperature anisotropy and, in particular, to compute its bispectrum on small angular scales. Restricting to equilateral configurations, we show that the non-linear evolution accounts for a contribution that would be equivalent to a constant primordial non-Gaussianity of order fNL~25 on scales ranging approximately from l~1000 to l~3000.

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arXiv2008

Propagators in Lagrangian space

It has been found recently that propagators, e.g. the cross-correlation spectra of the cosmic fields with the initial density field, decay exponentially at large-k in an Eulerian description of the dynamics. We explore here similar quantities defined for a Lagrangian space description. We find that propagators in Lagrangian space do not exhibit the same properties: they are found not to be monotonic functions of time, and to track back the linear growth rate at late time (but with a renormalized amplitude). These results have been obtained with a novel method which we describe alongside. It allows the formal resummation of the same set of diagrams as those that led to the known results in Eulerian space. We provide a tentative explanation for the marked differences seen between the Eulerian and the Lagrangian cases, and we point out the role played by the vorticity degrees of freedom that are specific to the Lagrangian formalism. This provides us with new insights into the late-time behavior of the propagators.

astro-ph↗

arXiv2007

Time drift of cosmological redshifts and its variance

The contribution of cosmological perturbations to the time drift of the cosmological redshift is derived. It is shown that the dominant correction arises from the local acceleration of both the emitter and the observer. The amplitude of this effect is estimated to be of the order of 1% of the drift signal at z=2-4, but can easily be lowered down to 0.1% by using many absorption lines and quasars.

astro-ph↗

arXiv2007

Non-Gaussianities in extended D-term inflation

We explore extensions of hybrid inflationary models in the context of supersymmetric D-term inflation. We point out that a large variety of inflationary scenarios can be encountered when the field content is extended. It is not only possible to get curvaton type models but also scenarios in which different fields, with nontrivial statistical properties, contribute to the primordial curvature fluctuations. We explore more particularly the parameter space of these multiple field inflationary models. It is shown that there exists a large domain in which significant primordial non-Gaussianities can be produced while preserving a scale free power spectrum for the metric fluctuations. In particular we explicitly compute the expected bi- and trispectrum for such models and compared the results to the current and expected observational constraints. It is shown that it is necessary to use both the bi- and tri-spectra of CMB anisotropies to efficiently reduce their parameter space.

hep-ph↗

arXiv2006

Models of inflation with primordial non-Gaussianities

We present a class of models in which the primordial metric fluctuations do not necessarily obey Gaussian statistics. These models are realizations of mechanisms in which non-Gaussianity is first generated by a light scalar field and then transferred into curvature fluctuations during or at the end of inflation. For this class of models we present generic results for the probability distribution functions of the metric perturbation at the end of inflation. It is stressed that finite volume effects can induce non trivial effects that we sketch.

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arXiv2004

Constraints on higher-dimensional gravity from the cosmic shear three-point correlation function

With the developments of large galaxy surveys or cosmic shear surveys it is now possible to map the dark matter distribution at truly cosmological scales. Detailed examinations of the statistical properties of the dark matter distribution reveal the detail of the large-scale structure growth of the Universe. In particular it is shown here that the behavior of the density field bi-spectrum is sensitive to departure from normal gravity in a way which depends only weakly on the background evolution. The cosmic shear bispectrum appears to be particularly sensitive to changes in the Poisson equation: we show that the current cosmic shear data can already be used to infer constraints on the scale of a possible higher-dimensional gravity, above 2 h^{-1}Mpc.

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arXiv2004

Constraints on mode couplings and modulation of the CMB with WMAP data

We investigate a possible asymmetry in the statistical properties of the cosmic microwave background temperature field and to do so we construct an estimator aiming at detecting a dipolar modulation. Such a modulation is found to induce correlations between multipoles with $Δ\ell=1$. Applying this estimator, to the V and W bands of the WMAP data, we found a significant detection in the V band. We argue however that foregrounds and in particular point sources are the origin of this signal.

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