arXiv subjects

Cyril Pitrou

Publications and source records attributed to Cyril Pitrou.

At least 55 records · Page 3Linked to original sources

arXiv2018

The radiative transfer at second order: a full treatment of the Boltzmann equation with polarization

This article investigates the full Boltzmann equation up to second order in the cosmological perturbations. Describing the distribution of polarized radiation by a tensor valued distribution function, we study the gauge dependence of the distribution function and summarize the construction of the gauge-invariant distribution function. The Liouville operator which describes the free streaming of electrons, and the collision term which describes the scattering of photons on free electrons are computed up to second order. Finally, the remaining dependence in the direction of the photon momentum is handled by expanding in projected symmetric trace-free multipoles and also in the more commonly used normal modes components. The results obtained remain to be used for computing numerically the contribution in the cosmic microwave background bispectrum which arises from the evolution of second order perturbations, in order to disentangle the primordial non-Gaussianity from the one generated by the subsequent non-linear evolution.

gr-qc↗

arXiv2018

Direction and redshift drifts for general observers and their applications in cosmology

High precision astrometry now enables to measure the time drift of astrophysical observables in real time, hence providing new ways to probe different cosmological models. This article presents a general derivation of the redshift and direction drifts for general observers. It is then applied to the standard cosmological framework of a Friedmann-Lemaitre space- time including all effects at first order in the cosmological perturbations, as well as in the class of spatially anisotropic universe models of the Bianchi I family. It shows that for a general observer, the direction drift splits into a parallax and an aberration drifts and order of magnitude estimates of these two components are provided. The multipolar decomposition of the redshift and aberration drifts is also derived and shows that the observer's peculiar velocity contributes only as a dipole whereas the anisotropic shear contributes as a quadrupole.

astro-ph.CO↗

arXiv2018

First predictions of the angular power spectrum of the astrophysical gravitational wave background

We present the first predictions for the angular power spectrum of the astrophysical gravitational wave background constituted of the radiation emitted by all resolved and unresolved astrophysical sources. Its shape and amplitude depend on both the astrophysical properties on galactic scales and on cosmological properties. We show that the angular power spectrum behaves as $C_{\ell}\propto 1/{\ell}$ on large scales and that relative fluctuations of the signal are of order 30% at 100 Hz. We also present the correlations of the astrophysical gravitational wave background with weak-lensing and galaxy distribution. These numerical results pave the way to the study of a new observable at the crossroad between general relativity, astrophysics and cosmology.

astro-ph.CO↗

arXiv2018

One-dimensional reduction of viscous jets. I. Theory

We build a general formalism to describe thin viscous jets as one-dimensional objects with an internal structure. We present in full generality the steps needed to describe the viscous jets around their central line, and we argue that the Taylor expansion of all fields around that line is conveniently expressed in terms of symmetric trace-free tensors living in the two dimensions of the fiber sections. We recover the standard results of axisymmetric jets and we report the first and second corrections to the lowest order description, also allowing for a rotational component around the axis of symmetry. When applied to generally curved fibers, the lowest order description corresponds to a viscous string model with circular sections. However, when including the first corrections we find that curved jets generically develop elliptic sections. Several subtle effects imply that the first corrections cannot be described by a rod model, since it amounts to selectively discard some corrections. For completeness, we also recover the constitutive relations for forces and torques in rod models and exhibit a missing term in the lowest order expression of viscous torque. Given that our method is based on tensors, the complexity of all computations has been beaten down by using an appropriate tensor algebra package such as {\it xAct}, allowing us to obtain a one-dimensional description of curved viscous jets with all the first order corrections consistently included. Finally, we find a description for straight fibers with elliptic sections as a special case of these results, and recover that ellipticity is dynamically damped by surface tension. An application to toroidal viscous fibers is presented in the companion paper [Pitrou, Phys. Rev. E 97, 043116 (2018)].

physics.flu-dyn↗

arXiv2018

One-dimensional reduction of viscous jets. II. Applications

In a companion paper [Pitrou, Phys. Rev. E 97, 043115 (2018)], a formalism allowing to describe viscous fibers as one-dimensional objects was developed. We apply it to the special case of a viscous fluid torus. This allows to highlight the differences with the basic viscous string model and with its viscous rod model extension. In particular, an elliptic deformation of the torus section appears because of surface tension effects, and this cannot be described by viscous string nor viscous rod models. Furthermore, we study the Rayleigh-Plateau instability for periodic deformations around the perfect torus, and we show that the instability is not sufficient to lead to the torus breakup in several droplets before it collapses to a single spherical drop. Conversely, a rotating torus is dynamically attracted toward a stationary solution, around which the instability can develop freely and split the torus in multiple droplets.

physics.flu-dyn↗

arXiv2018

The signal of the stochastic gravitational wave background and the angular correlation of its energy density

The gravitational wave radiation emitted by all, resolved and unresolved, astrophysical sources in the observable universe generates a stochastic background. This background has a directional dependence inherited from the inhomogeneities of the matter distribution. This article proposes a new and independent derivation of the angular dependence of its energy density by focusing on the total gravitational wave signal produced by an ensemble of incoherent sources. This approach clarifies the origin of the angular correlation and the relation between the gravitational wave signal that can be measured by interferometers and the energy density of the stochastic background.

astro-ph.CO↗

arXiv2018

Graph representation of balance sheets: from exogenous to endogenous money

The nature of monetary arrangements is often discussed without any reference to its detailed construction. We present a graph representation that allows for a clear understanding of modern monetary systems. First, we show that systems based on commodity money are incompatible with credit. We then study the current chartalist systems based on pure fiat money, and we discuss the consolidation of the central bank with the Treasury. We obtain a visual explanation about how commercial banks are responsible for endogenous money creation whereas the Treasury and the central bank are in charge of the total amount of net money. Finally we draw an analogy between systems based on gold convertibility and currency pegs to show that fixed exchange rates can never be maintained.

econ.GN↗

arXiv2017

Kinetic theory of fermions in curved spacetime

We build a statistical description of fermions, taking into account the spin degree of freedom in addition to the momentum of particles, and we detail its use in the context of the kinetic theory of gases of fermions particles. We show that the one-particle distribution function needed to write a Liouville equation is a spinor valued operator. The degrees of freedom of this function are covariantly described by an intensity function and by a polarisation vector which are parallel transported by free streaming. Collisions are described on the microscopic level and lead to a Boltzmann equation for this operator. We apply our formalism to the case of weak interactions, which at low energies can be considered as a contact interaction between fermions, allowing us to discuss the structure of the collision term for a few typical weak-interaction mediated reactions. In particular we find for massive particles that a dipolar distribution of velocities in the interacting species is necessary to generate linear polarisation, as opposed to the case of photons for which linear polarisation is generated from the quadrupolar distribution of velocities.

cond-mat.stat-mech↗

arXiv2017

Are we living near the center of a local void?

The properties of the cosmic microwave background (CMB) temperature and polarisation anisotropies measured by a static, off-centered observer located in a local spherically symmetric void, are described. In particular in this paper we compute, together with the standard 2- point angular correlation functions, the off-diagonal correlators, which are no more vanishing by symmetry. While the energy shift induced by the off-centered position of the observer can be suppressed by a proper choice of the observer velocity, a lensing-like effect on the CMB emission point remains. This latter effect is genuinely geometrical (e.g. non-degenerate with a boost) and reflects in the structure of the off-diagonal correlators. At lowest order in this effect, the temperature and polarisation correlation matrices have non-vanishing diagonal elements, as usual, and all the off-diagonal terms are excited. This particular signature of a local void model allows one, in principle, to disentangle geometrical effects from local kinematical ones in CMB observations.

astro-ph.CO↗

arXiv2017

Weak-lensing $B$-modes as a probe of the isotropy of the universe

We compute the angular power spectrum of the $B$-modes of the weak-lensing shear in a spatially anisotropic spacetime. We find that there must also exist off-diagonal correlations between the $E$-modes, $B$-modes, and convergence that allow one to reconstruct the eigendirections of expansion. Focusing on future surveys such as Euclid and SKA, we show that observations can constrain the geometrical shear in units of the Hubble rate at the percent level, or even better, offering a new and powerful method to probe our cosmological model.

astro-ph.CO↗

arXiv2017

Weak-lensing by the large scale structure in a spatially anisotropic universe: theory and predictions

This article details the computation of the two-point correlators of the convergence, $E$- and $B$-modes of the cosmic shear induced by the weak-lensing by large scale structure assuming that the background spacetime is spatially homogeneous and anisotropic. After detailing the perturbation equations and the general theory of weak-lensing in an anisotropic universe, it develops a weak shear approximation scheme in which one can compute analytically the evolution of the Jacobi matrix. It allows one to compute the angular power spectrum of the $E$- and $B$-modes. In the linear regime, the existence of $B$-modes is a direct tracer of a late time anisotropy and their angular power spectrum scales as the square of the shear. It is then demonstrated that there must also exist off-diagonal correlations between the $E$-modes, $B$-modes and convergence that are linear in the geometrical shear and allow one to reconstruct the eigendirections of expansion. These spectra can be measured in future large scale surveys, such as Euclid and SKA, and offer a new tool to test the isotropy of the expansion of the universe at low redshift.

astro-ph.CO↗

arXiv2016

Redshift-space distortions with wide angular separations

Redshift-space distortions are generally considered in the plane parallel limit, where the angular separation between the two sources can be neglected. Given that galaxy catalogues now cover large fractions of the sky, it becomes necessary to consider them in a formalism which takes into account the wide angle separations. In this article we derive an operational formula for the matter correlators in the Newtonian limit to be used in actual data sets, both in configuration and in Fourier spaces without relying on a plane-parallel approximation. We then recover the plane-parallel limit not only in configuration space where the geometry is simpler, but also in Fourier space, and we exhibit the first corrections that should be included in large surveys as a perturbative expansion over the plane-parallel results. We finally compare our results to existing literature, and show explicitly how they are related.

astro-ph.CO↗

arXiv2015

Isotropization of the universe during inflation

A primordial inflationary phase allows one to erase any possible anisotropic expansion thanks to the cosmic no-hair theorem. If there is no global anisotropic stress, then the anisotropic expansion rate tends to decrease. What are the observational consequences of a possible early anisotropic phase? We first review the dynamics of anisotropic universes and report analytic approximations. We then discuss the structure of dynamical equations for perturbations and the statistical properties of observables, as well as the implication of a primordial anisotropy on the quantization of these perturbations during inflation. Finally we briefly review models based on primordial vector field which evade the cosmic no-hair theorem.

astro-ph.CO↗

arXiv2015

A precise numerical estimation of the magnetic field generated around recombination

We investigate the generation of magnetic fields from non-linear effects around recombination. As tight-coupling is gradually lost when approaching $z\simeq 1100$, the velocity difference between photons and baryons starts to increase, leading to an increasing Compton drag of the photons on the electrons. The protons are then forced to follow the electrons due to the electric field created by the charge displacement; the same field, following Maxwell's laws, eventually induces a magnetic field on cosmological scales. Since scalar perturbations do not generate any magnetic field as they are curl-free, one has to resort to second-order perturbation theory to compute the magnetic field generated by this effect. We reinvestigate this problem numerically using the powerful second-order Boltzmann code SONG. We show that: i) all previous studies do not have a high enough angular resolution to reach a precise and consistent estimation of the magnetic field spectrum; ii) the magnetic field is generated up to $z\simeq 10$; iii) it is in practice impossible to compute the magnetic field with a Boltzmann code for scales smaller than $1\,{\rm Mpc}$. Finally we confirm that for scales of a few ${\rm Mpc}$, this magnetic field is of order $2\times 10^{-29}{\rm G}$, many orders of magnitude smaller than what is currently observed on intergalactic scales.

astro-ph.CO↗

arXiv2015

Light propagation in a homogeneous and anisotropic universe

This article proposes a comprehensive analysis of light propagation in an anisotropic and spatially homogeneous Bianchi I universe. After recalling that null geodesics are easily determined in such a spacetime, we derive the expressions of the redshift and direction drifts of light sources; by solving analytically the Sachs equation, we then obtain an explicit expression of the Jacobi matrix describing the propagation of narrow light beams. As a byproduct, we recover the old formula by Saunders for the angular diameter distance in a Bianchi I spacetime, but our derivation goes further since it also provides the optical shear and rotation. These results pave the way to the analysis of both supernovae data and weak lensing by the large-scale structure in Bianchi universes.

gr-qc↗

arXiv2015

Parameterization of temperature and spectral distortions in future CMB experiments

CMB spectral distortions are induced by Compton collisions with electrons. We review the various schemes to characterize the anisotropic CMB with a non-Planckian spectrum. We advocate using logarithmically averaged temperature moments as the preferred language to describe these spectral distortions, both for theoretical modeling and observations. Numerical modeling is simpler, the moments are frame-independent, and in terms of scattering the mode truncation is exact.

astro-ph.CO↗

arXiv2014

On the stability and causality of scalar-vector theories

Various extensions of standard inflationary models have been proposed recently by adding vector fields. Because they are generally motivated by large-scale anomalies, and the possibility of statistical anisotropy of primordial fluctuations, such models require to introduce non-standard couplings between vector fields on the one hand, and either gravity or scalar fields on the other hand. In this article, we study models involving a vector field coupled to a scalar field. We derive restrictive necessary conditions for these models to be both stable (Hamiltonian bounded by below) and causal (hyperbolic equations of motion).

hep-th↗

arXiv2014

Spectral distortions in the cosmic microwave background polarization

We compute the spectral distortions of the Cosmic Microwave Background (CMB) polarization induced by non-linear effects in the Compton interactions between CMB photons and cold intergalactic electrons. This signal is of the $y$-type and is dominated by contributions arising from the reionized era. We stress that it is not shadowed by the thermal SZ effect which has no equivalent for polarization. We decompose its angular dependence into $E$- and $B$-modes, and we calculate the corresponding power spectra, both exactly and using a suitable Limber approximation that allows a simpler numerical evaluation. We find that $B$-modes are of the same order of magnitude as $E$-modes. Both spectra are relatively flat, peaking around $\ell=280$, and their overall amplitude is directly related to the optical depth to reionization. Moreover, we find this effect to be one order of magnitude larger than the non-linear kinetic Sunyaev-Zel'dovich effect in galaxy clusters. Finally, we discuss how to improve the detectability of our signal by cross-correlating it with other quantities sourced by the flow of intergalactic electrons.

astro-ph.CO↗