Cyril Pitrou

Cosmic microwave background bispectrum on small angular scales

This article investigates the nonlinear evolution of cosmological perturbations on sub-Hubble scales in order to evaluate the unavoidable deviations from Gaussianity that arise from the nonlinear 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 nonlinear evolution of the dark matter component. The perturbation equations, involving, in particular, the first moments of the Boltzmann equation for 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 one 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 nonlinear evolution accounts for a contribution that would be equivalent to a constant primordial non-Gaussianity of order f{sub NL}{approx}25 on scales ranging approximately from l{approx}1000 to l{approx}3000.

Gravitational waves generated by second order effects during inflation

The generation of gravitational waves during inflation due to the non-linear coupling of scalar and tensor modes is discussed. Two methods describing gravitational wave perturbations are used and compared: a covariant and local approach, as well as a metric based analysis based on the Bardeen formalism. An application to slow-roll inflation is also described.

Gauge-invariant Boltzmann equation and the fluid limit

This paper investigates the collisionless Boltzmann equation up to second order in the cosmological perturbations. It describes the gauge dependence of the distribution function and the construction of a gauge-invariant distribution function and brightness, and then derives the gauge-invariant fluid limit.

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.

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.

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 Bmodes 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 o-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 oer a new tool to test the isotropy of the expansion of the universe at low redshift.

Quantization of perturbations during inflation in the 1+3 covariant formalism

This note derives the analogue of the Mukhanov-Sasaki variables both for scalar and tensor perturbations in the 1+3 covariant formalism. The possibility of generalizing them to nonflat Friedmann-Lemaitre universes is discussed.

Isotropization of the universe during inflation

Abstract 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 review briefly models based on primordial vector field that evade the cosmic no-hair theorem.

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.

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.