Showing papers by "Camille Bonvin published in 2010"

Full-sky lensing shear at second order

Abstract: 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 a 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 nonlinear 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 and between two photon deflections, as well as nonlinear 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.

CMB temperature anisotropy at large scales induced by a causal primordial magnetic field

Abstract: We present an analytical derivation of the Sachs Wolfe effect sourced by a primordial magnetic field. In order to consistently specify the initial conditions, we assume that the magnetic field is generated by a causal process, namely a first order phase transition in the early universe. As for the topological defects case, we apply the general relativistic junction conditions to match the perturbation variables before and after the phase transition which generates the magnetic field, in such a way that the total energy momentum tensor is conserved across the transition and Einstein's equations are satisfied. We further solve the evolution equations for the metric and fluid perturbations at large scales analytically including neutrinos, and derive the magnetic Sachs Wolfe effect. We find that the relevant contribution to the magnetic Sachs Wolfe effect comes from the metric perturbations at next-to-leading order in the large scale limit. The leading order term is in fact strongly suppressed due to the presence of free-streaming neutrinos. We derive the neutrino compensation effect dynamically and confirm that the magnetic Sachs Wolfe spectrum from a causal magnetic field behaves as l(l+1) CBl∝l2 as found in the latest numerical analyses.

CMB temperature anisotropy at large scales induced by a causal primordial magnetic field

Abstract: We present an analytical derivation of the Sachs Wolfe effect sourced by a primordial magnetic field. In order to consistently specify the initial conditions, we assume that the magnetic field is generated by a causal process, namely a first order phase transition in the early universe. As for the topological defects case, we apply the general relativistic junction conditions to match the perturbation variables before and after the phase transition which generates the magnetic field, in such a way that the total energy momentum tensor is conserved across the transition and Einstein's equations are satisfied. We further solve the evolution equations for the metric and fluid perturbations at large scales analytically including neutrinos, and derive the magnetic Sachs Wolfe effect. We find that the relevant contribution to the magnetic Sachs Wolfe effect comes from the metric perturbations at next-to-leading order in the large scale limit. The leading order term is in fact strongly suppressed due to the presence of free-streaming neutrinos. We derive the neutrino compensation effect dynamically and confirm that the magnetic Sachs Wolfe spectrum from a causal magnetic field behaves as l(l+1)C_l^B \propto l^2 as found in the latest numerical analyses.

Impact of a causal primordial magnetic field on the Sachs Wolfe Effect

Abstract: We present an analytical derivation of the Sachs Wolfe effect sourced by a primordial magnetic field, generated by a causal process, such as a first order phase transition in the early universe. As for the topological defects case, we apply the general relativistic junction conditions to match the perturbation variables before and after the phase transition, in such a way that the total energy momentum tensor is conserved across the transition. We find that the relevant contribution to the magnetic Sachs Wolfe effect comes from the metric perturbations at next-to-leading order in the large scale limit. The leading order term is strongly suppressed due to the presence of free-streaming neutrinos. We derive the neutrino compensation effect and confirm that the magnetic Sachs Wolfe spectrum from a causal magnetic field behaves as l(l+1)C_l^B ~ l^2 as found in the latest numerical analyses.