The remarkable properties of the recently proposed geodesic light-cone (GLC) gauge allow to explicitly solve the geodesic-deviation equation, and thus to derive an exact expression for the Jacobi map J A B (s, o) connecting a generic source s to a geodesic observer o in a generic space time. In this gauge J A B factorizes into the product of a local quantity at s times one at o, implying similarly factorized expressions for the area and luminosity distance. In any other coordinate system J A B is simply given by expressing the GLC quantities in terms of the corresponding ones in the new coordinates. This is explicitly done, at first and second order, respectively, for the synchronous and Poisson gauge-fixing of a perturbed, spatially-flat cosmological background, and the consistency of the two outcomes is checked. Our results slightly amend previous calculations of the luminosity-redshift relation and suggest a possible non-perturbative way for computing the effects of inhomogeneities on observations based on light-like signals.

Abstract. We investigate the weak lensing corrections to the cosmic microwave background temperature anisotropies considering effects beyond the Born approximation. To this aim, we use the small deflection angle approximation, to connect the lensed and unlensed power spectra, via expressions for the deflection angles up to third order in the gravitational potential. While the small deflection angle approximation has the drawback to be reliable only for multipoles 2500, it allows us to consistently take into account the non-Gaussian nature of cosmological perturbation theory beyond the linear level. The contribution to the lensed temperature power spectrum coming from the non-Gaussian nature of the deflection angle at higher order is a new effect which has not been taken into account in the literature so far. It turns out to be the leading contribution among the post-Born lensing corrections. On the other hand, the effect is smaller than corrections coming from non-linearities in the matter power spectrum, and its imprint on CMB lensing is too small to be seen in present experiments.

No abstract