A Light-Cone Approach to Higher-Order Cosmological Observables

TL;DR

This paper develops a second-order light-cone perturbation theory for cosmology, enabling precise calculations of observables like luminosity distance, and clarifies gauge issues in a fully gauge-invariant framework.

Contribution

It introduces a novel second-order light-cone perturbation formalism and connects it with standard gauge choices, improving the analysis of cosmological observables.

Findings

Derived second-order luminosity distance-redshift relation with anisotropic stress.

Established gauge fixing corresponding to the Observational Synchronous Gauge.

Showed divergences at the observer position can be eliminated in a model-independent way.

Abstract

We develop a second-order cosmological perturbation theory on a background geometry expressed in terms of light-cone coordinates, extending the first-order analyses available in the literature. In particular, we investigate the gauge transformations of second-order perturbative quantities on the light-cone and establish their connection with standard perturbation theory. Through a consistent matching procedure, we identify the second-order gauge fixing that corresponds to the non-linear Geodesic Light-Cone gauge within standard perturbation theory, known as the Observational Synchronous Gauge. We then emphasize its conceptual similarities and differences wrt the standard Synchronous Gauge. Finally, within this new perturbative framework, and adopting a fully gauge-invariant approach, we compute the luminosity distance-redshift relation up to second order with anisotropic stress as seen by a free-falling observer. Remarkably, we show how divergences at the observer position can be eliminated in a completely model independent way. These results validate our perturbative framework and establish it as a novel formalism for evaluating cosmological observables at second order.