On perfect fluid models in non-comoving observational spherical coordinates

TL;DR

This paper develops inhomogeneous cosmological models using null spherical coordinates, allowing analysis in a non-comoving frame and revealing that dust models are incompatible with these coordinates.

Contribution

It introduces a new approach to inhomogeneous cosmological models using null coordinates, enabling non-comoving analysis and addressing integrability issues of null geodesics.

Findings

Null coordinates simplify null geodesic integration.

Non-comoving frames reveal shear, acceleration, and expansion.

Dust models are incompatible with the proposed coordinates.

Abstract

We use null spherical (observational) coordinates to describe a class of inhomogeneous cosmological models. The proposed cosmological construction is based on the observer past null cone. A known difficulty in using inhomogeneous models is that the null geodesic equation is not integrable in general. Our choice of null coordinates solves the radial ingoing null geodesic by construction. Furthermore, we use an approach where the velocity field is uniquely calculated from the metric rather than put in by hand. Conveniently, this allows us to explore models in a non-comoving frame of reference. In this frame, we find that the velocity field has shear, acceleration and expansion rate in general. We show that a comoving frame is not compatible with expanding perfect fluid models in the coordinates proposed and dust models are simply not possible. We describe the models in a non-comoving frame. We use the dust models in a non-comoving frame to outline a fitting procedure.