Peculiar velocity fields from analytic solutions of General Relativity

TL;DR

This paper explores how analytic solutions of Einstein's equations can model complex peculiar velocity fields in cosmology, providing a new physically motivated framework that aligns with observational data like the CMB dipole.

Contribution

It introduces a novel approach using Lorentzian boosts of Einstein's solutions to generate realistic peculiar velocity fields in an Eulerian frame.

Findings

Generated peculiar velocities are compatible with CMB dipole observations.

Analytic solutions can model time and space varying velocity fields.

Provides a physically viable interpretation of Einstein's solutions without isometries.

Abstract

Peculiar velocities are analyzed through cosmological perturbations in the Newtonian longitudinal gauge characterized by irrotational shear-free congruences in an Eulerian frame. We show that non-trivial peculiar velocity fields can be generated through Lorentzian boosts in the non-relativistic limit, where the Eulerian frame is obtained from analytic solutions of Einstein's equations sourced by an irrotational shear-free fluid with nonzero energy flux. This approach provides a physically viable interpretation of these analytic solutions, which (in general) admit no isometries, thus allowing, in principle, for modeling time and space varying 3-dimensional fields of peculiar velocities that can be contrasted with observational data on our local cosmography. As a ``proof of concept'' we examine the peculiar velocities of varying dark matter and dark energy perfect fluids with respect to the CMB frame using a simple, spherically symmetric particular solution. The resulting peculiar velocities are qualitatively compatible with observational data on the CMB dipole.