Solar System, Astrophysics, and Cosmology from the Derivative Expansion

TL;DR

This paper introduces a unified derivative expansion framework that models the solar system, galaxy, and cosmological scales, accurately capturing key observations at each level within a single theoretical approach.

Contribution

It develops a locally inertial static metric based on Einstein equations and derivative expansion, unifying descriptions of different cosmic scales and their main observational features.

Findings

Accurately models Keplerian physics in the solar system.

Reproduces flat galaxy rotation curves and Baryonic Tully-Fisher relation.

Captures cosmological redshift, acceleration, and matches Robertson-Walker spacetime.

Abstract

In this paper we show how the solar system, the galactic, and the cosmological scales, are accommodated in a single framework, namely, in the derivative expansion framework. We construct a locally inertial static metric, based on the Einstein equations and on the derivative expansion method, which describes a Schwarzschild black hole immersed in dark matter and dark energy. The leading order metric in the expansion corresponds to the solar system, the first order metric to the galaxy, and the second order metric to cosmology. It is shown how this metric captures the main observations at each scale: in the solar system it trivially gives the Keplerian physics, in the galaxy it gives the flat part of the rotation curve and the Baryonic Tully-Fisher relation, and in the cosmological scale it gives the cosmological redshift, the accelerating expansion, and it coincides with the Robertson-Walker spacetime in the appropriate limit and approximation.