General Parallel Cosmology

TL;DR

This paper derives a unique homogeneous and isotropic solution in General Parallel Cosmology, a relativistic extension of Einstein's gravity, highlighting novel features and unifying previous cosmological models.

Contribution

It provides a first-principles derivation of cosmological solutions in G$_\parallel$R, establishing their uniqueness and contrasting with incomplete theories.

Findings

Unified derivation of cosmological solutions in G$_\parallel$R

Identification of novel features in the cosmological background

Contrast with incomplete geometrical theories

Abstract

General (tele)parallel Relativity, G$_\parallel$R, is the relativistic completion of Einstein's theories of gravity. The focus of this article is the derivation of the homogeneous and isotropic solution in G$_\parallel$R. The first-principles derivation, based on a non-trivial realisation of the symmetry, supersedes and unifies previous constructions of Riemannian and teleparallel cosmologies, and establishes the uniqueness of the physical solution. The constitutive law and the form of the material and inertial source currents is presented in the tensor (Palatini) formalism and adapted to the cosmological background, which exhibits novel features absent in the previously studied, static solutions to the theory. The results are contrasted with those in some incomplete theories, such as sitting at the three corners of the geometrical trinity and corresponding to particular reference frames in G$_\parallel$R.