Cosmological frames for theories with absolute parallelism

TL;DR

This paper investigates the challenges of formulating cosmological models with absolute parallelism, focusing on the invariance issues in f(T) and Born-Infeld gravity theories, and highlights the singularity-free, inflationary early universe in Born-Infeld gravity.

Contribution

It clarifies the invariance problems in vierbein formulations of absolute parallelism theories and demonstrates the natural inflationary, singularity-free early universe in Born-Infeld gravity.

Findings

Born-Infeld gravity yields a singularity-free early universe.

Invariance issues hinder the use of vierbein in some theories.

Born-Infeld gravity naturally leads to inflation.

Abstract

The vierbein (tetrad) fields for closed and open Friedmann-Robertson-Walker cosmologies are hard to work out in most of the theories featuring absolute parallelism. The difficulty is traced in the fact that these theories are not invariant under local Lorentz transformations of the vierbein. We illustrate this issue in the framework of f(T) theories and Born-Infeld determinantal gravity. In particular, we show that the early Universe as described by the Born-Infeld scheme is singularity free and naturally inflationary as a consequence of the very nature of Born-Infeld gravitational action.