Effective $F(T)$ gravity from the higher-dimensional Kaluza-Klein and Randall-Sundrum theories

TL;DR

This paper derives four-dimensional $F(T)$ gravity models from higher-dimensional theories like Kaluza-Klein and Randall-Sundrum, showing they can explain inflation and dark energy through torsion effects alone.

Contribution

It presents a novel derivation of $F(T)$ gravity from higher-dimensional theories and demonstrates their cosmological implications without curvature effects.

Findings

Realization of inflation via KK-derived $F(T)$ gravity.

Dark energy dominated stage from RS model with $F(T)$ contributions.

Effective four-dimensional $F(T)$ gravity coupled to scalar fields.

Abstract

We explore the four-dimensional effective $F(T)$ gravity with $T$ the torsion scalar in teleparallelism originating from higher-dimensional space-time theories, in particular the Kaluza-Klein (KK) and Randall-Sundrum (RS) theories. First, through the KK dimensional reduction from the five-dimensional space-time, we obtain the four-dimensional effective theory of $F(T)$ gravity with its coupling to a scalar field. Second, taking the RS type-II model in which there exist the five-dimensional Anti-de Sitter (AdS) space-time with four-dimensional Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) brane, we find that there will appear the contribution of $F(T)$ gravity on the four-dimensional FLRW brane. It is demonstrated that inflation and the dark energy dominated stage can be realized in the KK and RS models, respectively, due to the effect of only the torsion in teleparallelism without that of the curvature.