Particle creation in flat FRW Universe in the framework of $f(T)$ gravity

TL;DR

This paper investigates particle creation in a flat FRW universe within $f(T)$ gravity, revealing the role of torsion scalar in particle production and its equivalence to $f(R)$ gravity under minimal coupling.

Contribution

It demonstrates the equivalence between $f(T)$ and $f(R)$ gravity regarding massless particle production in the minimally coupled case, especially during the phantom phase.

Findings

Vacuum state corresponds to vanishing torsion scalar.

Particle production increases as torsion scalar diverges.

Equivalence between $f(T)$ and $f(R)$) gravity holds under minimal coupling.

Abstract

We study particle production aspect in the flat FRW universe in the framework of $f(T)$ gravity. The matter is minimally coupled with the gravity and an exact power-law solution is obtained by solving the Friedmann equations, and matter is assumed to be minimally coupled with gravitation. The torsion scalar $T$ appears to plays the same role as the the curvature (Ricci scalar) in the the General Relativity (GR) and its modified theories $f(R)$. Specially in phantom phase, we observe that the vacuum state corresponds to a vanishing torsion scalar and particle production becomes important as the torsion scalar diverges. This aspect, not only provides the equivalence between the teleparallel gravity and the GR, but also between their respective modified versions, f(T) and f(R), in the view of massless particle production phenomenon when the matter is minimally coupled with the gravity. However, when the gravitational and scalar fields are not minimally coupled, it appears that this similarity between the teleparallel and GR may break down, due to the fact that the torsion scalar has no longer the same time dependent expression as the Ricci scalar.