Modified Teleparallel Gravity induced by quantum fluctuations

TL;DR

This paper explores how quantum fluctuations in a teleparallel gravity framework induce non-minimal torsion-matter couplings, leading to new cosmological models with late-time acceleration and energy transfer phenomena.

Contribution

It extends semi-classical quantum correction ideas to teleparallel gravity, introducing a new class of $f(T,B, ext{T})$ models with novel cosmological implications.

Findings

Derived a subclass of $f(T,B, ext{T})$ gravity from quantum fluctuations.

Found cosmological solutions with decelerating and accelerating phases.

Showed energy transfer between gravity and matter due to torsion-matter couplings.

Abstract

In the semi-classical regime, quantum fluctuations embedded in a Riemannian spacetime can be effectively recast as classical back reactions and manifest themselves in the form of non-minimal couplings between matter and curvature. In this work, we exhibit that this semi-classical description can also be applied within the teleparallel formulation. In the teleparallel formulation, quantum fluctuations generically lead to non-minimal torsion-matter couplings. Due to the equivalence between the (classical) Einstein gravity in the Riemannian description and that in teleparallel description, some effective models which were constructed using Riemannian description can be reproduced completely using the teleparallel description. Besides, when the effective quantum correction term is proportional to the torsion scalar $T$, we obtain a subclass of novel $f(T,B,\mathcal{T})$ gravity, where $B$ is a boundary term, and $\mathcal{T}$ is the trace of the energy-momentum tensor. Next, we investigate the cosmological properties in this $f(T,B,\mathcal{T})$ theory by assuming that the matter Lagrangian is solely constructed by a dynamical scalar field. We exhibit some interesting cosmological solutions, such as those with decelerating expansion followed by a late-time accelerating phase. In addition, the non-minimal torsion-matter couplings induced by quantum corrections naturally lead to energy transfers between gravity and cosmological fluids in the universe.