Mimetic f(T) Teleparallel gravity and cosmology

TL;DR

This paper develops a mimetic extension of f(T) teleparallel gravity, showing it can mimic dark matter and reproduce key cosmological eras through dynamical analysis.

Contribution

It introduces a novel mimetic f(T) gravity formulation that does not require an auxiliary metric and analyzes its cosmological implications.

Findings

Identifies five fixed points corresponding to different cosmological eras.

Demonstrates the dynamical behavior of mimetic dark matter in f(T) gravity.

Analyzes power-law models and their phase trajectories.

Abstract

We formulate mimetic theory in f(T) teleparallel gravity where T is torsion scalar. It is shown that the construction of the mimetic theory in the teleparallel gravity requires the vierbeins to be left unchanged and the confomal transformation performed on the Minkowski metric of the tangent space. It is further argued that the conformal degree of freedom in this teleparallel mimetic theory becomes dynamical and mimics the behavior of cold dark matter. We also show that it is possible to employ the Lagrange multipliers method to formulate the mimetic theory in an f(T) theory without any auxiliary metric. The mimetic f(T) theory is examined by the method of dynamical system and it is found that there are five fixed points representing inflation, radiation, matter, mimetic dark matter and dark energy dominated eras in the theory if some conditions are satisfied. We examined the power-law model and its phase trajectories with these conditions.