Future singularities and Teleparallelism in Loop Quantum Cosmology

TL;DR

This paper explores how loop quantum cosmology (LQC) modifies the Friedmann equation to avoid certain future singularities like the Big Rip, investigates the fate of other singularities, and extends the analysis to modified teleparallel gravity.

Contribution

It demonstrates the avoidance of Big Rip and Little Rip singularities in LQC and extends the framework to $F(T)$ gravity and other modified theories.

Findings

Holonomy corrections prevent the Big Rip singularity.

Little Rip cosmology does not occur in LQC.

Pseudo-Rip cosmology persists but with delayed disintegration of structures.

Abstract

We demonstrate how holonomy corrections in loop quantum cosmology (LQC) prevent the Big Rip singularity by introducing a quadratic modification in terms of the energy density $\rho$ in the Friedmann equation in the Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) space-time in a consistent and useful way. In addition, we investigate whether other kind of singularities like Type II,III and IV singularities survive or are avoided in LQC when the universe is filled by a barotropic fluid with the state equation $P=-\rho-f(\rho)$, where $P$ is the pressure and $f(\rho)$ a function of $\rho$. It is shown that the Little Rip cosmology does not happen in LQC. Nevertheless, the occurrence of the Pseudo-Rip cosmology, in which the phantom universe approaches the de Sitter one asymptotically, is established, and the corresponding example is presented. It is interesting that the disintegration of bound structures in the Pseudo-Rip cosmology in LQC always takes more time than that in Einstein cosmology. Our investigation on future singularities is generalized to that in modified teleparallel gravity, where LQC and Brane Cosmology in the Randall-Sundrum scenario are the best examples. It is remarkable that $F(T)$ gravity may lead to all the kinds of future singularities including Little Rip.