Bouncing cosmology, $F(T)$ teleparallel gravity and entropy of apparent horizon

TL;DR

This work investigates a nonsingular bouncing cosmology within $F(T)$ teleparallel gravity using a two-parameter scale factor $a(t)=a_B(1+\alpha t^2)^n$, yielding analytic expressions for the Hubble rate and deceleration parameter that can match the Planck-era value $q_0\approx-0.535$. It derives a first-order differential equation for the $F(T)$ function and presents analytic solutions for special choices of $C=3n(1+w)$, illustrating how the torsion scalar $T$ shapes the bounce. The paper also applies entropic cosmology by computing the apparent-horizon entropy $S_h$ in terms of the incomplete beta function, with tractable closed forms in specific cases and discussion of positivity domains. Together, these results provide a coherent framework in which a bouncing Universe emerges in $F(T)$ gravity and is compatible with horizon thermodynamics and cosmological observations.

Abstract

Two parameters scale factor leading to bouncing cosmology is considered. We show that at some model parameters we obtain the deceleration parameter $q_0\approx -0.535$ at the current epoch which is in agreement with the Planck data. The equation for the transition point when the universe expands from acceleration to deceleration phases is obtained. We find the equation for the function $F(T)$ within the teleparallel gravity with torsion field $T$ which provides bouncing cosmology. For some parameters of the model the function $F(T)$ was computed. At the same time, in the framework of entropic cosmology, the associated entropy was obtained for particular model parameters.

Figures (4)

• Figure 1: The scale factor $a(\bar{t})/a_B$ vs. $\bar{t}$ for $n=1/3,1/2,2/3$. When parameter $n$ increases the scale factor also increases.
• Figure 2: The $\bar{H}$ vs. $\bar{t}$ at $n=1/3,1/2,2/3$.
• Figure 3: The deceleration parameter $q$ vs. reduced time $\bar{t}=\sqrt{\alpha}t$ at $n=1.3,~1/2,~2/3$.
• Figure 4: Reduced entropy $\bar{S}_h=S_h\alpha^2n^3/((1+w)\rho_B)$ vs. reduced time $\bar{t}=t\sqrt{\alpha}$ for $C=1,~2$.