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

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.

💡 Research Summary

The paper investigates a simple two‑parameter bouncing cosmology within the framework of teleparallel F(T) gravity and entropic cosmology. The authors adopt a scale factor of the form
 a(t)=a_B (1+α t²)ⁿ,
where α>0 controls the duration of the bounce and n is a dimensionless exponent governing how sharply the universe contracts and expands. This ansatz yields a non‑singular bounce at t=0 with Hubble parameter H(t)=2α n t/(1+α t²) and Ḣ>0 throughout the transition, guaranteeing a smooth passage from contraction (H<0) to expansion (H>0).

From the definition of the deceleration parameter q=−1−Ḣ/H² they obtain an analytic expression
 q(t)=((1−2n)α t²−1)/(2n α t²).
For n<½ the model exhibits a phase of acceleration (q<0) followed by deceleration (q>0). The transition time when q=0 is found to be
 t_tr = 1/