Chaplygin and Polytropic gases Teleparallel Robertson-Walker $F(T)$ gravity solutions

TL;DR

This work develops teleparallel $F(T)$ gravity in a Robertson--Walker cosmology with Chaplygin and general polytropic gas sources. It derives the symmetric field equations, adopts TRW geometry, and analyzes flat ($k=0$) and curved ($k=\pm1$) sectors to obtain analytical hypergeometric solutions for $k=0$ and approximated double power-law solutions for $k=\pm1$. For Chaplygin gas, the flat case yields a closed form $F(T)$ involving $_2F_1$ functions, while curved cases give power-law forms with roots $r_{\pm}$; for polytropes, $F(T)$ is expressed via an integral $I_p(T)$ that reduces to hypergeometric functions for $p\ge0$. The results provide a framework for quartessence cosmologies in teleparallel gravity and set the stage for future data-driven comparisons (e.g., DESI, BAO, $H(z)$) to constrain the non-flat and non-linear gas parameters and assess the potential role of AdS/quartessence dynamics.

Abstract

This paper investigates the Teleparallel Robertson-Walker (TRW) $F(T)$ gravity solutions for a Chaplygin gas, and then for any polytropic gas cosmological source. We use the TRW $F(T)$ gravity field equations (FEs) for each $k$-parameter value case and the relevant gas equation of state (EoS) to find the new teleparallel $F(T)$ solutions. For flat $k=0$ cosmological case, we find analytical solutions valid for any cosmological scale factor. For curved $k=\pm 1$ cosmological cases, we find new approximated teleparallel $F(T)$ solutions for slow, linear, fast and very fast universe expansion cases summarizing by a double power-law function. All the new solutions will be relevant for future cosmological applications on dark matter, dark energy (DE) quintessence, phantom energy, Anti-deSitter (AdS) spacetimes and several other cosmological processes.

Figures (1)

• Figure 1: Plot of flat cosmological $k=0$ teleparallel $F(T)$ solutions for Chaplygin and polytropic cosmological gas sources (top left: $n=\frac{1}{2}$ and any $p$, top right: Chaplygin, bottom left: $p\,\rightarrow\,0$ limit, bottom right: $p=3$).