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

## TL;DR

This paper derives new analytical and approximate solutions in $F(T)$ teleparallel gravity for cosmological models with Chaplygin and polytropic gases, applicable to various universe expansion scenarios and relevant for dark energy and dark matter studies.

## Contribution

It introduces novel $F(T)$ gravity solutions for flat and curved universes with Chaplygin and polytropic gases, including analytical and approximate forms for different expansion rates.

## Key findings

- Analytical solutions for flat universe case.
- Approximate solutions for curved universe cases.
- Relevance for dark energy and dark matter models.

## 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.