Chaplygin and Polytropic Gases Teleparallel Robertson-Walker F(T) Gravity Solutions

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=±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.