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Non-singular models of universes in teleparallel theories

Different models of universes are considered in the context of teleparallel theories. Assuming that the universe is filled by a fluid with equation of state (EoS) $P=-ρ-f(ρ)$, for different teleparallel theories and different EoS we study its dynamics. Two particular cases are studied in detail: in the first one we consider a function $f$ with two zeros (two de Sitter solutions) that mimics a huge cosmological constant at early times and a pressureless fluid at late times. In the second one, in the context of loop quantum cosmology with a small cosmological constant, we consider a pressureless fluid ($P=0\Leftrightarrow f(ρ)=-ρ$) which means that there are a de Sitter and an anti de Sitter solution. In both cases one obtains a non-singular universe that at early times is in an inflationary phase, after leaving this phase it passes trough a matter dominated phase and finally at late times it expands in an accelerated way.