Nonsingular 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 an equation of state P=-ρ-f(ρ), for different teleparallel theories and different equation of state 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⇔f(ρ)=-ρ) which means there are de Sitter and anti-de Sitter solutions. In both cases one obtains a nonsingular 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.