A new class of f(R)-gravity model with wormhole solutions and cosmological properties

Abstract

Abstract A spherically symmetric wormhole family of solutions, with null red-shift, in the context of f(R)-gravity is presented. The model depends on two parameters: m and $$\beta $$ β and meets all requirements to be an asymptotically and traversable wormhole. To solve the field equations, an EoS is imposed: $$p_{\perp }=-\rho $$ p⊥=-ρ . It is found that for $$m=1$$ m=1 the solution satisfies the null energy condition, although $$F(R)<0$$ F(R)<0 everywhere. For $$m=0$$ m=0 , the model satisfies the null energy condition away from the throat, where the function F(R) is everywhere positive and together with dF(R)/dR vanish at the throat of the wormhole. This fact is beyond the scope of the non-existence theorem. Furthermore, the cosmological viability of the model, to address the late – time accelerated epoch, is analyzed on the background of a flat FLRW space-time. The model satisfies consistency of local gravity tests, stability under cosmological perturbations, ghosts free and stability of the de Sitter point.