A bridge between unified cosmic history by f(R)-gravity and BIonic system

Abstract

Recently, the cosmological deceleration-acceleration transition redshift in f(R) gravity has been considered in order to address consistently the problem of cosmic evolution. It is possible to show that the deceleration parameter changes sign at a given redshift according to observational data. Furthermore, a f(R) gravity cosmological model can be constructed in brane-antibrane system starting from the very early universe and accounting for the cosmological redshift at all phases of cosmic history, from inflation to late time acceleration. Here we propose a f(R) model where transition redshifts correspond to inflation-deceleration and deceleration-late time acceleration transitions starting froma BIon system. At the point where the universe was born, due to the transition of k black fundamental strings to the BIon configuration, the redshift is approximately infinity and decreases with reducing temperature $(z\sim T^{2})$. The BIon is a configuration in flat space of a universe-brane and a parallel anti-universe-brane connected by a wormhole. This wormhole is a channel for flowing energy from extra dimensions into our universe, occurring at inflation and decreasing with redshift as $z\sim T^{4+1/7}$. Dynamics consists with the fact that the wormhole misses its energy and vanishes as soon as inflation ends and deceleration begins. Approaching two universe branes together, a tachyon is originated, it grows up and causes the formation of a wormhole. We show that, in the framework of f(R) gravity, the cosmological redshift depends on the tachyonic potential and has a significant decrease at deceleration-late time acceleration transition point $(z\sim T^{2/3})$. As soon as today acceleration approaches, the redshift tends to zero and the cosmological model reduces to the standard $\Lambda$CDM cosmology.