Nonlocal modified Einstein’s field equation and geometric origin of a small cosmological constant

Abstract

We show that the description of the spacetime in terms of backward-forward extension of its corresponding metric leads to the geometric origin of a small cosmological constant. The nonlocal cosmological constant appears in the Einstein’s field equation and its mathematical expression depends on the nonlocal metric, Ricci scalar and the infinitesimal nonlocal parameter introduced in the theory. The modified theory has interesting consequences in FRW cosmology, mainly a nonsingular universe, the occurrence of a late-time accelerated expansion of the universe and an early universe dominated by a negative energy density and a positive pressure. Our model can explain the acceleration of the universe without a fine-tuned cosmological constant $\Lambda$ .