Abstract
We investigate the future evolution of the dark energy universe in modified gravities, includingF(R) gravity, and string-inspired scalar Gauss–Bonnet and modified Gauss–Bonnet ones,and ideal fluid with an inhomogeneous equation of state (EoS). The modifiedFriedmann–Robertson–Walker dynamics for all of these theories may be presented in auniversal form by using the effective ideal fluid with an inhomogeneous EoS withoutspecifying its explicit form. We construct several examples of a modified gravity whichproduces accelerating cosmologies ending at the finite-time future singularities ofall four known types by applying a reconstruction program. Some scenarios forresolving a finite-time future singularity are presented. Among these scenarios,the most natural one is related to additional modification of the gravitationalaction in the early universe. In addition, late-time cosmology in the non-minimalMaxwell–Einstein theory is considered. We investigate the forms of non-minimalgravitational coupling which generate finite-time future singularities and the generalconditions for this coupling such that the finite-time future singularities cannot emerge.Furthermore, it is shown that the non-minimal gravitational coupling can remove thefinite-time future singularities or make the singularity stronger (or weaker) in modifiedgravity.
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