Vacuum solution of a linear red-shift based correction in f (R) gravity

Abstract

In this paper we have considered a red-shift based linear correction in derivative of action in the context of vacuum f (R) gravity. Here we have found out that the linear correction may describe the late time acceleration which is appeared by SuperNovae Ia with no need of dark energy. Also we have calculated the asymptotic action for the desired correction. The value of all solutions may reduce to de' Sitter universe in the absence of correction term.

Dark Energy Constraints on Red-Shift-Based Gravity

“…Now we may solve Hubble parameter that depends on the definition of ( ) [63,64,73]. In this paper we consider ( ) as a linear function of :…”

“…For the case of our obtained action from (15), we have ( = 0 ) = 0 /2 + when = 0. Since we would like to have the same solution for de'Sitter model and our obtained action in present of = 0 we force constant of integration, , to be equal to zero [73]. One of main late time cosmological constraint which is tested for redshift-based correction of ( ) gravity is SNeIa distance module with respect to redshift constraint.…”

“…One of main late time cosmological constraint which is tested for redshift-based correction of ( ) gravity is SNeIa distance module with respect to redshift constraint. The result of this comparison is shown in Figure 3 [73].…”

“…Vacuum solutions of ( ) gravity theories is one of interesting subjects which are obtained for constant Ricci scalar [66][67][68][69][70][71][72], allowing derivation of non constant curvature scalar vacuum solutions. In this paper, following our other work [73], we have considered vacuum solutions of ( ) gravity in a different way which does not assume constant scalar curvature to obtain vacuum solutions.…”

“…Then we have tried to reconstruct an appropriate action for the modified gravity through the semi-inverse solution method. We do not assume any FRW cosmology to reconstruct its related ( ) action [63][64][65][66][67][68][69][70][71][72][73][74][75][76][77][78][79][80][81]. Indeed, as curvature scalar itself is a function of red-shift, by introducing a linear correction which is also a function of , we can reconstruct Taylor expansion of ( ) action around present time value of red-shift ( = 0).…”