Modified Friedmann equations from DSR-GUP

Abstract

Considering the modified entropy-area relation from DSR-GUP (Doubly special relativity-Generalized uncertainity principle), we obtain the modified Friedmann equations from the first law of thermodynamics at apparent horizon. Due to the importance of GUP at Planck scale, we investigate the Friedmann equations and show the maximum energy density ρ at Planck scale. Since GUP implies a minimal length, we find a minimum apparent horizon which has a potential to remove the Big Bang singularity. Furthermore, we analyse the effects of DSR-GUP on deceleration parameter q for the equation of state p = ωρ and the flat case. Finally, we check the validity of the generalized second law (GSL) of thermodynamics and show that it is valid for all eras of the universe for any spatial curvature. 1 We use the unitsh = c = G N = l 2 P l = 1 2 We recall that the extended gravity framework arises from the necessity to extend standard general relativity in order to attempt to achieve the famous Dark Energy and Dark Matter problems [26]. In this framework, the recent starting of the gravitational wave astronomy with the famous detections of LIGO [27] could be, in principle, decisive to confirm the physical consistence of standard general relativity, or, alternatively, to endorse the framework of extended theories of gravity [28]. In fact, some differences between general relativity and alternative theories can be pointed out in the linearized theory of gravity through different interferometer response functions [28].

Quantum Cosmology with Dynamical Vacuum in a Minimal-Length Scenario

“…It is no possible to solve Eq. ( 55) analytically since we do not know all initial or boundary conditions 13 , that is, ϕ (N ) (x 0 ), for N = 0, 1, ..., 5. A way to get around this problem is considering x small.…”

“…12 From now on, for the sake of simplicity we are going to omit the subscript ω. 13 In Ref. [2] the author has solved a modified Wheeler-DeWitt equation of forth order d 4 dx 4…”

Quantum cosmology with dynamical vacuum in a minimal-length scenario

“…Thus, an effective description of the effects of quantum gravity through a phenomenological approach can be obtained by considering a minimal-length scenario [1][2][3][4]. Some results in the literature indicate that the introduction of a minimal length could also solve the problems like the initial singularity (big bang singularity) [5][6][7][8][9][10][11][12][13], the black hole complete evaporation (catastrophic evaporation of a black hole) [3,[14][15][16][17][18], the cosmological constant [12,[19][20][21], the Chandrasekhar limit [4,18,20], the instability of the Einstein static universe (emergent universe) [22], the vanishing of cosmological constant in multiverse theories [19], and so on.…”

“…In the same way as in[63] we hope that the cosmological constant arises from the degrees of freedom of the vacuum and not being postulated from the start as a geometric term. Note also that if from the start Λ > 0 we can always redefine ω as ω := ω + 2Λ 13. From now on, for the sake of simplicity we are going to omit the subscript ω 14.…”

Observational Tests of the Generalized Uncertainty Principle: Shapiro Time Delay, Gravitational Redshift, and Geodetic Precession

“…Since GUP introduces quantum gravity effects, modification of black hole thermodynamics may be necessary near the Planck scale . Moreover, GUP can be considered for various problems such as cosmological applications [38][39][40], particle accelerators [41][42][43] and density of states applications [44][45][46][47], etc 1 .…”