Scalar field cosmology modified by the generalized uncertainty principle

Abstract

We consider quintessence scalar field cosmology in which the Lagrangian of the scalar field is modified by the Generalized Uncertainty Principle. We show that the perturbation terms which arise from the deformed algebra are equivalent with the existence of a second scalar field, where the two fields interact in the kinetic part. Moreover, we consider a spatially flat Friedmann-Lemaître-Robertson-Walker spacetime (FLRW), and we derive the gravitational field equations. We show that the modified equation of state parameter wGUP can cross the phantom divide line; that is wGUP < −1. Furthermore, we derive the field equations in the dimensionless parameters, the dynamical system which arises is a singular perturbation system in which we study the existence of the fixed points in the slow manifold. Finally, we perform numerical simulations for some well known models and we show that for these models with the specific initial conditions, the parameter wGUP crosses the phantom barrier. 95.35.+d, 95.36.+x, 11.10.Ef

Cosmological evolution and exact solutions in a fourth-order theory of gravity

“…Recall that now the partial differential equation (13) has been reduced to the Clairaut first-order differential equation…”

“…As dark energy is characterized as the matter source which provides the missing terms in the field equations of Einstein's General Relativity and which leads to solutions that describe the accelerating expansion of the universe. The proposed solutions for the nature of dark energy can be categorized into two big classes: (i) the dark energy models where an energy momentum tensor, which describes an exotic matter source [5][6][7][8][9][10][11][12][13], is introduced into Einstein's General Relativity and/or (ii) the Einstein-Hilbert action is modified such that the new field equations provide additional terms which are assumed to contribute to the acceleration of the universe; for instance see [14][15][16][17][18][19][20][21][22][23][24][25][26][27]. In the second approach, the dark energy has a geometrical origin and description [28].…”

Constraints on quintessence scalar field models using cosmological observations

“…We note that the canonical scalar field models are more informative compared to the non-canonical scalar field models. The physics of canonical scalar field models, which is mostly contained in the potential, V (φ(t)) where φ(t) is the underlying field, have gained a considerable interest in the cosmological community due to explaining various stages of the universe evolution, see [30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57] (also see [58,59,60,61,62]). The selection of quintessence scalar field models should not be much arbitrary, according to recently introduced swampland [63,64] and refined swampland [65] criteria.…”

The past and future dynamics of quintom dark energy models

“…Furthermore, interacting quintom in nonminimal coupling has been studied in [59], and quintom with nonminimal derivative coupling was studied in [60]. An extension of the quintom scenario, in which the scalar fields are coupled through a kinetic interaction, have been studied in [61,62] while an interacting quintom model was recently constructed by the application of the generalized uncertainty principle (GUP) in the scalar field Lagrangian [63]. In particular, the second scalar field of the quintom model in [63] corresponds to higher-order derivatives given by the GUP.…”

“…An extension of the quintom scenario, in which the scalar fields are coupled through a kinetic interaction, have been studied in [61,62] while an interacting quintom model was recently constructed by the application of the generalized uncertainty principle (GUP) in the scalar field Lagrangian [63]. In particular, the second scalar field of the quintom model in [63] corresponds to higher-order derivatives given by the GUP. Furthermore, one of the particularly exciting solutions of quintom type models is that they can provide a classically stable bouncing solution.…”