Scalar-tensor quintessence with a linear potential: Avoiding the big crunch cosmic doomsday

Abstract

All quintessence potentials that are either monotonic with negative interval or have a minimum at negative values of the potential, generically predict a future collapse of the scale factor to a "doomsday" singularity. We show that this doomsday is generically avoided in models with a proper non-minimal coupling of the quintessence scalar field to the curvature scalar R. For simplicity we consider linear quintessence potential V = −sφ and linear non-minimal coupling F = 1 − λφ. However our result is generic and is due to the fact that the non-minimal coupling modifies the effective potential that determines the dynamics of the scalar field. Thus for each positive value of the parameter s we find a critical value λcrit(s) such that for λ > λcrit(s) the negative potential energy does not dominate the universe and the cosmic doomsday Big Crunch singularity is avoided because the scalar field eventually rolls up its potential. We find that λcrit(s) increases approximately linearly with s. For λ > λcrit(s) the potential energy of the scalar field becomes positive and it eventually dominates while the dark energy equation of state parameter tends to w = −1 leading to a deSitter Universe.PACS numbers: 98.80. Es,98.65.Dx,98.62.Sb

Sudden future singularities in quintessence and scalar-tensor quintessence models

“…Some of these dark energy models predict the existence of exotic cosmological singularities, involving divergences of the scalar spacetime curvature and/or its derivatives. These singularities can be either geodesically complete [14][15][16][17] (geodesics continue beyond the singularity and the Universe may remain in existence) or geodesically incomplete [18] (geodesics do not continue beyond the singularity and the Universe ends at * alymperis@upatras.gr † leandros@uoi.gr ‡ magda@physics.upatras.gr the classical level). They appear in various physical theories such as superstrings [19], scalar field quintessence with negative potentials [20], modified gravities and others [17,21,22].…”

“…modified gravity [23], quantum effects [24]), has been shown to eliminate or weaken both geodesically complete and incomplete singularities [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44]. Geodesically incomplete singularities include the Big-Bang [45], the Big-Rip [46,47] where the scale factor diverges at a finite time due to infinite repulsive forces of phantom dark energy, the Little-Rip [48] and the Pseudo-Rip [49] singularities where the scale factor diverges at a infinite time and the Big-Crunch [16,17,20,[50][51][52] where the scale factor vanishes due to the strong attractive gravity of future envolved dark energy, as e.g. in quintessence models with negative potential.…”

Fate of bound systems through sudden future singularities

“…A variety of extensions of ΛCDM predict the existence (mostly in the future) of a wide range of singularities [30][31][32][33]. These singularities can be either geodesically incomplete (eg [34][35][36][37]) (geodesics do not continue beyond the singularity and the universe ends at the classical level) or geodesically complete [33] (geodesics continue beyond the 1 on leave from the Department of Physics, University of Ioannina, 45110 Ioannina, Greece * leandros@uoi.gr singularity and the universe may remain in existence).…”

Generalised teleparallel quintom dark energy non-minimally coupled with the scalar torsion and a boundary term

“…In this section we shall analyse the behavior of the present generalised quintom model in the teleparallel gravity theory by adopting a numerical approach previously considered by Perivolaropoulos in scalar tensor theories [69,70], and recently applied to a quintom scenario [34]. The present numerical approach enables us to analyse the effects of the scalar torsion and boundary coupling in the evolution of the corresponding quintom fields.…”