Cosmological scaling solutions and multiple exponential potentials

Abstract

We present a phase-space analysis of cosmology containing multiple scalar fields with positive and negative exponential potentials. We show that there exist power-law multi-kineticpotential scaling solutions for sufficiently flat positive potentials or steep negative potentials. The former is the unique late-time attractor and the well-known assisted inflationary solution, but the later is never unstable in an expanding universe. Moreover, for steep negative potentials there exist a kinetic-dominated regime in which each solution is a late-time attractor. We briefly discuss the physical consequences of these results.

De Sitter and scaling solutions in a higher-order modified teleparallel theory

“…That is an analogue of the analysis in [6,[62][63][64] for the canonical scalar field and others [65][66][67][68][69][70].…”

Nonsingular power-law and assisted inflation in loop quantum cosmology

“…In the regime ρ ≪ ρ max , the modified Friedmann and Raychaudhuri equations (2.18,2.20) approximate their classical counterparts (2.13,2.14), and, as expected, solutions in classical theory and LQC 6 These properties also generalize to the case of the multi-field potential with n = i 2/k 2 i (see for eg. [11,12,18]). …”

Cosmological scaling solutions for multiple scalar fields

“…The dark energy dynamics based on the separate exponential potentials characterized by the Lagrangian P = X 1 + X 2 − V 1 e −λ1φ1 − V 2 e −λ2φ2 have been studied in detail in Refs. [23][24][25][26][27]. In such models, i.e., µ 1 = 0 and µ 2 = −λ 2 , the potential V 2 e −λ2φ2 is suppressed relative to the other one V 1 e −λ1φ1 during most of the cosmic expansion history, but the former comes out at late times to drive the accelerated expansion.…”

“…In this model, the dynamics of scaling solutions followed by the assisted dark energy attractor has been studied in Refs. [23][24][25][26][27].…”