Late time evolution of negatively curved FLRW models

Abstract

We study the late time evolution of negatively curved Friedmann-Lemaître-Robertson-Walker (FLRW) models with a perfect fluid matter source and a scalar field nonminimally coupled to matter. Since, under mild assumptions on the potential V , it is already known -see e.g.[18] -that equilibria corresponding to non-negative local minima for V are asymptotically stable, we classify all cases where one of the energy components eventually dominates. In particular for nondegenerate minima with zero critical value, we rigorously prove that if γ, the parameter of the equation of state is larger than 2/3, then there is a transfer of energy from the fluid and the scalar field to the energy density of the scalar curvature. Thus, the scalar curvature, if present, has * roberto.giambo@unicam.it † imyr@aegean.gr ‡ annagiulia.pezzola@studenti.unicam.it, a.pezzola1@unimc.it 1 arXiv:1905.01742v3 [gr-qc]

Averaging generalized scalar-field cosmologies III: Kantowski–Sachs and closed Friedmann–Lemaître–Robertson–Walker models

“…The only equilibrium point that remains a sink for KS for 0 ≤ γ < 2 3 in the extended phase space is P 6 . Figures 13,14,15,16,17,18,19, and 20 are a numerical confirmation that main Theorem 1 presented in Sect. 4 is fulfilled for the KS metric.…”

“…Figures 19 and 20 show solutions for a fluid corresponding to stiff fluid (γ = 2). Figures 13,14,15,16,17,18,19, and 20 are a numerical confirmation that main theorem 1 presented in Sect. 4 is fulfilled for the KS metric.…”

“…In Figs. 13,14,15,16,17,18,19, and 20 projections of some solutions of the full system (93) and time-averaged system (127) in the (Σ, D/(1 + D), 2 ) and (Q, D/(1 + D), 2 ) space are presented with their respective projections when D = 0. Figures 13 and 14 show solutions for a fluid corresponding to CC (γ = 0).…”

Averaging generalized scalar field cosmologies I: locally rotationally symmetric Bianchi III and open Friedmann–Lemaître–Robertson–Walker models

“…For FLRW metrics, global minimum is unstable to curvature perturbations for γ > 2 3 . Therefore, the result in [107] is confirmed, that for γ > 2 3 the curvature has a dominant effect on late evolution of the universe and it will eventually dominate both perfect fluid and scalar field energy densities. For Bianchi I model, the global minimum with V (0) = 0 is unstable to shear perturbations.…”

“…Seven initial data sets for simulation of full system (71) and time-averaged system(107). All the conditions are chosen in order to fulfill equalityΩ2 (0) +Ω k (0) +Ω m (0) = 1 Sol.…”