Dynamics and cosmological evolution in $$\Lambda $$-varying cosmology

Abstract

We study the dynamical properties of a large body of varying vacuum cosmologies for which dark matter interacts with vacuum. In particular, performing the critical point analysis we investigate the existence and the stability of cosmological solutions which describe de-Sitter, radiation and matter dominated eras. We find several cases of varying vacuum models that admit stable critical points, hence they can be used in describing the cosmic history. 95.35.+d, 95.36.+x

Dynamics in varying vacuum Finsler–Randers cosmology

“…Models Q A , Q B and Q C have been studied in a previous work in the case of GR [130]. In this work we recover the results of the previous study, that is, the limit of GR relativity is recovered, while there exists one possible era in the cosmological history which corresponds to the epoch where only the geometrodynamical term of the FR geometry contributes.…”

“…Following our previous works [130,131] we study how the implementation of the Finsler geometry affects the varying vacuum scenarios studied in GR as well as how the implementation of the varying vacuum responds in a Finsler Randers scenario.…”

“…Thus for a healthy theory to be viable, the critical point analysis should provide points where the universe will be accelerating and also these points to be stable. This analysis has been applied in various cosmological models, for instance see and references therein [130,131,[135][136][137][138][139][140][141][142][143][144][145][146][147] .…”

“…In this work we study various functional forms for the interaction term Q. In order to extend the results of [130], we assume that (A) the interaction term Q is proportional to the density of dark matter [102], that is, Q A = 9n Hρ m or equivalent Q A 9n H 3 m , where the dimensionless parameter n is an indicator of the interaction strength; (B) Q is proportional to the density of the dark energy term, i.e. Q B = 9n H 3 ρ [99,103]; (C) Q C is proportional to the sum of the energy density of the dark sector of the universe, that gives Q C = 9n H(ρ + ρ m ).…”

“…Motivated by the above functional forms Q, which have given interesting results in General Relativity, [130], we propose some new interaction terms which are proportional to the energy density z . In particular we select the models (D)…”