Dynamical System Analysis of Cosmologies with Running Cosmological Constant from Quantum Einstein Gravity

We discuss a mechanism that induces a time-dependent vacuum energy on cosmological scales. It is based on the instability induced renormalization triggered by the low energy quantum fluctuations in a Universe with a positive cosmological constant. We employ the dynamical systems approach to study the qualitative behavior of Friedmann-Robertson-Walker cosmologies where the cosmological constant is dynamically evolving according with this nonperturbative scaling at low energies. It will be shown that it is possible to realize a "two regimes" dark energy phases, where an unstable early phase of power-law evolution of the scale factor is followed by an accelerated expansion era at late times.Comment: 26 pages, 4 figures. To appear in New Journal of Physic

Consequences of energy conservation violation: Late time solutions of Λ(T)CDM\Lambda(T) CDM subclass of f(R,T)f(R,T) gravity using dynamical system approach

Very recently, the authors of [PRL {\bf 118} (2017) 021102] have shown that violation of energy-momentum tensor (EMT) could result in an accelerated expansion state via appearing an effective cosmological constant, in the context of unimodular gravity. Inspired by this outcome, in this paper we investigate cosmological consequences of violation of the EMT conservation in a particular class of $f(R,T)$ gravity when only the pressure-less fluid is present. In this respect, we focus on the late time solutions of models of the type $f(R,T)=R+\beta \Lambda(-T)$. As the first task, we study the solutions when the conservation of EMT is respected and then we proceed with those in which violation occurs. We have found, provided that the EMT conservation is violated, there generally exist two accelerated expansion solutions which their stability properties depend on the underlying model. More exactly, we obtain a dark energy solution for which the effective equation of state (EoS) depend on model parameters and a de Sitter solution. We present a method to parametrize $\Lambda(-T)$ function which is useful in dynamical system approach and has been employed in the herein model. Also, we discuss the cosmological solutions for models with $\Lambda(-T)=8\pi G(-T)^{\alpha}$ in the presence of the ultra relativistic matter.Comment: 27 pages, 4 figure