Scalar field cosmologies with a generalized harmonic potential and matter with energy density $rho_m$, pressure $p_m$, and barotropic equation of state (EoS) $p_m=(gamma-1)rho_m, ; gammain[0,2]$ in Kantowski-Sachs (KS) and closed Friedmann--Lema^itre
--Robertson--Walker (FLRW) metrics are investigated. We use methods from non--linear dynamical systems theory and averaging theory considering a time--dependent perturbation function $D$. We define a regular dynamical system over a compact phase space, obtaining global results. That is, for KS metric the global late--time attractors of full and time--averaged systems are two anisotropic contracting solutions, which are non--flat locally rotationally symmetric (LRS) Kasner and Taub (flat LRS Kasner) for $0leq gamma leq 2$, and flat FLRW matter--dominated universe if $0leq gamma leq frac{2}{3}$. For closed FLRW metric late--time attractors of full and averaged systems are a flat matter--dominated FLRW universe for $0leq gamma leq frac{2}{3}$ as in KS and Einstein-de Sitter solution for $0leqgamma<1$. Therefore, time--averaged system determines future asymptotics of full system. Also, oscillations entering the system through Klein-Gordon (KG) equation can be controlled and smoothed out when $D$ goes monotonically to zero, and incidentally for the whole $D$-range for KS and for closed FLRW (if $0leq gamma< 1$) too. However, for $gammageq 1$ closed FLRW solutions of the full system depart from the solutions of the averaged system as $D$ is large. Our results are supported by numerical simulations.
Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $gamma$ for the Locally Rotationally Symmetric (LRS) Bianchi I and flat Friedmann-Lema^itre-Robertson-Wa
lker (FLRW) metrics are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averag
Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $gamma$ for Locally Rotationally Symmetric (LRS) Bianchi III metric and open Friedmann-Lema^itre-Roberts
on-Walker (FLRW) metric are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averag
Unimodular gravity is an appealing approach to address the cosmological constant problem. In this scenario, the vacuum energy density of quantum fields does not gravitate and the cosmological constant appears merely as an integration constant. Recent
ly, it has been shown that energy diffusion that may arise in quantum gravity and in theories with spontaneous collapse is compatible with this framework by virtue of its restricted diffeomorphism invariance. New studies suggest that this phenomenon could lead to higher-order equations in the context of homogeneous and isotropic Universe, affecting the well-posedness of their Cauchy initial-value problem. In this work, we show that this issue can be circumvented by assuming an equation of state that relates the energy density to the function that characterizes the diffusion. As an application, we solve the field equations analytically for an isotropic and homogeneous Universes in a barotropic model and in the mass-proportional continuous spontaneous localization (CSL) scenario, assuming that only dark matter develops energy diffusion. Different solutions possessing phase transition from decelerated to accelerated expansion are found. We use cosmological data of type Ia Supernovae and observational Hubble data to constrain the free parameters of both models. It is found that very small but nontrivial energy nonconservation is compatible with the barotropic model. However, for the CSL model, we find that the best-fit values are not compatible with previous laboratory experiments. We comment on this fact and propose future directions to explore energy diffusion in cosmology.
