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. Recently, 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 diffusion. As an application, we solve the field equations analytically for an isotropic and homogeneous universe 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.

This paper investigates exact solutions of cosmological interest in fractional cosmology. Given $\mu$, the order of Caputo’s fractional derivative, and w, the matter equation of state, we present specific exact power-law solutions. We discuss the exact general solution of the Riccati Equation, where the solution for the scale factor is a combination of power laws. Using cosmological data, we estimate the free parameters. An analysis of type Ia supernovae (SNe Ia) data and the observational Hubble parameter data (OHD), also known as cosmic chronometers, and a joint analysis with data from SNe Ia + OHD leads to best-fit values for the free parameters calculated at $1\sigma$, $2\sigma$ and $3\sigma$ confidence levels (CLs). On the other hand, these best-fit values are used to calculate the age of the Universe, the current deceleration parameter (both at $3\sigma$ CL) and the current matter density parameter at $1\sigma$ CL. Finding a Universe roughly twice as old as the one of $\Lambda$CDM is a distinction of fractional cosmology. Focusing our analysis on these results, we can conclude that the region in which $\mu >2$ is not ruled out by observations. This parameter region is relevant because fractional cosmology gives a power-law solution without matter, which is accelerated for $\mu >2$. We present a fractional origin model that leads to an accelerated state without appealing to $\Lambda$ or dark energy.

In this paper we explore the different types of singularities that arise in the $\mathrm{\Lambda }\mathrm{CDM}$ model when dissipative processes are considered, in the framework of the Eckart’s theory. In particular, we study the late-time behavior of $\mathrm{\Lambda }\mathrm{CDM}$ model with viscous cold dark matter (CDM) and an early-time viscous radiation domination era with cosmological constant (CC). The fluids are described by the barotropic equation of state (EoS) $p=(\gamma -1)\rho$, where $p$ is the equilibrium pressure of the fluid, $\rho$ their energy density, and $\gamma$ is the barotropic index. We explore two particular cases for the bulk viscosity $\xi$, a constant bulk viscosity $\xi ={\xi }_0$, and a bulk viscosity proportional to the energy density of the fluid $\xi ={\xi }_0\rho$. Due to some previous investigations that have explored how to describe the behavior of the Universe with a negative CC, we extend our analysis to this case. We found that future singularities like Big Rip are allowed but without having a phantom EoS associated with the DE fluid. Big Crunch singularities also appears when a negative CC is present, but also de Sitter and even Big Rip types are allowed due to the negative pressure of the viscosity, which opens the possibility of an accelerated expansion in anti–de Sitter (AdS) cosmologies. We also discuss a very particular solution without Big Bang singularity that arises in the early-time radiation dominant era of our model known as soft-Big Bang.

Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $$\gamma $$γ for locally rotationally symmetric (LRS) Bianchi III metric and open Friedmann–Lemaître–Robertson–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-averaged versions have the same late-time dynamics. Therefore, simple time-averaged systems determine the future asymptotic behavior. Depending on values of barotropic index $$\gamma $$γ late-time attractors of physical interests for LRS Bianchi III metric are Bianchi III flat spacetime, matter dominated FLRW universe (mimicking de Sitter, quintessence or zero acceleration solutions) and matter-curvature scaling solution. For open FLRW metric late-time attractors are a matter dominated FLRW universe and Milne solution. With this approach, oscillations entering nonlinear system through Klein–Gordon (KG) equation can be controlled and smoothed out as the Hubble factor H – acting as a time-dependent perturbation parameter – tends monotonically to zero. Numerical simulations are presented as evidence of such behaviour.

Cosmological fluids with a generalized equation of state (GEoS) are here considered, whose corresponding EoS parameter $\omega$ describes a fluid with phantom behavior, namely, $\omega <-1$, but leading to universes free of singularities at any past or future, finite time, thus avoiding, in particular, the big bang and the big rip singularities, the last one considered to be typical in phantom fluid models. More specifically, such GEoS fluid cosmologies lead to regular little rip universes. A remarkable new property of these solutions is proven here, namely, that they avoid the initial singularity at early times; therefore, they are able to describe emergent universes. Solutions of this kind had been studied previously, but only either as late-time or as early-time solutions, never as solutions covering both epochs simultaneously. Appropriate conditions are proposed here that relate the little rip cosmologies with the initial regular universe, for the future and past regimes, respectively. This is done by taking as a starting point the conditions under which a given scale factor corresponds to a little rip universe.