Cosmological models with running cosmological term and decaying dark matter

TL;DR

This paper explores a dynamic cosmological model where the cosmological constant varies with time and dark matter decays, providing a better fit to observational data and addressing the cosmological constant problem.

Contribution

It introduces a generalized $ ext{Lambda}$CDM model with a running $ ext{Lambda}(t)$ and decaying dark matter, supported by statistical analysis of diverse observational data.

Findings

The model fits low and high redshift data with different energy transfer directions.

Decaying dark matter leads to lighter, relativistic particles and a natural solution to the cosmological constant problem.

The model outperforms standard $ ext{Lambda}$CDM based on AIC criteria.

Abstract

We investigate the dynamics of the generalized $\Lambda$CDM model, which the $\Lambda$ term is running with the cosmological time. The $\Lambda(t)$ term emerges from the covariant theory of the scalar field $\phi$ with the self-interacting potential $V(\phi)$. On the example of the model $\Lambda(t)=\Lambda_{\text{bare}}+\frac{\alpha^2}{t^2}$ we show the existence of a mechanism of the modification of the scaling law for energy density of dark matter: $\rho_{\text{dm}}\propto a^{-3+\lambda(t)}$. We discuss the evolution of $\Lambda(t)$ term and pointed out that during the cosmic evolution there is a long phase in which this term is approximately constant. This effect justifies Alcaniz and Lima's approach to $\Lambda(H)$ cosmologies. We also present the statistical analysis of both the $\Lambda(t)$CDM model with dark energy and decaying dark matter and the $\Lambda$CDM standard cosmological model. We divide the observational data into two groups: low $z$ data (SNIa, BAO, $H(z)$ and AP test) and high $z$ data (Planck, WP and lensing). While for the former we find the best fit value of the parameter $\lambda$ is positive ($\lambda=0.0338$, energy transfer is from the dark energy to dark matter sector), for the latter we find that $\lambda$ is $-0.0199$ which is an evidence that the energy transfer is from decaying dark matter. This disagreement correlates with estimated values of $H_0$ ($67.77$ km/(s Mpc) and $65.62$ km/(s Mpc) respectively). The decaying dark matter causes to lowering a mass of dark matter particles which are lighter than CDM particles and remain relativistic. The rate of the process of decaying matter is estimated. We show that in the models of decaying dark matter, the cosmological constant problem disappears naturally. The model with decaying dark matter possesses one parameter more but in light of the AIC it is better than the $\Lambda$CDM standard cosmological model.