Hubble expansion & Structure Formation in Time Varying Vacuum Models

TL;DR

This paper explores time-varying vacuum energy models in cosmology, analyzing their properties, constraining parameters with observational data, and examining their effects on structure formation and cluster distributions.

Contribution

It provides analytical solutions for various $\Lambda(t)$ models, constrains their parameters with recent data, and studies their impact on structure growth and halo mass functions.

Findings

Tight constraints on $\Lambda(t)$ models from supernovae, CMB, and BAO data.

Models produce similar cluster distributions at low redshift, challenging their differentiation.

Sunyaev-Zeldovich surveys may distinguish models at high redshift.

Abstract

We investigate the properties of the FLRW flat cosmological models in which the vacuum energy density evolves with time, $\Lambda(t)$. Using different versions of the $\Lambda(t)$ model, namely quantum field vacuum, power series vacuum and power law vacuum, we find that the main cosmological functions such as the scale factor of the universe, the Hubble expansion rate $H$ and the energy densities are defined analytically. Performing a joint likelihood analysis of the recent supernovae type Ia data, the Cosmic Microwave Background (CMB) shift parameter and the Baryonic Acoustic Oscillations (BAOs) traced by the Sloan Digital Sky Survey (SDSS) galaxies, we put tight constraints on the main cosmological parameters of the $\Lambda(t)$ scenarios. Furthermore, we study the linear matter fluctuation field and the growth rate of clustering of the above vacuum models. Finally, we derived the theoretically predicted dark-matter halo mass function and the corresponding distribution of cluster-size halos for all the models studied. Their expected redshift distribution indicates that it will be difficult to distinguish the closely resembling models (constant vacuum, quantum field and power-law vacuum), using realistic future X-ray surveys of cluster abundances. However, cluster surveys based on the Sunayev-Zeldovich detection method give some hope to distinguish the closely resembling models at high redshifts.