# Constraints on running vacuum model with $H(z)$ and $f \sigma_8$

## TL;DR

This paper tests a running vacuum cosmological model against observational data, finding a small but non-zero parameter value that slightly improves the fit over the standard Lambda-CDM model.

## Contribution

It provides observational constraints on the running vacuum model using multiple cosmological data sets, including $H(z)$ and $f \sigma_8(z)$ measurements.

## Key findings

- The parameter $
u$ is constrained to $(1.37^{+0.72}_{-0.95})\times 10^{-4}$.
- The model achieves a slightly better fit than $\\Lambda$CDM.
- The data supports a small running of the vacuum energy.

## Abstract

We examine the running vacuum model with $\Lambda (H) = 3 \nu H^2 + \Lambda_0$, where $\nu$ is the model parameter and $\Lambda_0$ is the cosmological constant. From the data of the cosmic microwave background radiation, weak lensing and baryon acoustic oscillation along with the time dependent Hubble parameter $H(z)$ and weighted linear growth $f (z)\sigma_8(z)$ measurements, we find that $\nu=(1.37^{+0.72}_{-0.95})\times 10^{-4}$ with the best fitted $\chi^2$ value slightly smaller than that in the $\Lambda$CDM model.