Improved Lemaitre-Tolman model and the mass and turn-around radius in group of galaxies II: the role of dark energy

TL;DR

This study extends the Lemaitre-Tolman model to include dark energy with variable equation of state and additional effects like angular momentum and dynamical friction, analyzing their impact on galaxy group dynamics and constraining dark energy properties.

Contribution

It introduces a modified LT model incorporating dark energy with different $w$ values, angular momentum, and dynamical friction, providing new insights into mass-radius relations and dark energy constraints.

Findings

Mass decreases by up to 25% when changing $w$ from -1 to -1/3.

Hubble constant increases as $w$ shifts from -1 to -1/3.

Model fits to galaxy group data constrain dark energy parameters.

Abstract

In this paper, we extend our previous study \cite{DelPopolo2021} on the Lemaitre-Tolman (LT) model showing how the prediction of the model changes when the equation of state parameter ($w$) of dark energy is modified. In the previous study, it was considered that dark energy was merely constituted by the cosmological constant. In this paper, as in the previous study, we also took into account the effect of angular momentum and dynamical friction ($J\eta$ LT model) that modifies the evolution of a perturbation, initially moving with the Hubble flow. As a first step, solving the equation of motion, we calculated the relationship between mass, $M$, and the turn-around radius, $R_0$. If one knows the value of the turn-around radius $R_0$, it is possible to obtain the mass of the studied objects. As a second step, we build up, as in the previous paper, a relationship between the velocity, $v$, and radius, $R$. The relation was fitted to data of groups and clusters. Since the relationship $v-R$ depends on the Hubble constant and the mass of the object, we obtained optimized values of the two parameters of the objects studied. The mass decreases of a factor of maximum 25\% comparing the $J\eta$ LT results (for which $w=-1$) and the case $w=-1/3$, while the Hubble constant increases going from $w=-1$ to $w=-1/3$. Finally, the obtained values of the mass, $M$, and $R_0$ of the studied objects can put constraints to the dark energy equation of state parameter, $w$.