Turnaround radius in $f(R)$ model

TL;DR

This paper analyzes how modified gravity, specifically $f(R)$ models, affects the turnaround radius and collapse thresholds in spherical collapse, revealing measurable differences from General Relativity.

Contribution

It provides the first detailed calculation of the impact of $f(R)$ gravity on the turnaround radius and collapse density contrasts in spherical collapse models.

Findings

Effective scalar mass impacts $ ext{delta}_t$ by up to 10%.

Collapse density contrast $ ext{delta}_c$ increases by about 1%.

Turnaround radius $R_t$ can be up to 6% larger at $z \,\simeq\ 0$ in $f(R)$ models.

Abstract

We investigate the turnaround radius in the spherical collapse model, both in General Relativity and in modified gravity, in particular $f(R)$ scenarios. The phases of spherical collapse are marked by the density contrast in the instant of turnaround $\delta_t$, and by the linear density contrast in the moment of collapse, $\delta_c$. We find that the effective mass of the extra scalar degree of freedom which arises in modified gravity models has an impact on $\delta_t$ of up to $\sim10\%$, and that $\delta_c$ can increase by $\sim1.0\%$. We also compute the turnaround radius, $R_t$, which in modified gravity models can increase by up to $\sim 6\%$ at $z \simeq 0$.