Initial conditions for the scalaron dark matter

TL;DR

This paper explores the initial conditions and observational constraints for scalaron dark matter in $f(R)$ gravity, highlighting the role of inflationary quantum diffusion and anthropic reasoning in setting these conditions.

Contribution

It provides an analysis of initial condition issues for scalaron dark matter, including quantum diffusion effects during inflation and resulting bounds on inflationary energy scales.

Findings

Initial conditions for scalaron are largely unpredictable due to quantum diffusion.

Anthropic considerations are necessary to explain observed dark matter abundance.

Constraints on inflationary energy scale are derived from primordial inhomogeneity limits.

Abstract

The scalaron of the metric $f(R)$ gravity can constitute dark matter if its mass is in the range $4\,\text{meV} \lesssim m \lesssim 1\,\text{MeV}$. We give an overview of such $f (R)$ gravity theory minimally coupled to the Standard Model. Similarly to other dark-matter models based on scalar fields, this model has the issue of initial conditions. Firstly, the initial conditions for the scalaron are to be tuned in order to produce the observed amount of dark matter. Secondly, the primordial spatial inhomogeneities in the field are to be sufficiently small because they generate entropy (or isocurvature) perturbations, which are constrained by observations. We consider these issues in the present paper. The initial conditions for the scalaron presumably emerge at the inflationary stage. We point out that the homogeneous part of the scalaron initial value is largely unpredictable because of quantum diffusion during inflation. Thus, to account for the observed amount of dark matter, one has to resort to anthropic considerations. Observational constraints on the primordial spatial inhomogeneity of the scalaron are translated into upper bounds on the energy scale of inflation, which happen to be low but not too restrictive.