Freeze-in production of scalaron dark matter in $f(R)$ gravity

TL;DR

The paper investigates whether the scalaron, a scalar degree of freedom arising in $f(R)$ gravity, can constitute dark matter produced non-thermally via UV freeze-in. By transforming to the Einstein frame, the authors show the scalaron couples to SM fields with Planck-suppressed strength, enabling feebly interacting freeze-in production whose efficiency is highly sensitive to the maximum temperature of the thermal bath, identified with the reheating temperature $T_{\rm rh}$. An analysis of two representative $f(R)$ models—Scenario-A with $f(R)=R+\alpha R^n$ (favoring the Starobinsky case $n=2$) and Scenario-B with $f(R)=R+\gamma\ln(R/\mu^2)+\lambda R^2$—yields a viable MeV-scale scalaron mass only within narrow regions of parameter space, with $T_{\rm rh}$ typically around $10^{14}$--$10^{15}$ GeV to reproduce the observed DM relic density. The work links high-scale inflationary contexts to DM phenomenology in modified gravity, and discusses stringent constraints from scalaron decay signatures in gamma/X-ray and CMB observations, outlining a path for future exploration of post-inflationary reheating effects and observational probes.

Abstract

We demonstrate that the scalaron, a scalar degree of freedom, emerging from the $f(R)$ theory of gravity, can account for the observed dark matter (DM) abundance if its mass is around the MeV scale, to ensure its cosmological stability. Focusing on two well-known $f(R)$ gravity models, we systematically show that if scalaron production proceeds via the freeze-in mechanism, the right relic abundance is satisfied over a very narrow window of reheating temperature $10^{14}\lesssim T_{\rm rh}\lesssim 10^{16}$ GeV. We delineate the viable parameter space of the $f(R)$ models consistent with the observed DM abundance, and highlight relevant experimental constraints from searches targeting DM decay signatures.

Figures (11)

• Figure 1: Lifetime of scalaron as a function of its mass before (left panel) and after (right panel) EW symmetry breaking. The horizontal and vertical shaded regions are disallowed from DM lifetime shorter than that of the Universe as well as the warm DM limit, respectively.
• Figure 2: Scenario-A: The left panel shows the scalaron potential, for different choices of $n$ as shown with different patterns and for a fixed $\alpha=0.1$. Corresponding scalaron mass as a function of $\alpha$, for $n=2$ is shown in the right panel. The red shaded region is disallowed from warm dark matter (WDM) bound.
• Figure 3: Scenario-A: Lifetime of scalaron as DM, as a function of $\alpha$. In the left and right panel, respectively, we show scenarios before and after the electroweak symmetry breaking (EWSB).
• Figure 4: Scenario-B: The left panel show the scalaron potential for different choices of $\mu$, with a fixed $\lambda=0.1\,\text{GeV}^2$ and $\gamma=-0.2\,\text{GeV}^2$. The right panel shows the same for $\lambda=0$ and $\gamma=-0.2\,\text{GeV}^2$.
• Figure 5: Scenario-B: DM decay lifetime as a function of $\lambda$ before (left) and after (right) EWSB. In both panels we have fixed $\mu=0.1$ GeV.