Scalaron dark matter dynamics: effects of Higgs non-minimal coupling to gravity

Abstract

One of the key features of the $R^2$-gravity is the embedding of a scalar field, scalaron, into the gravity sector. The scalaron interacts with the Standard Model (SM) matter fields through Planck-suppressed couplings. If the scalaron serves as a viable dark matter (DM) candidate, it can account for the lack of evidence of DM interactions beyond gravity in experimental and observational probes to date. The realization of the scalaron, as a cold DM candidate, depends on an induced trilinear interaction with the SM Higgs via its quartic self coupling. Here, we introduce a Higgs non-minimal coupling to gravity that additionally contributes to the induced trilinear interaction with its existing competing part, originated from the $R^2$-gravity. We study the interplay between these two contributions in the early universe, which determines both the initial conditions and evolution of the scalaron, leading to cold DM behavior at a later epoch. The trilinear interaction vanishes at the leading order for certain combinations of the Higgs non-minimal coupling ($ξ$) and the scalaron mass ($m$), thereby setting the scalaron density through misalignment mechanism, as in axions. In this case, the scalaron DM mass is obtained as, $2.7 ~{\rm meV} \lesssim m \lesssim 0.7 ~\rm{MeV}$. The lower limit on the mass is set by the fifth force constraints, whereas the upper bound arises from INTEGRAL/SPI limits on the excess gamma-ray flux due to scalaron decaying into two photons. On the other hand, when the trilinear interaction is non-zero and dominated by the Higgs quartic self coupling, the DM relic density is satisfied with $m \simeq 3.6$ meV. When the Higgs non-minimal coupling dominates, the mass lies within 10-120 meV. We also obtain, for the first time within the scalaron-Higgs mixed model, an upper bound on $|ξm|$ of $2.35\times 10^{16}$ GeV, from Higgs mass measurement at the LHC.

Figures (6)

• Figure 1: Scenario-I: Evolution of the scalaron energy density (shown by the pink solid line) in the absence of non-minimal Higgs coupling to gravity. It first redshifts as radiation density (shown by the black dashed line), then as matter density (shown by the blue solid line). This feature is retained even with non-zero non-minimal Higgs coupling, as long as $3\xi m^2 \neq \lambda v^2$. See text for details.
• Figure 2: Scenario-I: Evolutions of the scalaron field (pink solid line) and its minima (blue dashed line) at early epochs. To note, the scalaron follows its minima that shifts continuously due to induced trilinear interaction with the SM Higgs. See text for details.
• Figure 3: Scenario-II: Evolution of the scalaron field ($\phi/\phi_i$) (left panel) and its energy density ($\rho_{\phi}$) (right panel) for $\xi \sim \mathcal{O}(10^{15})$, which fixes $m \sim \mathcal{O}$(keV). The initial field value $\phi_i$, is determined from the observed DM relic density. See text for details.
• Figure 4: Constraint on the scalaron decay rate : The scalaron decay rate (red solid line) as a function of its mass, compared with the exclusion limit at $95\%$ C.L. (green shaded region) on the light DM decaying into a pair of photons, taken from Ref.Calore:2022pks. See text for details.
• Figure 5: Summary of constraints on $m$ and $\xi$: The relic density constraint in scenario-I (non-zero scalaron-Higgs interaction) is shown by the red solid line, whereas that in scenario-II (negligible scalaron-Higgs interaction) is shown by the black dot-dashed line. Constraints from the LHC, the torsion balance experiment and the INTEGRAL/SPI telescope are shown using purple dashed, blue dashed and green dashed lines respectively. These constraints allow scalaron mass ranging from $2.7$ meV to $0.7$ MeV and non-minimal coupling $0\leq\xi \lesssim 10^{26}$.