The Standard Model Higgs Boson-Inflaton and Dark Matter

TL;DR

The paper investigates whether the Standard Model Higgs can serve as the inflaton in slow-roll inflation when it has a large non-minimal coupling to gravity, and how coupling to a SM singlet scalar dark matter field $S$ modifies this scenario. It computes the one-loop renormalization-group (RG) improved effective potential in the Einstein frame, incorporating the Higgs propagator suppression factor $s(t)$ from the large $\xi$ regime and the Higgs–dark matter interactions via the coupling $\kappa$ and self-coupling $\lambda_S$. Inflationary observables are derived from the potential $V_E(\sigma)=V(t)/f(t)^2$ with a canonically normalized field $\sigma$ and slow-roll parameters $\epsilon$, $\eta$, and $\zeta^2$, while the amplitude of density perturbations fixes $\xi(t_i)$. The analysis imposes vacuum stability, triviality, and a 'wrong way roll' constraint to ensure inflation proceeds toward the origin; this constraint, together with cosmological data on the spectral index $n_s$, narrows the viable parameter space and links the allowed Higgs mass to the Higgs–DM coupling. The results show that dark matter can broaden the cosmologically allowed Higgs mass range, but the wrong-way-roll and $n_s$ constraints still favor a Higgs mass in the ~155–180 GeV region for small $\kappa$, with lower masses possible for larger $\kappa$ up to a limit, beyond which no region remains.

Abstract

The standard model Higgs boson can serve as the inflaton field of slow roll inflationary models provided it exhibits a large non-minimal coupling with the gravitational scalar curvature. The Higgs boson self interactions and its couplings with a standard model singlet scalar serving as the source of dark matter are then subject to cosmological constraints. These bounds, which can be more stringent than those arising from vacuum stability and perturbative triviality alone, still allow values for the Higgs boson mass which should be accessible at the LHC. As the Higgs boson coupling to the dark matter strengthens, lower values of the Higgs boson mass consistent with the cosmological data are allowed.

Figures (10)

• Figure 1: The Einstein frame renormalization group improved effective potential as a function of the canonically normalized Higgs-inflaton field. The magnitude and shape of this potential in the inflationary cosmological state varies with the strength of the Higgs-inflaton and dark matter coupling constant $\kappa$. The thickened portion of the potential curve corresponds to the $N_e =60$ e-folds of inflation with onset and exit values of $\sigma$ as shown.
• Figure 2: The Einstein frame renormalization group improved effective potential as a function of the canonically normalized Higgs-inflaton field. The magnitude and shape of this potential in the inflationary cosmological state varies with the strength of the dark matter self-coupling constant $\lambda_S$ as compared to Fig. 1 for the different Higgs-inflaton to dark matter coupling $\kappa$. The thickened portion of the potential curve corresponds to the $N_e =60$ e-folds of inflation with onset and exit values of $\sigma$ as shown.
• Figure 3: The running coupling constants for the scalar fields. The initial conditions for the coupling constants correspond to the effective potential plot of Fig. \ref{['EffPotential-2']} with $\kappa (0) =0.2$, $\xi (0)=8,315$ and $\xi_S (0) =0.0$. In this case the onset of inflation occured at the scale $t_i=35$ with exit at $t_f=32.7$ after 60 e-folds of expansion.
• Figure 4: The running of the non-minimal gravitational coupling constants for the scalar fields. The initial conditions for the coupling constants correspond to the effective potential plot of Fig. \ref{['EffPotential-2']} with $\kappa (0) =0.2$, $\xi (0)=8,315$ and $\xi_S (0) =0.0$. In this case the onset of inflation occured at the scale $t_i=35$ with exit at $t_f=32.7$ after 60 e-folds of expansion.
• Figure 5: The wrong way roll constraints for parameter space are added to those of vacuum stability and triviality (compare to Fig. \ref{['suppression']}). These are displayed for typical initial non-minimal gravitational couplings of $\xi (0) = 10^4$ and $\xi_S (0) =0.0$. The grey colored areas mark the wrong way roll excluded regions of parameter space. The constraints apply to scales up to those typical of the onset of inflation, $t_i=34.5$.