Gauge singlet scalar as inflaton and thermal relic dark matter

TL;DR

This work proposes a minimal extension of the Standard Model by adding a gauge-singlet scalar $S$ with a large nonminimal coupling to gravity, aiming to realize both inflation and thermal-relic dark matter. The authors perform an RG-improved, Coleman–Weinberg–level analysis in the Jordan frame and transform to the Einstein frame to compute inflationary observables, while ensuring vacuum stability and perturbativity up to the Planck scale and matching the observed dark matter density. They find viable regions in the $(m_s,m_h)$ parameter space where the spectral index $n$ is enhanced by radiative corrections relative to the classical value, with a Higgs mass range roughly $145$–$170$ GeV and $m_s$ in the GeV–TeV range, depending on the self-coupling $\lambda_s$ and whether $S$ is real or complex. The model makes testable predictions for collider phenomenology (e.g., $h\to SS$) and direct dark matter searches, offering a way to distinguish S-inflation from Higgs inflation in upcoming Planck and LHC-era data.

Abstract

We show that, by adding a gauge singlet scalar S to the standard model which is nonminimally coupled to gravity, S can act both as the inflaton and as thermal relic dark matter. We obtain the allowed region of the (m_s, m_h) parameter space which gives a spectral index in agreement with observational bounds and also produces the observed dark matter density while not violating vacuum stability or nonperturbativity constraints. We show that, in contrast to the case of Higgs inflation, once quantum corrections are included the spectral index is significantly larger than the classical value (n = 0.966 for N = 60) for all allowed values of the Higgs mass m_h. The range of Higgs mass compatible with the constraints is 145 GeV < m_h < 170 GeV. The S mass lies in the range 45 GeV < ms < 1 TeV for the case of a real S scalar with large quartic self-coupling lambdas, with a smaller upper bound for smaller lambdas. A region of the parameter space is accessible to direct searches at the LHC via h-->SS, while future direct dark matter searches should be able to significantly constrain the model.

Figures (7)

• Figure 1: Classical potential in Einstein frame, in limit $s \gg M_P/\sqrt{\xi}$. This figure is plotted for real $S$ with $m_h = 160$ GeV and $\lambda_s = 0.2$. Inflation occurs along the exponentially flat plateau.
• Figure 2: Running of scalar couplings showing the effect of suppressing the $s$ propagator. The dash line shows the corresponding value of $c_s$ when $\mu = s$. This figure is plotted for real $S$ with $m_h = 160$ GeV, $\lambda_s(m_t) = 0.2$ and $\lambda_{hs}(m_t) = 0.1$.
• Figure 3: Running of the non-minimal couplings of $s$ and $h$ to the Ricci scalar. In this, $\xi_h$ is set to zero at $\mu = m_{t}$. It can be seen that $\xi_h \ll \xi_s$ throughout. The figure is plotted for real $S$ with $m_h = 160$ GeV, $\lambda_s(m_t) = 0.2$ and $\lambda_{hs}(m_t) = 0.1$.
• Figure 4: The value of $m_s$ as a function of $\lambda_{hs}(m_{t})$ necessary to produce the correct density of thermal relic dark matter. In this example $m_h = 160.0$ GeV. The solid line indicates real $S$ and the dashed line complex $S$ scalars.
• Figure 5: Allowed region for inflation in the $s$-direction. Excluded regions are shown in grey. Limits from couplings in the $s$-direction are shown with dashed lines, those from the couplings running in the $h$-direction have solid lines and the 1-$\sigma$ upper limit on $n$ is dot-dashed. In (a) we show the line $n = 0.981$ (dot-dot-dash) demonstrating the variation of $n$.