Cosmological implications of the Higgs mass measurement

TL;DR

The paper explores how a Higgs mass measurement, interpreted under the assumption that the Standard Model extends to very high energies, informs early-Universe physics. It develops bounds on the reheating temperature from electroweak vacuum metastability, analyzes Higgs fluctuations during inflation via a stochastic framework, and examines the interplay with cosmological perturbations and tensor modes within a landscape picture. A key result is that, in large-field inflation, the simultaneous realization of a light Higgs and observed curvature perturbations or primordial gravity waves is exponentially unlikely without new physics beyond the Standard Model. These findings yield probabilistic links between Higgs physics, inflationary dynamics, and potential high-energy extensions of the theory.

Abstract

We assume the validity of the Standard Model up to an arbitrary high-energy scale and discuss what information on the early stages of the Universe can be extracted from a measurement of the Higgs mass. For Mh < 130 GeV, the Higgs potential can develop an instability at large field values. From the absence of excessive thermal Higgs field fluctuations we derive a bound on the reheat temperature after inflation as a function of the Higgs and top masses. Then we discuss the interplay between the quantum Higgs fluctuations generated during the primordial stage of inflation and the cosmological perturbations, in the context of landscape scenarios in which the inflationary parameters scan. We show that, within the large-field models of inflation, it is highly improbable to obtain the observed cosmological perturbations in a Universe with a light Higgs. Moreover, independently of the inflationary model, the detection of primordial tensor perturbations through the B-mode of CMB polarization and the discovery of a light Higgs can simultaneously occur only with exponentially small probability, unless there is new physics beyond the Standard Model.

Figures (6)

• Figure 1: The instability scale $\Lambda$ as a function of the Higgs mass $M_h$ for three different values of the top mass $M_t$.
• Figure 2: Lower bounds on $M_h$ from absolute stability (upper curves) and $T=0$ metastability (lower curves). The width corresponds to $\alpha_s(M_Z)=0.1176\pm 0.0020$ (with the higher curve corresponding to lower $\alpha_s$) and we do not show the uncertainty from higher-order effects, which we estimate to be below 2--3 GeV. The horizontal line is the LEP mass bound.
• Figure 3: Upper bounds on $T_{RH}$, as functions of $M_h$, from sufficient stability of the electroweak vacuum against thermal fluctuations in the hot early Universe for three different values of the top mass. The lower curves are for $H_f=10^{13}$ GeV, the upper ones for $H_f$ deduced from eq. (\ref{['limtrh']}), $H_f=[4\pi^3 g_* (T_{RH})/45]^{1/2} (T_{RH}^2/M_p)$, which corresponds to the case of instant reheating. We take $\alpha_S(M_Z)=0.1176$. Lowering (increasing) $\alpha_S(M_Z)$ by one standard deviation lowers (increases) the bound on $T_{RH}$ by up to one order of magnitude.
• Figure 4: The quantity $\log_{10}\left[\int_{\zeta>\zeta_{\rm obs}}d\zeta \,P_\Lambda/ \int_{\zeta>10^{-6}}d\zeta \,P_\Lambda\right]$ as a function of the Higgs mass for three values of $M_t$ and $p=2$.
• Figure 5: Upper bound on $\sqrt{|\xi|}H$ as a function of $M_h$ obtained by requiring that the electroweak vacuum is stable. Here $\xi$ is the negative coupling between the Higgs bilinear and the scalar curvature, and $H$ is the maximal Hubble rate during inflation.