(No) Eternal Inflation and Precision Higgs Physics

TL;DR

The paper investigates whether the current cosmological acceleration could be non-eternal by tying this fate to the metastability of the Standard Model vacuum. It develops a quantitative link between the bubble nucleation decay rate and precise SM parameters, showing that in a no-new-physics scenario up to the GUT scale, a narrow Higgs-mass window around 109 GeV (with small shifts from m_t and α_s) could render eternal inflation incompatible. It also discusses MSSM scenarios where squark vacua could yield fast decays, and entertains a speculative gravity-driven no-eternal-inflation principle grounded in de Sitter entropy arguments. The work emphasizes that testing this idea requires extreme experimental and theoretical precision, offering a potential deep connection between particle physics measurements and the ultimate fate of the Universe.

Abstract

Even if nothing but a light Higgs is observed at the LHC, suggesting that the Standard Model is unmodified up to scales far above the weak scale, Higgs physics can yield surprises of fundamental significance for cosmology. As has long been known, the Standard Model vacuum may be metastable for low enough Higgs mass, but a specific value of the decay rate holds special significance: for a very narrow window of parameters, our Universe has not yet decayed but the current inflationary period can not be future eternal. Determining whether we are in this window requires exquisite but achievable experimental precision, with a measurement of the Higgs mass to 0.1 GeV at the LHC, the top mass to 60 MeV at a linear collider, as well as an improved determination of alpha_s by an order of magnitude on the lattice. If the parameters are observed to lie in this special range, particle physics will establish that the future of our Universe is a global big crunch, without harboring pockets of eternal inflation, strongly suggesting that eternal inflation is censored by the fundamental theory. This conclusion could be drawn even more sharply if metastability with the appropriate decay rate is found in the MSSM, where the physics governing the instability can be directly probed at the TeV scale.

Figures (3)

• Figure 1: Running of the Higgs quartic coupling $\lambda(\mu)$ for $m_t=170.9$ GeV for different Higgs masses (from below) $m_H=110$, $120$, $130$ and $135$ GeV (see appendix for formulæ and notations). For low masses $\lambda$ turn negative at high scales $\mu$ and the SM vacuum become unstable.
• Figure 2: Left: measured $m_t(GeV)$ and $\alpha_s(m_Z)$ at 1, 2, 3 and 5$\sigma$ (ellipses) vs the percolation bound for different Higgs masses (blue lines). The line in the middle of the shaded strip corresponds to the LEP2 bound $m_H=114.4$ GeV (the excluded experimental region is green shaded), all the other lines are at step of 3 GeV in the Higgs mass. The shaded strip corresponds to the $\pm 3$ GeV theoretical error on the bound. This shows that, with the current experimental and theoretical errors, non-eternal inflation is excluded at less than $1\sigma$ level, i.e. it is compatible with current observations. Right up: Rule out scenario: all the values stay the same and an heavy Higgs mass is observed ($m_H\simeq 145$ GeV), eternal inflation is not excluded by the bound; Right down: Rule in scenario: both the experimental and the theoretical errors have been substantially decreased and the central values moved such that the bound on the Higgs mass (dashed blue line) ($m_H=115.2$ GeV in the figure) is above the experimental value (green line, $m_H=115$ GeV in this case) by $\sim2\sigma$; the Universe does not experience eternal inflation.
• Figure 3: Decrease of the upper bound on the Higgs mass in eq.(\ref{['eq:res']}) from lowering the cutoff $\Lambda$ for various values of the top mass (from the left $m_t=171$, $173$ and $175$ GeV).