Hill-top inflation from Dai-Freed anomaly in the standard model -- A solution to the iso-curvature problem of the axion dark matter

TL;DR

This paper proposes a hilltop inflation model based on a $Z_4$ symmetry in the Standard Model, which suppresses axion isocurvature fluctuations and allows for high reheating temperatures compatible with baryogenesis.

Contribution

The work extends previous inflation models by generalizing the inflaton potential under $Z_4$ symmetry, achieving consistent hilltop inflation with suppressed axion isocurvature fluctuations.

Findings

Hubble parameter during inflation can be below 10^9 GeV.

Spectral index running can reach 0.0018, testable in future CMB experiments.

Reheating temperature can be as high as 10^{10} GeV, enabling thermal leptogenesis.

Abstract

The discrete symmetry $Z_4$ in the standard model (SM) with three right-handed neutrinos is free from the Dai-Freed anomaly. Motivated by this $Z_4$ symmetry, we constructed a topological inflation model consistent with all known constraints and observations. However, we assumed a specific inflaton potential in the previous work. In this paper we extend the inflaton potential in a more general form allowed by the discrete $Z_4$ gauge symmetry and show that consistent hilltop inflation is realized. We find that the Hubble parameter $H_\mathrm{inf}$ can be smaller than $\simeq 10^{9}$ GeV so that the isocurvature fluctuations of the axion dark matter are sufficiently suppressed. Furthermore, the running of the spectral index can be as large as $dn_s/\ln k \simeq 0.0018$ which will be tested in future CMB observations. Since this discrete $Z_4$ acts on the SM, the inflaton can couple to pairs of the right-handed neutrinos and hence the reheating temperature can be high as $\sim 10^{10}$ GeV, producing the cosmic baryon asymmetry naturally through the thermal leptogenesis.