Axion inflation, proton decay, and leptogenesis in $SU(5)\times U(1{)}_{PQ}$

We implement inflation in a nonsupersymmetric $SU(5)$ model based on a nonminimal coupling of the axion field to gravity. The isocurvature fluctuations are adequately suppressed, axions comprise the dark matter, proton lifetime estimates are of order $8\times {10}^{34}–3\times {10}^{35}\mathrm{yr}$, and the observed baryon asymmetry arises via nonthermal leptogenesis. The presence of low-scale colored scalars ensures unification of the Standard Model gauge couplings and also helps in stabilizing the electroweak vacuum.

Figure 1

Evolution of the inverse coupling strengths with energy. Here $M_{R_8}=1\mathrm{TeV}$, $M_{R_3}\approx 6.1\times {10}^7\mathrm{GeV}$, and $M_{\mathrm{GUT}}\approx {10}^{16}\mathrm{GeV}$. The proton lifetime in this case is ${\tau }_p\approx 2.4\times {10}^{35}\mathrm{yr}$.

Figure 2

Vacuum stability of the Higgs potential. The red (upper) line shows the running of the Higgs quartic coupling in the model compatible with Fig. 1. We display in blue (lower line) its running in the SM for comparison.

Figure 3

Correlation between the inflaton’s quartic coupling ${\lambda }_{\sigma }$ and the nonminimal coupling $\xi$ for $N=50$ $e$-foldings (thick line) and $N=60$ $e$-foldings (thin line). $n_s$ is within the 68% confidence level of Planck’s measurement.

Figure 4

Upper bound on the PQ scale $f_a$ as a function of the nonminimal coupling $\xi$ due to isocurvature and DM relic abundance constraints. The two lines are for $N=50$ $e$-foldings (thick) and $N=60$ $e$-foldings (thin). $n_s$ is within the 68% confidence level of Planck’s measurement.