Inflation and leptogenesis in the 3-3-1-1 model

We consider the $\mathrm{SU}(3{)}_C\otimes \mathrm{SU}(3{)}_L\otimes \mathrm{U}(1{)}_X\otimes \mathrm{U}(1{)}_N$ (3-3-1-1) model at the grand unified theory scale with implication for inflation and leptogenesis. The mass spectra of the neutral Higgs bosons and neutral gauge bosons are reconsidered when the scale of the 3-3-1-1 breaking is much larger than that of the ordinary $\mathrm{SU}(3{)}_C\otimes \mathrm{SU}(3{)}_L\otimes \mathrm{U}(1{)}_X$ (3-3-1) breaking. We investigate how the 3-3-1-1 model generates an inflation by identifying the scalar field that spontaneously breaks the $\mathrm{U}(1{)}_N$ symmetry to inflaton as well as including radiative corrections for the inflaton potential. We figure out the parameter spaces appeared in the inflaton potential that satisfy the conditions for an inflation model and obtain the inflaton mass an order of ${10}^{13}\mathrm{GeV}$. The inflaton can dominantly decay into a pair of light Higgs bosons or a pair of heavy Majorana neutrinos which lead, respectively, to a reheating temperature of ${10}^9\mathrm{GeV}$ order appropriate to a thermal leptogenesis scenario or to a reduced reheating temperature corresponding to a nonthermal leptogenesis scenario. We calculate the lepton asymmetry which yields baryon asymmetry successfully for both the thermal and nonthermal cases.

Figure 1

$r$ vs $n_s$ (upper panel) and $\alpha$ vs $n_s$ (lower panel) for $\mathrm{\Delta }=0.1m_P$ (green dot), $\mathrm{\Delta }=30m_P$ (red minus), $\mathrm{\Delta }=50m_P$ (pink plus), and $\mathrm{\Delta }=500m_P$ (blue asterisk) in the range of $-{10}^3<a^{\prime }<{10}^3$, with the number of $e$-folds $N=60$.

Figure 2

One-loop diagram contributing to the asymmetry from the decay ${\nu }_M\to e+H_5^{+}$.

Figure 3

One-loop diagram contributing to the asymmetry from the decay ${\nu }_M\to N+{H^{\prime }}^{*}$.

Figure 4

Contour plot of ${\eta }_B$ in the region $5\times {10}^{-11}<{\eta }_B<{10}^{-10}$ on the plane of the complex angle $\widehat{\theta }$ for $\delta =4.3\mathrm{rad}$, $\sigma =-1.5\mathrm{rad}$, $\rho =-1\mathrm{rad}$, $m_{{\nu }_{2M}}=m_{{\nu }_{3M}}={10}^3{m}_{{\nu }_{1M}}$, $m_{{\nu }_{1M}}={10}^9\mathrm{GeV}$, $m_{{\nu }_1}=0.01\mathrm{eV}$.

Figure 5

${\eta }_B$ vs pure imaginary $\widehat{\theta }$ (red) and pure real $\widehat{\theta }$ (blue) for $\delta =4.3\mathrm{rad}$, $\sigma =-1.5\mathrm{rad}$, $\rho =-1\mathrm{rad}$, $m_{{\nu }_{2M}}=m_{{\nu }_{3M}}={10}^3{m}_{{\nu }_{1M}}$, $m_{{\nu }_{1M}}={10}^9\mathrm{GeV}$, $m_{{\nu }_1}=0.01\mathrm{eV}$.

Figure 6

${\eta }_B$ vs $\delta$ (left) and ${\eta }_B$ vs $\sigma =\rho$ (right) for $\widehat{\theta }=0.87I$ (red) and $\widehat{\theta }=-0.18I$ (blue), and other parameters given in (112).

Figure 7

Contour plot of ${\eta }_B$ in the region ($5\times {10}^{-11}<{\eta }_B<{10}^{-10}$) on the plane of the complex angle $\widehat{\theta }$ for $m_{{\nu }_{1M}}={10}^{11}\mathrm{GeV}$ (red) and $m_{{\nu }_{1M}}={10}^9\mathrm{GeV}$ (blue).

Figure 8

${\eta }_B$ vs pure imaginary (red) and pure real (blue) $\widehat{\theta }$.

Figure 9

${\eta }_B$ vs $\delta$ (left) and ${\eta }_B$ vs $\sigma =\rho$ (right) for $\widehat{\theta }=1.46I$ (red) and $\widehat{\theta }=-1.46I$ (blue).