Inflation, Proton Decay and Gravitational Waves from Metastable Strings in $SU(4)_C \times SU(2)_L \times U(1)_R$ Model

Author(s)

Ahmed, Waqas, Mehmood, Maria, Rehman, Mansoor Ur, Zubair, Umer

Abstract

We present a realistic supersymmetric $\mu$-hybrid inflation model within the framework of $SU(4)_C \times SU(2)_L \times U(1)_R$ gauge symmetry, wherein the symmetry breaking $SU(4)_C \times SU(2)_L \times U(1)_R\rightarrow SU(3)_C\times SU(2)_L \times U(1)_{B-L}\times U(1)_R$ occurs before observable inflation, effectively eliminating topologically stable primordial monopoles. Subsequent breaking of $U(1)_{B-L} \times U(1)_R \rightarrow U(1)_Y$ after inflation leads to the formation of superheavy metastable cosmic strings (CSs), capable of producing a stochastic gravitational wave background (SGWB) consistent with the recent PTA data. Moreover, the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$ align with Planck 2018 observations. A consistent scenario for reheating and non-thermal leptogenesis is employed to explain the observed matter content of the universe. Finally, the embedding of $G_{421}$ into the Pati-Salam gauge symmetry $G_{422}$ is briefly discussed, predicting potentially observable proton decay rates detectable at facilities such as Hyper Kamiokande and DUNE.

Figures

Evolution of two loop RGEs of gauge couplings for gauge groups $G_{421}$, $G_{3211}$ and $G_{321}$.

Evolution of two loop RGEs of gauge couplings for gauge groups $G_{421}$, $G_{3211}$ and $G_{321}$.


Behavior of $\kappa$ (left) and the symmetry breaking scale $M$ (right) with respect to the dimensionless parameter $G\mu$. The blue shaded region represents the Planck2018 2-$\sigma$ bounds, while the yellow hatched region is excluded by the NANOGrav 15-year data bound on $G\mu$. The red cutoff on the right corresponds to the third advanced LVK bound on $G\mu$.

Behavior of $\kappa$ (left) and the symmetry breaking scale $M$ (right) with respect to the dimensionless parameter $G\mu$. The blue shaded region represents the Planck2018 2-$\sigma$ bounds, while the yellow hatched region is excluded by the NANOGrav 15-year data bound on $G\mu$. The red cutoff on the right corresponds to the third advanced LVK bound on $G\mu$.


Behavior of the non-minimal coupling $\kappa_S$ (left) and the tensor-to-scalar ratio $r$ (right) with respect to the dimensionless parameter $G\mu$. The blue shaded region represents the Planck2018 2-$\sigma$ bounds, while the yellow hatched region is excluded by the NANOGrav 15-year data bound on $G\mu$. The red cutoff on the right corresponds to the third advanced LVK bound on $G\mu$.

Behavior of the non-minimal coupling $\kappa_S$ (left) and the tensor-to-scalar ratio $r$ (right) with respect to the dimensionless parameter $G\mu$. The blue shaded region represents the Planck2018 2-$\sigma$ bounds, while the yellow hatched region is excluded by the NANOGrav 15-year data bound on $G\mu$. The red cutoff on the right corresponds to the third advanced LVK bound on $G\mu$.


Behavior of the RHN mass $M_N$ (left) and the inflaton mass $m_{\text{inf}}$ (right) with respect to the symmetry-breaking scale $M$. The blue shaded region represents the Planck2018 2-$\sigma$ bounds, while the yellow hatched region is excluded by the NANOGrav 15-year data bound on $G\mu$. The red cutoff on the right corresponds to the third advanced LVK bound on $G\mu$.

Behavior of the RHN mass $M_N$ (left) and the inflaton mass $m_{\text{inf}}$ (right) with respect to the symmetry-breaking scale $M$. The blue shaded region represents the Planck2018 2-$\sigma$ bounds, while the yellow hatched region is excluded by the NANOGrav 15-year data bound on $G\mu$. The red cutoff on the right corresponds to the third advanced LVK bound on $G\mu$.


Breaking patterns of the Pati-Salam gauge symmetry $G_{422}$ down to the standard model gauge symmetry $G_{\text{SM}}$.

Breaking patterns of the Pati-Salam gauge symmetry $G_{422}$ down to the standard model gauge symmetry $G_{\text{SM}}$.


 : $ QQ(U^cE^c)^\dagger$

: $ QQ(U^cE^c)^\dagger$


 : $ QL(U^cD^c)^\dagger$ : Four fermion LLRR chirality non-flipping dimension six proton decay operators mediated via color triplets $d_H$, $\bar{d}_H$.

: $ QL(U^cD^c)^\dagger$ : Four fermion LLRR chirality non-flipping dimension six proton decay operators mediated via color triplets $d_H$, $\bar{d}_H$.


Predictions of proton lifetime for various decay channels, potentially observable in the next-generation of experiments such as Hyper Kamiokande and DUNE.

Predictions of proton lifetime for various decay channels, potentially observable in the next-generation of experiments such as Hyper Kamiokande and DUNE.


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