Supersymmetric hybrid inflation and current-carrying metastable cosmic strings in $SU(4)_c \times SU(2)_L \times U(1)_R$

TL;DR

This work presents a realistic supersymmetric model based on $SU(4)_c \times SU(2)_L \times U(1)_R$ that generates superheavy, current-carrying cosmic strings after inflation. It employs shifted $\mu$-hybrid inflation to inflate away monopoles while a late breaking $U(1)_{B-L} \times U(1)_R \to U(1)_Y$ yields strings with right-handed neutrino zero modes, producing a stochastic gravitational wave background compatible with PTA data and LIGO O3. The analysis includes two-loop RG evolution, nonminimal Kähler corrections in SUGRA, and a consistent reheating/leptogenesis setup with non-thermal leptogenesis and $T_r \sim 2 \times 10^9$ GeV. The resulting GW spectra, controlled by the string tension $G\mu_{\rm cs}$ and metastability parameter $\kappa_{\rm cs}$, can accommodate NANOGrav observations while satisfying CMB bounds, offering a concrete link between GUT-scale physics and current GW measurements at multiple frequencies.

Abstract

We construct a realistic supersymmetric model for superheavy metastable cosmic strings (CSs) that can be investigated in the current pulsar timing array (PTA) experiments. It is based on shifted $μ$-hybrid inflation in which the symmetry breaking $SU(4)_c \times SU(2)_L \times U(1)_R\rightarrow SU(3)_c\times SU(2)_L \times U(1)_{B-L}\times U(1)_R$ proceeds along an inflationary trajectory such that the topologically unstable primordial monopoles are inflated away. {{The breaking of $U(1)_{B-L} \times U(1)_R \rightarrow U(1)_Y$ after inflation ends yields the superheavy metastable CSs carrying the right handed neutrino zero modes that generate the stochastic gravitational wave background (SGWB), which we show is consistent with the current PTA data set and the LIGO O3 run}}. The scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$ are compatible with the Planck 2018 and Atacama Cosmology Telescope measurements. Both reheating and leptogenesis are briefly discussed.

Figures (4)

• Figure 1: Two loop RG evolution of the gauge couplings for the symmetries $SU(3)_c\times SU(2)_L \times U(1)_Y$, $U(1)_{B-L}$ and $SU(4)_c\times SU(2)_L \times U(1)_R$. Matching conditions at $v_{\text{str}}$ are $\alpha^{-1}_{1Y}=\sqrt{3/5}\ \alpha^{-1}_{1R}+\sqrt{2/5}\ \alpha^{-1}_{1(B-L)}$ and $\alpha^{-1}_{2L}=\alpha^{-1}_{2L}$, and at $v_m$, $\alpha^{-1}_{3c}=\alpha^{-1}_{4c}=\alpha^{-1}_{1(B-L)}$.
• Figure 2: Schematic display of shifted hybrid track for $\xi=0.3$. The two minima at $y_1=0$ and $y_2\simeq 2.3$, correspond to standard and shifted trajectory respectively.
• Figure 3: Two loop RG evolution of the gauge couplings for the symmetries $SU(3)_c\times SU(2)_L \times U(1)_Y$, $U(1)_{B-L}$ and $SU(4)_c\times SU(2)_L \times U(1)_R$ with an additional 15-plet and a pair of $H,\bar{H}$. With this additional content, we obtain $g_m \sim 2$.
• Figure 4: The GW spectra of the current carrying CSs for the benchmark points in \ref{['assign3']}. This not only explains the NANOGrav 15-year dataset for $G\mu_\text{cs}\simeq 10^{-6}\,(10^{-7})$ with $\sqrt{\kappa_\text{cs}}\simeq8.09\,(8.23)$ but is also consistent with the LIGO O3 run. The standard scenario has also been presented with the dashed lines. The colored shaded regions indicate the sensitivity curves of present (solid boundaries) LIGO O3 KAGRA:2021kbb, NANOGrav NANOGrav:2023gor, and future (dashed boundaries) SKA Smits:2008cf, THEIA Garcia-Bellido:2021zgu, LISA amaroseoane2017laser, ET Punturo:2010zz, BBO Corbin:2005ny, $\mu$-ARES Sesana:2019vho and CE Reitze:2019iox experiments.