Sneutrino Tribrid Inflation, Metastable Cosmic Strings and Gravitational Waves

We present a successful realization of sneutrino tribrid inflation model based on a gauged $U(1)_{B-L}$ extension of Minimal Supersymmetric Standard Model (MSSM). A single interaction term involving the $B-L$ Higgs field and the right-handed neutrinos serves multiple purposes. These include the generation of heavy Majorana masses for the right-handed neutrinos to provide an explanation for the tiny neutrino masses via the seesaw mechanism, a realistic scenario for reheating and non-thermal leptogenesis with a reheat temperature as low as $10^6$ GeV, and a successful realization of inflation with right-handed sneutrino as the inflaton. The matter parity which helps avoid rapid proton decay survives as a $Z_{2}$ subgroup of a $U(1)$ $R$-symmetry. Depending on the choice of model parameters yields the following predicted range of the tensor to scalar ratio, $3 times 10^{-11}lesssim rlesssim 7times 10^{-4}$ ($ 6 times 10^{-7} lesssim r lesssim 0.01 $), and the running of the scalar spectral index, $-0.00022 lesssim dn_s/dln k lesssim -0.0026$ ($-0.00014 lesssim dn_s/dln k lesssim 0.005$), along with the $B-L$ breaking scale, $ 3 times 10^{14}lesssim M/ text{GeV}lesssim 5 times 10^{15}$ ($ 6 times 10^{15}lesssim M/ text{GeV}lesssim 2 times 10^{16}$), calculated at the central value of the scalar spectral index, $n_s =0.966$, reported by Planck 2018. The possibility of realizing metastable cosmic strings in a grand unified theory setup is briefly discussed. The metastable cosmic string network admits string tension values in the range $10^{-8} lesssim Gmu_s lesssim 10^{-6}$, and predicts a stochastic gravitational wave background lying within the 2-$sigma$ bounds of the recent NANOGrav 12.5-yr data.

Observable Proton Decay in Flipped SU(5)

We explore proton decay in a class of realistic supersymmetric flipped $SU(5)$ models supplemented by a $U(1)_R$ symmetry which plays an essential role in implementing hybrid inflation. Two distinct neutrino mass models, based on inverse seesaw and type I seesaw, are identified, with the latter arising from the breaking of $U(1)_R$ by nonrenormalizable superpotential terms. Depending on the neutrino mass model an appropriate set of intermediate scale color triplets from the Higgs superfields play a key role in proton decay channels that include $p rightarrow (e^{+},mu^+), pi^0$, $p rightarrow ( e^+,mu^{+}), K^0 $, $p rightarrow overline{ u}, pi^{+}$, and $p rightarrow overline{ u}, K^+ $. We identify regions of the parameter space that yield proton lifetime estimates which are testable at Hyper-Kamiokande and other next generation experiments. We discuss how gauge coupling unification in the presence of intermediate scale particles is realized, and a $Z_4$ symmetry is utilized to show how such intermediate scales can arise in flipped $SU(5)$. Finally, we compare our predictions for proton decay with previous work based on $SU(5)$ and flipped $SU(5)$.

Proton Decay in Supersymmetric $SU(4)_c times SU(2)_L times SU(2)_R$

We discuss proton decay in a recently proposed model of supersymmetric hybrid inflation based on the gauge symmetry $SU(4)_c times SU(2)_L times SU(2)_R$. A $U(1), R$ symmetry plays an essential role in realizing inflation as well as in eliminating some undesirable baryon number violating operators. Proton decay is primarily mediated by a variety of color triplets from chiral superfields, and it lies in the observable range for a range of intermediate scale masses for the triplets. The decay modes include $p rightarrow e^{+}(mu^+) + pi^0$, $p rightarrow bar{ u} + pi^{+}$, $p rightarrow K^0 + e^+(mu^{+})$, and $p rightarrow K^+ + bar{ u}$, with a lifetime estimate of order $10^{34}-10^{36}$ yrs and accessible at Hyper-Kamiokande and future upgrades. The unification at the Grand Unified Theory (GUT) scale $M_{rm GUT}$ ($sim 10^{16}$ GeV) of the Minimal Supersymmetric Standard Model (MSSM) gauge couplings is briefly discussed.

Shifted $mu$-hybrid inflation, gravitino dark matter, and observable gravity waves

We investigate supersymmetric hybrid inflation in a realistic model based on the gauge symmetry $SU(4)_c times SU(2)_L times SU(2)_R$. The minimal supersymmetric standard model (MSSM) $mu$ term arises, following Dvali, Lazarides, and Shafi, from the coupling of the MSSM electroweak doublets to a gauge singlet superfield which plays an essential role in inflation. The primordial monopoles are inflated away by arranging that the $SU(4)_c times SU(2)_L times SU(2)_R$ symmetry is broken along the inflationary trajectory. The interplay between the (above) $mu$ coupling, the gravitino mass, and the reheating following inflation is discussed in detail. We explore regions of the parameter space that yield gravitino dark matter and observable gravity waves with the tensor-to-scalar ratio $r sim 10^{-4}-10^{-3}$.

Pseudosmooth Tribrid Inflation in $SU(5)$

A realistic tribrid model of sneutrino inflation is constructed in an $R$-symmetric $SU(5)$ grand unified theory (GUT). To avoid the monopole problem, a pseudosmooth inflationary trajectory is generated with the help of an additional $Z_5$ symmetry which is broken during and after inflation. The predictions of inflationary parameters are made at the central value of the scalar spectral index, $n_s =0.968$. The largest possible value of the tensor to scalar ratio, $rlesssim 0.0027$, is obtained with sub-Planckian field values ($lesssim m_P$). A successful realization of reheating and leptogenesis is achieved by avoiding the gravitino problem with a reheat temperature as low as $10^6$ GeV. The predicted range of the gauge symmetry breaking scale, $ 5 times 10^{16} lesssim M/text{GeV} lesssim 5 times 10^{17}$, turns out to be somewhat larger than the typical GUT scale. With additional vector-like families, a successful gauge coupling unification is achieved by avoiding the no-go theorem related to $R$-symmetric $SU(5)$ GUT.

New Inflation in Supersymmetric SU(5) and Flipped SU(5) GUT Models

We study the feasibility of realizing supersymmetric new inflation model, introduced by Senoguz and Shafi in [1], for $SU(5)$ and flipped $SU(5)$ models of grand unified theories (GUTs). This realization requires an additional $U(1)_R times Z_{n}$ symmetry for its successful implementation. The standard model (SM) gauge singlet scalar components of $24_H$ and $10_H$ GUT Higgs superfields are respectively employed to realize successful inflation in $SU(5)$ and flipped $SU(5)$ models. The predictions of the various inflationary observables lie within the recent Planck bounds on the scalar spectral index, $n_s$, for $n geq 5$ in $SU(5)$ model and for $n geq 6$ in flipped $SU(5)$ model. In particular, the tensor to scalar ratio $r$ and the running of spectral index $d n_s/ dln k$ are negligibly small and lie in the range, $10^{-12} lesssim r lesssim 10^{-8}$ and $10^{-9} lesssim dn_s/dln k lesssim 10^{-3}$, for realistic values of $n$. In numerical estimation of the various predictions, we fix the gauge symmetry breaking scale, $M$, around $2 times 10^{16}$ GeV. The issue of gauge coupling unification in $R$-symmetric $SU(5)$ is evaded by adding vectorlike families with mass splitting within their multiplets. The dilution of monopoles beyond the observable limit is naturally achieved in the breaking of $SU(5)$ gauge symmetry during inflation. A realistic scenario of reheating with non-thermal leptogenesis is employed for both models. The predicted range of reheat temperature within Planck bounds, $3 times 10^{7}text{ GeV }lesssim T_r lesssim 2 times 10^{9}$ GeV, is safe from the gravitino problem for the gravitino mass, $m_{3/2} gtrsim 10$ TeV. Finally, the $U(1)_R times Z_{n}$ symmetry is also observed to play a crucial role in suppressing the various fast proton decay operators.

Gravity Waves and Proton Decay in Flipped SU(5) Hybrid Inflation Model

We revisit supersymmetric hybrid inflation in the context of flipped $SU(5)$ model. With minimal superpotential and minimal Kahler potential, and soft SUSY masses of order $(1 - 100)$ TeV, compatibility with the Planck data yields a symmetry breaking scale $M$ of flipped $SU(5)$ close to $(2 - 4) times 10^{15}$ GeV. This disagrees with the lower limit $M gtrsim 7 times 10^{15}$ GeV set from proton decay searches by the Super-Kamiokande collaboration. We show how $M$ close to the unification scale $2times 10^{16}$ GeV can be reconciled with SUSY hybrid inflation by employing a non-minimal Kahler potential. Proton decays into $e^+ pi^0$ with an estimated lifetime of order $10^{36}$ years. The tensor to scalar ratio $r$ in this case can approach observable values $sim 10^{-4} - 10^{-3}$.

$mu$-Hybrid Inflation with Low Reheat Temperature and Observable Gravity Waves

In $mu$-hybrid inflation a nonzero inflaton vacuum expectation value induced by supersymmetry breaking is proportional to the gravitino mass $m_{3/2}$, which can be exploited to resolve the minimal supersymmetric standard model $mu$ problem. We show how this scenario can be successfully implemented with $m_{3/2} sim 1-100$ TeV and reheat temperature as low as $10^6$ GeV by employing a minimal renormalizable superpotential coupled with a well defined non-minimal Kahler potential. The tensor-to-scalar ratio $r$, a canonical measure of primordial gravity waves in most cases is less than or of the order of $10^{-6}-10^{-3}$.

Quantum Smearing in Hybrid Inflation with Chaotic Potentials

We study the impact of one-loop radiative corrections in a non-supersymmetric model of hybrid inflation with chaotic (polynomial-like) potential, $V_0 + lambda_p phi^p$. These corrections can arise from the possible couplings of inflaton with other fields which may play active role in the reheating process. The tree-level predictions of these models are shown to lie outside of the Plancks latest bounds on the scalar spectral index $n_s$ and the tensor to scalar ratio $r$. However, the radiatively corrected version of these models, $ V_0 + lambda_p phi^p + A phi^4 ln phi$, is fully consistent with the Plancks data. More specifically, fermionic radiative correction ($A<0$) reduces the tensor to scalar ratio significantly and a red-tilted spectral index $n_s<1$, consistent with Plancks data, is obtained even for sub-Planckian field-values.

Simplified Smooth Hybrid Inflation in Supersymmetric SU(5)

A scheme of simplified smooth hybrid inflation is realized in the framework of supersymmetric $SU(5)$. The smooth model of hybrid inflation provides a natural solution to the monopole problem that appears in the breaking of $SU(5)$ gauge symmetry. The supergravity corrections with nonminimal Kahler potential are shown to play important role in realizing inflation with a red-tilted scalar spectral index $n_s <1$, within Plancks latest bounds. As compared to shifted model of hybrid inflation, relatively large values of the tensor-to-scalar ratio $r lesssim 0.01$ are achieved here, with nonminimal couplings $-0.05 lesssim kappa_S lesssim 0.01$ and $-1 lesssim kappa_{SS} lesssim 1$ and the gauge symmetry-breaking scale $M simeq (2.0 - 16.7) times 10^{16}$ GeV.