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Register a new userSimplified Smooth Hybrid Inflation in Supersymmetric SU(5)
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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.
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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.
We consider the extended supersymmetric Pati-Salam model which, for mu>0 and universal boundary conditions, succeeds to yield experimentally acceptable b-quark masses by moderately violating Yukawa unification. It is known that this model can lead to new shifted or new smooth hybrid inflation. We show that a successful two-stage inflationary scenario can be realized within this model based only on renormalizable superpotential interactions. The cosmological scales exit the horizon during the first stage of inflation, which is of the standard hybrid type and takes place along the trivial flat direction with the inflaton driven by radiative corrections. Spectral indices compatible with the recent data can be achieved in global supersymmetry or minimal supergravity by restricting the number of e-foldings of our present horizon during the first inflationary stage. The additional e-foldings needed for solving the horizon and flatness problems are naturally provided by a second stage of inflation, which occurs mainly along the built-in new smooth hybrid inflationary path appearing right after the destabilization of the trivial flat direction at its critical point. Monopoles are formed at the end of the first stage of inflation and are, subsequently, diluted by the second stage of inflation to become utterly negligible in the present universe for almost all (for all) the allowed values of the parameters in the case of global supersymmetry (minimal supergravity).
We consider the extension of the supersymmetric Pati-Salam model which solves the b-quark mass problem of supersymmetric grand unified models with exact Yukawa unification and universal boundary conditions and leads to the so-called new shifted hybrid inflationary scenario. We show that this model can also lead to a new version of smooth hybrid inflation based only on renormalizable interactions provided that a particular parameter of its superpotential is somewhat small. The potential possesses valleys of minima with classical inclination, which can be used as inflationary paths. The model is consistent with the fitting of the three-year Wilkinson microwave anisotropy probe data by the standard power-law cosmological model with cold dark matter and a cosmological constant. In particular, the spectral index turns out to be adequately small so that it is compatible with the data. Moreover, the Pati-Salam gauge group is broken to the standard model gauge group during inflation and, thus, no monopoles are formed at the end of inflation. Supergravity corrections based on a non-minimal Kaehler potential with a convenient choice of a sign keep the spectral index comfortably within the allowed range without generating maxima and minima of the potential on the inflationary path. So, unnatural restrictions on the initial conditions for inflation can be avoided.
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 $sim 10^{-4} - 10^{-3}$.
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.
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