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 $n\ge 5$ in $SU(5)$ model and for $n\ge 6$ in flipped $SU(5)$ model. In particular, the tensor to scalar ratio $r$ and the running of spectral index $d{n}_s\mathrm{/}d\ln k$ are negligibly small and lie in the range, ${10}^{-12}\lesssim r\lesssim {10}^{-8}$ and $10^{-9} \lesssim dn_s/d\ln k \lesssim 10^{-3}$,forrealisticvaluesof$n$. In numerical estimation of the various predictions, we fix the gauge symmetry breaking scale, $M$, around $2 \times 10^{16}$GeV\mathrm{.}Theissueofgaugecouplingunificationin$R$-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, $m_{3\mathrm{/}2}\gtrsim 10$ 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.