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 × 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 ≥ 5 in SU(5) model and for n ≥ 6 in flipped SU(5) model. In particular, the tensor to scalar ratio r and the running of spectral index dn s /d ln k are negligibly small and lie in the range, 10 −12 r 10 −8 and 10 −9 dn s /d ln k 10 −3 , for realistic values of n. In numerical estimation of the various predictions, we fix the gauge symmetry breaking scale, M , around 2 × 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 × 10 7 GeV T r 2 × 10 9 GeV, is safe from the gravitino problem for the gravitino mass, m 3/2 10 TeV. Finally, the U(1) R × Z n symmetry is also observed to play a crucial role in suppressing the various fast proton decay operators.

A supersymmetric hybrid inflation framework is employed to realize a class of non-minimal inflation models with U (1) R × Z n global symmetry. This framework naturally incorporates models based on grand unified theories by avoiding the most commonly faced monopole problem. The predictions of inflationary observables, the scalar spectral index n s = 0.960 − 0.966 and the tensor to scalar ratio r = 0.0031 − 0.0045, are in perfect agreement with the Planck 2018 data. For sub-Planckian values of the field the Z n symmetry is only allowed for n ≤ 4.

We have realized non-minimal Higgs inflation and standard hybrid inflation in the supersymmetric flipped SU(5) model with U(1) R symmetry using the no-scale form of the Kähler potential. In non-minimal Higgs inflation the waterfall Higgs field plays the role of inflaton, and in standard hybrid inflation the gauge singlet field S is employed as an inflaton. The predictions of both models are in good agreement with the Planck 2018 data. For numerical calculations we have fixed the gauge symmetry breaking scale, M, around 2 × 1016 GeV. In both models the inflaton field values are constrained below mP . The tensor to scalar ratio r in non-minimal inflation is of the order of 10-3 and for standard hybrid inflation r is tiny, of order 10-15–10-4. The scalar spectral index in both cases lie within the Planck 1-σ bounds, and the running of the scalar spectral index lies in the range, -dns /d ln k ∼ 6 × 10-4 for non-minimal model and 10-9–10-3 for the standard hybrid model. A realistic scenario of reheating and non-thermal leptogenesis is employed with reheat temperature Tr  ∼ 109 GeV for non-minimal model and 106–1010 GeV for standard hybrid model. The R-symmetry plays a vital role in forbidding rapid proton decay, but at the same time it also suppresses terms responsible for generating right handed neutrino masses. A realistic scenario of right handed neutrino masses is obtained by considering effective R symmetry breaking at the nonrenormalizable level with adequate suppression of rapid proton decay.