We consider inflationary models with the inflaton coupled to the Gauss-Bonnet term assuming a special relation δ 1 = 2λ 1 between the two slow-roll parameters δ 1 and 1 . For the slow-roll inflation, the assumed relation leads to the reciprocal relation between the Gauss-Bonnet coupling function ξ(φ) and the potential V (φ), and it leads to the relation r = 16(1 − λ) 1 that reduces the tensor-to-scalar ratio r by a factor of 1 − λ. For the constant-roll inflation, we derive the analytical expressions for the scalar and tensor power spectra, the scalar and tensor spectral tilts, and the tensor-to-scalar ratio to the first order of 1 by using the method of Bessel function approximation.The tensor-to-scalar ratio is reduced by a factor of 1 − λ + λη. Comparing the derived n s -r with the observations, we obtain the constraints on the model parametersη and λ. *

In the large extra dimensional braneworld inflation, Friedmann equation is modified to include a quadratic term in energy density with an additional parameter λ called brane tension in addition to the usual linear term. The high energy brane corrections modify the slow-roll parameters and affect the behaviour of inflation. We analyse the superconformal inflation for E-models and find that there exist α-attractors in brane inflation. The predictions for the scalar spectral index n s and the tensor-to-scalar ratio r are computed numerically, and approximate analytic formulas in the high energy limit have been given for the observable n s and r. The constraints on the model parameters are obtained by using Planck 2018 and BICEP2 observational data.

No abstract

A supersymmetric Pati-Salam model with wrapping number equal to 5 has been constructed in Type IIA orientifolds on T6/(ℤ2× ℤ2) with intersecting D6-branes recently. In particular, the string-scale gauge coupling unification can be achieved due to the intermediate-scale vector-like particles from $$ \mathcal{N} $$ N = 2 sector. We calculate the supersymmetry breaking soft terms, and study the Standard Model (SM) fermion masses and mixings. There are nine pairs of Higgs doublets from $$ \mathcal{N} $$ N = 2 sector. Interestingly, we can explain the SM quark masses and mixings, as well as the charged leptons masses from three point and four-point Yukawa interactions. Moreover, we calculate the supersymmetry breaking soft terms in a previous model with gauge coupling unification since we find a typo in the previous study.

We consider a class of helical phase inflation models from the N=1 supergravity where the phase component of a complex field acts as an inflaton. This class of models avoids the eta problem in supergravity inflation due to the phase monodromy of the superpotential. We study the inflationary predictions of this class of models in the context of both standard and large extra dimensional brane cosmology, and find that they can easily accommodate the Planck 2018 and BICEP2 constraints. We find that the helical phase inflation has α-attractors and the attractors depend on one model parameter only.