Using analytic expressions, we explore the parameter space for hilltop inflation models with a potential of the form V0 ± m 2 φ 2 − aφ p . With the positive sign and p > 2 this converts the original hybrid inflation model into a hilltop model, allowing the spectral index to agree with the observed value n = 0.95. In some cases the observed value is theoretically favored, while in others there is only the generic prediction |n − 1| 1. PACS numbers:

The primordial black hole (PBH) formation is studied in light of the inflating curvaton. The typical scale of the PBH formation is determined by curvaton inflation, which may generate PBH with 10 14 g ≤ MPBH ≤ 10 38 g when curvaton inflation gives the number of e-foldings 5 ≤ N2 ≤ 38. The non-Gaussianity of the inflating curvaton does not prevent the PBH formation.

Supernatural inflation is an attractive model based just on a flat direction with soft SUSY breaking mass terms in the framework of supersymmetry. The beauty of the model is inferred from its name that the model needs no fine-tuning. However, the prediction of the spectral index is n s > ∼ 1, in contrast to experimental data. In this paper, we show that the beauty of supernatural inflation with the spectral index reduced to n s = 0.96 without any fine-tuning, by considering the general feature that a flat direction is lifted by a non-renormalizable term with an A-term.

We construct a model of cosmological inflation and perturbation based on the higherdimensional gauge theory. The inflaton and curvaton are the scalar fields arising from the extra space components of the gauge field living in more than four dimensions. We take the six-dimensional (6D) Yang-Mills theory compactified on T 2 as a toy model, and apply the one-loop effective potential of the inflaton and the curvaton to the curvaton scenario. We have found that the curvaton is subdominant for the linear curvature perturbation, but that a significant non-Gaussianity and a sizable tensor to scalar ratio are generated. It is possible to set a twisted boundary condition associated with a global U (1) symmetry with the phase α for this fermion. Here we set α = 0.

In this paper, we show that if passive fluctuations are considered, primordial black holes (PBHs) can be easily produced in the framework of single-field, slow-roll inflation models. The formation of PBHs is due to the blue spectrum of passive fluctuations and an enhancement of the spectral range which exits horizon near the end of inflation. Therefore the PBHs are light with masses 10 15 g depending on the number of e-folds when the scale of our observable universe leaves horizon. These PBHs are likely to have evaporated and cannot be a candidate for dark matter but they may still affect the early universe.

In this paper, we show that single-field chaotic inflation on the brane with the potential V = aφ p is compatible with the Swampland criteria. The spectral index and the running spectral index are within experimental bounds for 0 < p ≤ 2. The tensor to scalar ratio is within observational bounds if p O(1).

Supergravity corrections due to the energy density of a right-handed sneutrino can generate a negative mass squared for the inflaton, flattening the inflaton potential and reducing the spectral index and inflaton energy density. For the case of D-term hybrid inflation, we show that the spectral index can be lowered from the conventional value n = 0.98 to a value within the range favoured by the latest WMAP analysis, n = 0.951 +0.015 −0.019 . The modified energy density is consistent with non-observation of cosmic strings in the CMB if n < 0.946.The WMAP lower bound on the spectral index implies that the D-term cosmic string contribution may be very close present CMB limits, contributing at least 5% to the CMB multipoles.

The swampland criteria put significant constraints on inflation models. In this paper, I show that hilltop inflation on the brane may provide an initial condition for hilltop inflation and produce topological eternal inflation without violating the swampland distance and refined de Sitter criteria. This shows a way that string theory may not be incompatible with eternal inflation.