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Register a new userElliptic Inflation: Interpolating from natural inflation to $R^2$-inflation
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We propose an extension of natural inflation, where the inflaton potential is a general periodic function. Specifically, we study elliptic inflation where the inflaton potential is given by Jacobi elliptic functions, Jacobi theta functions or the Dedekind eta function, which appear in gauge and Yukawa couplings in the string theories compactified on toroidal backgrounds. We show that in the first two cases the predicted values of the spectral index and the tensor-to-scalar ratio interpolate from natural inflation to exponential inflation such as $R^2$- and Higgs inflation and brane inflation, where the spectral index asymptotes to $n_s = 1-2/N simeq 0.967$ for the e-folding number $N = 60$. We also show that a model with the Dedekind eta function gives a sizable running of the spectral index due to modulations in the inflaton potential. Such elliptic inflation can be thought of as a specific realization of multi-natural inflation, where the inflaton potential consists of multiple sinusoidal functions. We also discuss examples in string theory where Jacobi theta functions and the Dedekind eta function appear in the inflaton potential.
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We propose a novel scenario of inflation, in which the inflaton is identified as the lightest mode of an angular field in a compactified fifth dimension. The periodic effective potential exhibits exponentially flat plateaus, so that a sub-Planckian field excursion without hilltop initial conditions is naturally realized. We can obtain consistent predictions with observations on the spectral index and the tensor-to-scalar ratio.
We show that the recently proposed multi-natural inflation can be realized within the framework of 4D ${cal N}=1$ supergravity. The inflaton potential mainly consists of two sinusoidal potentials that are comparable in size, but have different periodicity with a possible non-zero relative phase. For a sub-Planckian decay constant, the multi-natural inflation model is reduced to axion hilltop inflation. We show that, taking into account the effect of the relative phase, the spectral index can be increased to give a better fit to the Planck results, with respect to the hilltop quartic inflation. We also consider a possible UV completion based on a string-inspired model. Interestingly, the Hubble parameter during inflation is necessarily smaller than the gravitino mass, avoiding possible moduli destabilization. Reheating processes as well as non-thermal leptogenesis are also discussed.
Motivated by recent cosmological observations of a possibly unsuppressed primordial tensor component $r$ of inflationary perturbations, we reanalyse in detail the 5D conformal SUGRA originated natural inflation model of Ref. [1]. The model is a supersymmetric variant of 5D extra natural inflation, also based on a shift symmetry, and leads to the potential of natural inflation. Coupling the bulk fields generating the inflaton potential via a gauge coupling to the inflaton with brane SM states we necessarily obtain a very slow gauge inflaton decay rate and a very low reheating temperature $T_rstackrel{<}{_sim }{cal O}(100)$~GeV. Analysis of the required number of e-foldings (from the CMB observations) leads to values of $n_s$ in the lower range of present Planck 2015 results. Some related theoretical issues of the construction, along with phenomenological and cosmological implications, are also discussed.
Weyl (scale) invariant theories of scalars and gravity can generate all mass scales spontaneously. In this paper we study a particularly simple version -- scale invariant $R^2$ gravity -- and show that, during an inflationary period, it leads to fluctuations which, for a particular parameter choice, are almost indistinguishable from normal $R^2$ inflation. Current observations place tight constraints on the primary coupling constant of this theory and predict a tensor to scalar ratio, $0.0033 > r > 0.0026$, which is testable with the next generation of cosmic microwave background experiments.
We revisit the recently proposed multi-natural inflation and its realization in supergravity in light of the BICEP2 results. Multi-natural inflation is a single-field inflation model where the inflaton potential consists of multiple sinusoidal functions, and it is known that a sizable running spectral index can be generated, which relaxes the tension between the BICEP2 and the Planck results. In this paper we show that multi-natural inflation can accommodate a wide range of values of $(n_s, r)$, including the spectral index close to or even above unity. This will be be favored if the tension is resolved by other sources such as dark radiation, hot dark matter, or non-zero neutrino mass. We also discuss the implications for the implementation in string theory.
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