We point out that domain wall formation is a more common phenomenon in the Axiverse than previously thought. Level crossing could take place if there is a mixing between axions, and if some of the axions acquire a non-zero mass through non-perturbative effects as the corresponding gauge interactions become strong. The axion potential changes significantly during the level crossing, which affects the axion dynamics in various ways. We find that, if there is a mild hierarchy in the decay constants, the axion starts to run along the valley of the potential, passing through many crests and troughs, until it gets trapped in one of the minima; the {it axion roulette}. The axion dynamics exhibits a chaotic behavior during the oscillations, and which minimum the axion is finally stabilized is highly sensitive to the initial misalignment angle. Therefore, the axion roulette is considered to be accompanied by domain wall formation. The cosmological domain wall problem can be avoided by introducing a small bias between the vacua. We discuss cosmological implications of the domain wall annihilation for baryogenesis and future gravitational wave experiments.
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.
We consider a possibility that one of the flat directions in the minimal supersymmetric standard model plays the role of the inflaton field and realizes large-field inflation. This is achieved by introducing a generalized shift symmetry on the flat direction, which enables us to control the inflaton potential over large field values. After inflation, higher order terms allowed by the generalized shift symmetry automatically cause a helical motion of the field to create the baryon number of the universe, while baryonic isocurvature fluctuations are suppressed.
We propose a landscape of many axions, where the axion potential receives various contributions from shift symmetry breaking effects. We show that the existence of the axion with a super-Planckian decay constant is very common in the axion landscape for a wide range of numbers of axions and shift symmetry breaking terms, because of the accidental alignment of axions. The effective inflation model is either natural or multi-natural inflation in the axion landscape, depending on the number of axions and the shift symmetry breaking terms. The tension between BICEP2 and Planck could be due to small modulations to the inflaton potential or steepening of the potential along the heavy axions after the tunneling. The total duration of the slow-roll inflation our universe experienced is not significantly larger than $60$ if the typical height of the axion potentials is of order $(10^{16-17}{rm ,GeV})^4$.
The most naive interpretation of the BICEP2 data is the chaotic inflation by an inflaton with a quadratic potential. When combined with supersymmetry, we argue that the inflaton plays the role of right-handed scalar neutrino based on rather general considerations. The framework suggests that the right-handed sneutrino tunneled from a false vacuum in a landscape to our vacuum with a small negative curvature and suppressed scalar perturbations at large scales.
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.
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.
We consider a simple class of models where dark radiation has self-interactions and therefore does not free stream. Such dark radiation has no anisotropic stress (or viscosity), leaving a distinct signature on the CMB angular power spectrum. Specifically we study a possibility that hidden gauge bosons and/or chiral fermions account for the excess of the effective number of neutrino species. They have gauge interactions and remain light due to the unbroken hidden gauge symmetry, leading to Delta N_{rm eff} simeq 0.29 in some case.
We propose a novel mechanism to suppress the isocurvature perturbations of the QCD axion. The point is that the QCD interactions become strong at an intermediate or high energy scale in the very early Universe, if the Higgs field has a sufficiently large expectation value. The effective QCD scale can be even higher in the presence of extra colored particles. We show that the QCD axion then becomes so heavy during inflation that its isocurvature perturbations are significantly suppressed, thereby relaxing the constraint on the inflation scale.
The baryon-dark matter coincidence is a long-standing issue. Interestingly, the recent observations suggest the presence of dark radiation, which, if confirmed, would pose another coincidence problem of why the density of dark radiation is comparable to that of photons. These striking coincidences may be traced back to the dark sector with particle contents and interactions that are quite similar, if not identical, to the standard model: a dark parallel world. It naturally solves the coincidence problems of dark matter and dark radiation, and predicts a sterile neutrino(s) with mass of ${cal O}(0.1 - 1)$,eV, as well as self-interacting dark matter made of the counterpart of ordinary baryons. We find a robust prediction for the relation between the abundance of dark radiation and the sterile neutrino, which can serve as the smoking-gun evidence of the dark parallel world.
