A Minimal Sub-Planckian Axion Inflation Model with Large Tensor-to-Scalar Ratio

We present a minimal axion inflation model which can generate a large tensor-to-scalar ratio while remaining sub-Planckian. The modulus of a complex scalar field $\Phi$ with a $\lambda |\Phi|^4$ potential couples directly to the gauge field of a strongly-coupled sector via a term of the form $(|\Phi|/M_{Pl})^{m} F \tilde{F}$. This generates a minimum of the potential which is aperiodic in the phase. The resulting inflation model is equivalent to a $\phi^{4/(m+1)}$ chaotic inflation model. For the natural case of a leading-order portal-like interaction $\Phi^{\dagger}\Phi F \tilde{F}$, the model is equivalent to a $\phi^{4/3}$ chaotic inflation model and predicts a tensor-to-scalar ratio $r = 16/3N = 0.097$ and a scalar spectral index $n_{s} = 1-5/3N = 0.970$. The value of $|\Phi|$ remains sub-Planckian throughout the observable era of inflation, with $|\Phi| \lesssim 0.01 M_{Pl}$ for $N \lesssim 60$ when $\lambda \sim 1$.Comment: One minor alteration. Version to be published in JCA

Enhanced Dark Matter Annihilation Rate for Positron and Electron Excesses from Q-ball Decay

We show that Q-ball decay in Affleck-Dine baryogenesis models can account for dark matter when the annihilation cross-section is sufficiently enhanced to explain the positron and electron excesses observed by PAMELA, ATIC and PPB-BETS. For Affleck-Dine baryogenesis along a d = 6 flat direction, the reheating temperature is approximately 30 GeV and the Q-ball decay temperature is in the range 10-100 MeV. The LSPs produced by Q-ball decay annihilate down to the observed dark matter density if the cross-section is enhanced by a factor ~ 10^3 relative to the thermal relic cross-section.Comment: 4 pages, version to be published in Physical Review Letter

Hemispherical Power Asymmetry from a Space-Dependent Component of the Adiabatic Power Spectrum

The hemispherical power asymmetry observed by Planck and WMAP can be interpreted as due to a spatially-varying and scale-dependent component of the adiabatic power spectrum. We derive general constraints on the magnitude and scale-dependence of a component with a dipole spatial variation. The spectral index and the running of the spectral index can be significantly shifted from their inflation model values, resulting in a smaller spectral index and a more positive running. A key prediction is a hemispherical asymmetry of the spectral index and of its running. Measurement of these asymmetries can test the structure of the perturbation responsible for the CMB power asymmetry.Comment: 5 pages. Additional discussion, improved observational bound on the scale-dependence of the asymmetry. Version to be publishe

Sub-Planckian Two-Field Inflation Consistent with the Lyth Bound

The BICEP2 observation of a large tensor-to-scalar ratio, $r = 0.20^{+0.07}_{-0.05}$, implies that the inflaton $\phi$ in single-field inflation models must satisfy $\phi \sim 10M_{Pl}$ in order to produce sufficient inflation. This is a problem if interaction terms suppressed by the Planck scale impose a bound \phi \; ^{<}_{\sim} \; M_{Pl}. Here we consider whether it is possible to have successful sub-Planckian inflation in the case of two-field inflation. The trajectory in field space cannot be radial if the effective single-field inflaton is to satisfy the Lyth bound. By considering a complex field $\Phi$, we show that a near circular but aperiodic modulation of a $|\Phi|^{4}$ potential can reproduce the results of $\phi^2$ chaotic inflation for $n_{s}$ and $r$ while satisfying |\Phi|\; ^{<}_{\sim} \; 0.01 M_{Pl} throughout. More generally, for models based on a $|\Phi|^{4}$ potential, the simplest sub-Planckian models are equivalent to $\phi^{2}$ and $\phi^{4/3}$ chaotic inflation.Comment: 7 pages, 2 figures. Some additional references and discussion. Version published in JCA

Explaining the Dark Energy, Baryon and Dark Matter Coincidence via Domain-Dependent Random Densities

The dark energy, dark matter and baryon densities in the Universe are observed to be similar, with a factor of no more than 20 between the largest and smallest densities. We show that this coincidence can be understood via superhorizon domains of randomly varying densities when the baryon density at initial collapse of galaxy-forming perturbations is determined by anthropic selection. The baryon and dark matter densities are assumed to be dependent on random variables \theta_{d} and \theta_{b} according to \rho_{dm} ~ \theta_{d}^{\alpha} and \rho_{b} ~ \theta_{b}^{\beta}, while the effectively constant dark energy density is dependent upon a random variable \phi_{Q} according to \rho_{Q} ~ \phi_{Q}^{n}. The ratio of the baryon density to the dark energy density at initial collapse, r_{Q}, and the baryon-to-dark matter ratio, r, are then determined purely statistically, with no dependence on the anthropically-preferred baryon density. We compute the probability distribution for r_{Q} and r and show that the observed values of r_{Q} and r can be naturally understood within this framework. In particular, for the case \alpha = 2, \beta = 1 and n = 4, which can be physically realized via a combination of axion dark matter, Affleck-Dine baryogenesis and frozen quintessence with a \phi_{Q}^4 potential, the range of r_{Q} and r which corresponds to the observed Universe is a quite natural, with a probability which is broadly similar to other ranges of r_{Q} and r.Comment: 9 pages, 6 figures, version to be published in JCA

Negative Running of the Spectral Index, Hemispherical Asymmetry and the Consistency of Planck with Large rr

Planck favours a negative running of the spectral index, with the likelihood being dominated by low multipoles $l \lesssim 50$ and no preference for running at higher $l$. A negative spectral index is also necessary for the 2-$\sigma$ Planck upper bound on the tensor-to-scalar ratio $r$ to be consistent with values significantly larger than 0.1. Planck has also observed a hemispherical asymmetry of the CMB power spectrum, again mostly at low multipoles. Here we consider whether the physics responsible for the hemispherical asymmetry could also account for the negative running of the spectral index and the consistency of Planck with a large value of $r$. A negative running of the spectral index can be generated if the hemispherical asymmetry is due to a scale- and space-dependent modulation which suppresses the CMB power spectrum at low multipoles. We show that the observed hemispherical asymmetry at low $l$ can be generated while satisfying constraints on the asymmetry at higher $l$ and generating a negative spectral index of the right magnitude to account for the Planck observation and to allow Planck to be consistent with a large value of $r$.Comment: 5 pages, 3 figures. Title altered to reflect changed status of BICEP2 result. Clarified discussion of results with new figures. Version to be published in JCA

Hemispherical Power Asymmetry from Scale-Dependent Modulated Reheating

We propose a new model for the hemispherical power asymmetry of the CMB based on modulated reheating. Non-Gaussianity from modulated reheating can be small enough to satisfy the bound from Planck if the dominant modulation of the inflaton decay rate is linear in the modulating field $\sigma$. $\sigma$ must then acquire a spatially-modulated power spectrum with a red scale-dependence. This can be achieved if the primordial perturbation of $\sigma$ is generated via tachyonic growth of a complex scalar field. Modulated reheating due to $\sigma$ then produces a spatially modulated and scale-dependent sub-dominant contribution to the adiabatic density perturbation. We show that it is possible to account for the observed asymmetry while remaining consistent with bounds from quasar number counts, non-Gaussianity and the CMB temperature quadupole. The model predicts that the adiabatic perturbation spectral index and its running will be modified by the modulated reheating component.Comment: 11 pages, references correcte

Signatures of Planck Corrections in a Spiralling Axion Inflation Model

The minimal sub-Planckian axion inflation model accounts for a large scalar-to-tensor ratio via a spiralling trajectory in the field space of a complex field $\Phi$. Here we consider how the predictions of the model are modified by Planck scale-suppressed corrections. In the absence of Planck corrections the model is equivalent to a $\phi^{4/3}$ chaotic inflation model. Planck corrections become important when the dimensionless coupling $\xi$ of $|\Phi|^{2}$ to the topological charge density of the strongly-coupled gauge sector $F \tilde{F}$ satisfies $\xi \sim 1$. For values of $|\Phi|$ which allow the Planck corrections to be understood via an expansion in powers of $|\Phi|^{2}/M_{Pl}^{2}$, we show that their effect is to produce a significant modification of the tensor-to-scalar ratio from its $\phi^{4/3}$ chaotic inflation value without strongly modifying the spectral index. In addition, to leading order in $|\Phi|^2/M_{Pl}^{2}$, the Planck modifications of $n_{s}$ and $r$ satisfy a consistency relation, $\Delta n_{s} = - \Delta r/16$. Observation of these modifications and their correlation would allow the model to be distinguished from a simple $\phi^{4/3}$ chaotic inflation model and would also provide a signature for the influence of leading-order Planck corrections.Comment: 9 pages. Minor alterations to text. Planck n_s and r values updated. Version to be published in JCA

Baryon-to-Dark Matter Ratio from Random Angular Fields

We consider the baryon-to-dark matter ratio in models where the dark matter and baryon densities depend on angular fields \theta_{d} and \theta_{b} according to \rho_{d} ~ \theta_{d}^{\alpha} and \rho_{b} ~ \theta_{b}^{\beta}, with all values of \theta_{d} and \theta_{b} being equally probable in a given randomly-selected domain. Under the assumption that anthropic selection depends primarily on the baryon density in galaxies at spherical collapse, we show that the probability density function for the baryon-to-dark matter ratio r = \Omega_{B}/\Omega_{DM} is purely statistical in nature and is independent of anthropic selection. We compute the probability density function for r as a function of \alpha and \beta and show that the observed value of the baryon-to-dark matter ratio, r \approx 1/5, is natural in this framework.Comment: 6 pages, 4 figures, version published in JCA