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Non-Gaussianities and chiral gravitational waves in natural steep inflation

Mohamed M. Anber, Lorenzo Sorbo

TL;DR

This work analyzes non-Gaussianities and chiral gravitational waves in natural steep inflation, where an axion-like inflaton couples to ${\cal N}$ U(1) gauge fields via ${\cal L}_{\u03c6 F\tilde F}=\frac{\alpha}{f}\u03a\,F_{\mu\nu}\tilde F^{\mu\nu}$. Scalar perturbations are predominantly sourced by gauge-field fluctuations, giving a scalar power ${\cal P}_\zeta\simeq \frac{5\times 10^{-2}}{\xi^2\, {\cal N}}$ and equilateral non-Gaussianity ${f_{NL}^{\rm equil}}\approx -1.3\,\xi$, with ${\cal N}\,\xi^2\simeq 2\times 10^7$ to match observations, implying ${\cal N}\gtrsim 10^5$ for typical $\xi$ values. Tensor modes receive a significant contribution from the gauge-field gas, producing ${\cal P}^{t,L}$ and ${\cal P}^{t,R}$ that can yield $r$ in the range ${\cal O}(10^{-2})$ to ${\cal O}(0.1)$ even at low inflation scales, with the tensors being nearly fully chiral and yielding parity-violating CMB signatures. Non-observation of tensors places strong, scale-dependent bounds on $\alpha$ (roughly $\alpha\gtrsim 3\times 10^2$ to $10^4$), complementing potential Planck detections of $f_{NL}^{\rm equil}$; overall, the model predicts distinctive, testable signals in CMB polarization data and provides a concrete mechanism for inflation on a steep potential.

Abstract

In arXiv:0908.4089, we have proposed a model where natural inflation is realized on a steep potential as a consequence of the interaction of the inflaton with gauge fields through an axion-like coupling. In the present work we study the nongaussianities and the spectrum of tensor modes generated in this scenario. The nongaussianities turn out to be compatible with current observations and can be large enough to be detectable by Planck. The non-observation of tensor modes imposes new constraints on the parameter space of the system that are about one order of magnitude stronger than those found in our previous work. More importantly, in certain regions of the parameter space tensor modes might be detected by upcoming Cosmic Microwave Background experiments even if inflation occurs at energies as low as the TeV scale. In this case the tensor modes would be chiral, and would lead to distinctive parity-violating correlation functions in the CMB.

Non-Gaussianities and chiral gravitational waves in natural steep inflation

TL;DR

This work analyzes non-Gaussianities and chiral gravitational waves in natural steep inflation, where an axion-like inflaton couples to U(1) gauge fields via . Scalar perturbations are predominantly sourced by gauge-field fluctuations, giving a scalar power and equilateral non-Gaussianity , with to match observations, implying for typical values. Tensor modes receive a significant contribution from the gauge-field gas, producing and that can yield in the range to even at low inflation scales, with the tensors being nearly fully chiral and yielding parity-violating CMB signatures. Non-observation of tensors places strong, scale-dependent bounds on (roughly to ), complementing potential Planck detections of ; overall, the model predicts distinctive, testable signals in CMB polarization data and provides a concrete mechanism for inflation on a steep potential.

Abstract

In arXiv:0908.4089, we have proposed a model where natural inflation is realized on a steep potential as a consequence of the interaction of the inflaton with gauge fields through an axion-like coupling. In the present work we study the nongaussianities and the spectrum of tensor modes generated in this scenario. The nongaussianities turn out to be compatible with current observations and can be large enough to be detectable by Planck. The non-observation of tensor modes imposes new constraints on the parameter space of the system that are about one order of magnitude stronger than those found in our previous work. More importantly, in certain regions of the parameter space tensor modes might be detected by upcoming Cosmic Microwave Background experiments even if inflation occurs at energies as low as the TeV scale. In this case the tensor modes would be chiral, and would lead to distinctive parity-violating correlation functions in the CMB.

Paper Structure

This paper contains 10 sections, 43 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Natural steep inflation
  3. Generation of the gauge field
  4. The slow roll solution
  5. Perturbations
  6. The two-point function
  7. The three-point function
  8. Computation of the power spectrum and $f_{NL}$
  9. Gravitational waves
  10. Conclusions and discussion

Figures (2)

  • Figure 1: Evolution of background quantities for $\Lambda=10^{-3}\,M_P$, $f=0.1\,M_P$, $\alpha=300$ and ${\cal N}=10^5$. Left panel: evolution of $\xi(t)$. Right panel: the solid line correspond to the slow-roll parameter $\epsilon=-\dot{H}/H^2$, the dashed line gives the ratio of the energy in gauge modes over the energy in the inflaton. In the inset we plot the number of efoldings as a function of time. The time $t$ is in units of $M_P/\Lambda^2$.
  • Figure 2: Graphical representation of the correlation (\ref{['grand correlation function']}). The vertex (a) denotes the quantity ${\bf e}_+(\bf q)\cdot{\bf e}_+^*(\bf q-\bf k)\,{\cal I}(\tau,\,|\bf q|,\,|\bf q-\bf k|)$ as a function of the momenta $\bf q$ and $\bf q-\bf k$. Diagrams (b), and (c) are the two-point and three-point functions. Dashed lines are the scalar perturbations $\phi(\bf k)$.