Observational Constraints on Gauge Field Production in Axion Inflation

TL;DR

This work investigates observational constraints on gauge-field production in axion inflation with a shift-symmetric $\phi F\tilde{F}$ coupling. It derives a modified scalar power spectrum $\Delta_{\mathcal{R}}^2(k)=\Delta_{\mathcal{R},\mathrm{sr}}^2(k)[1+\Delta_{\mathcal{R},\mathrm{sr}}^2(k)f_2(\xi)e^{4\pi\xi}]$ and a bispectrum from inverse decay, then confronts these predictions with WMAP7 and ACT data, plus spectral distortions and Planck forecasts. The leading constraint arises from the CMB power spectrum, with bounds on $\xi_*$ around 2.2–2.5 depending on priors and model (quadratic vs generic). A generalized, massive gauge-field scenario can yield appreciable local non-Gaussianity if the accompanying Higgs-like field is light, while future Planck/ACTPol data promise tighter constraints or a potential detection of a nonzero gauge-field production signal.

Abstract

Models of axion inflation are particularly interesting since they provide a natural justification for the flatness of the potential over a super-Planckian distance, namely the approximate shift-symmetry of the inflaton. In addition, most of the observational consequences are directly related to this symmetry and hence are correlated. Large tensor modes can be accompanied by the observable effects of a the shift-symmetric coupling $φF\tilde F$ to a gauge field. During inflation this coupling leads to a copious production of gauge quanta and consequently a very distinct modification of the primordial curvature perturbations. In this work we compare these predictions with observations. We find that the leading constraint on the model comes from the CMB power spectrum when considering both WMAP 7-year and ACT data. The bispectrum generated by the non-Gaussian inverse-decay of the gauge field leads to a comparable but slightly weaker constraint. There is also a constraint from mu-distortion using TRIS plus COBE/FIRAS data, but it is much weaker. Finally we comment on a generalization of the model to massive gauge fields. When the mass is generated by some light Higgs field, observably large local non-Gaussianity can be produced.

Figures (13)

• Figure 1: The plot shows the primordial scalar power spectrum including Silk damping at three different times. More specifically we plot $\Delta_{\mathcal{R}}^{2}(k) e^{-k^{2}/k_{D}^{2}(z)}$ for $z=1100,\,5\times 10^{4},\,2\times 10^{6}$. Measurements of $\mu$-distortion are sensitive to the red region on the right side, i.e. much smaller scales than those probed by large scale structures and temperature anisotropies (on the left). Figure taken from Pajer:2012vz.
• Figure 2: The plot shows $\mu$ as function of $\xi_{\ast}$. $\mu<6\times 10^{-5}$ is the $95\%$ CL exclusion contours from the combination of TRIS tris and COBE/FIRAS cobe, while from forecasts of the PIXIE experiment Kogut:2011xw one gets $\mu<2 \times 10^{-8}$ at $95\%$ CL.
• Figure 3: As function of $\xi_{\ast}$, the plot shows $f^{ id}_{NL}$ (continuous black line) and the likelihood produced by the constraints on non-Gaussianity (dashed red line). For $\xi_{\ast}<2.4$, $f^{ id}_{NL}\sim0$ and the likelihood is completely flat. For $\xi_{\ast}\gtrsim 2.7$, $f^{ id}_{NL}\gg100$ and the likelihood drops to zero. The small peak corresponds to $f^{ id}_{NL}=12$ (thin dashed line), which is the central value for equilateral non-Gaussianity rescaled by the fudge factor in \ref{['fudge']}.
• Figure 4: The primordial power spectrum for $\xi_*=0,2.68,2.8,3$ for a quadratic potential.
• Figure 5: The late time spectrum for $\xi_*=0,2.68,2.8,3$ and using for all the other parameters the best fit values of $\Lambda$CDM (obtained for $\xi_{\ast}=0$). We also show the binned data points and errors (systematic and cosmic variance).