Stability analysis of chromo-natural inflation and possible evasion of Lyth's bound

Abstract

We perform the complete stability study of the model of chromo-natural inflation (Adshead and Wyman '12), where, due to its coupling to a SU(2) vector, a pseudo-scalar inflaton chi slowly rolls on a steep potential. As a typical example, one can consider an axion with a sub-Planckian decay constant f. The phenomenology of the model was recently studied (Dimastrogiovanni, Fasiello, and Tolley '12) in the m_g >> H limit, where m_g is the mass of the fluctuations of the vector field, and H the Hubble rate. We show that the inflationary solution is stable for m_g > 2 H, while it otherwise experiences a strong instability due to scalar perturbations in the sub-horizon regime. The tensor perturbations are instead standard, and the vector ones remain perturbatively small. Depending on the parameters, this model can give a gravity wave signal that can be detected in ongoing or forthcoming CMB experiments. This detection can occur even if, during inflation, the inflaton spans an interval of size Delta chi = O (f) which is some orders of magnitude below the Planck scale, evading a well known bound that holds for a free inflaton (Lyth '97).

Figures (4)

• Figure 1: Evolution of $\dot{\chi}$ during inflation for four different values of $y$. The other parameters are $\lambda = 500$ and $f=10^{-2} M_p$. The evolutions shown correspond to $60$ e-folds of inflation.
• Figure 2: Time evolution of the power (normalized to one at the initial time shown), for a mode that leaves the horizon $60$ e-folds before the end of inflation, and for the same background evolutions shown in Figure \ref{['fig:bck']}.
• Figure 3: Power spectra for $\lambda = 500$ and three different values of $y$. The spectral index (defined as $P_\zeta \propto k^{n_s-1}$) is $n_s \simeq 0.81$ for $y=1$, $n_s \simeq 0.92$ for $y=0.4$ and $n_s \simeq 0.96$ for $y=0.1$.
• Figure 4: Red/solid curve: Value of $\Delta \chi$ and $r$ obtained for $f = 0.01 M_p$ and $\lambda = 500$, and for different choices of $y$ in the $0.35 < y < 0.7$ interval (successive points along the curve denote $0.05$ increments in $y$); black/dotted vertical line: $r<0.13$ bound from Hinshaw:2012fq; the other black/dotted curves are the $1 \sigma$ detection lines for the Planck (P), SPIDER (S), CMB-Pol (C), and a cosmic-variance limited (CV) experiment. The signal needs to be above a line to be detectable at $1 \sigma$ by that experiment. These experimental forecasts are an approximate copy of the lines shown in Figure 2 of Gluscevic:2010vv.