Gauge field production in axion inflation: Consequences for monodromy, non-Gaussianity in the CMB, and gravitational waves at interferometers

Models of inflation based on axions, which owe their popularity to the robustness against uv corrections, have also a very distinct class of signatures. The relevant interactions of the axion are a nonperturbative oscillating contribution to the potential and a shift-symmetric coupling to gauge fields. We review how these couplings affect the cosmological perturbations via a unified study based on the in-in formalism. We then note that, when the inflaton coupling to gauge fields is high enough to lead to interesting observational results, the backreaction of the produced gauge quanta on the inflaton dynamics becomes relevant during the final stage of inflation, and prolongs its duration by about 10 e-foldings. We extend existing results on gravity wave production in these models to account for this late inflationary phase. The strong backreaction phase results in an enhancement of the gravity wave signal at the scales of interferometers. As a consequence, the signal is potentially observable at interferometers such as Advanced LIGO/Virgo for the most natural duration of inflation in such models. Finally, we explicitly compute the axion couplings to gauge fields in string theory construction of axion-monodromy inflation and identify cases where they can trigger interesting phenomenological effects.

Figure 1

Evolution of the inflaton as a function of the number of e-foldings to the end of inflation, starting from $|{\varphi }_{\mathrm{CMB}}|=-9.9M_p$, with (red solid line) and without (green dashed line) the coupling to gauge fields. For the first line, the strength of the inflaton-gauge field coupling is chosen so to lead to observable non-Gaussianity from inverse decay. For the second line, we have shifted the number of e-foldings to make manifest that the two evolutions coincide at early times.

Figure 2

Left panel: Friction terms in the equation of motion for $\varphi$. Right panel: relative strength of the energy density of the produced quanta; this term is neglected in the numerical evolution of the background equations.

Figure 3

Parameter space for axion-monodromy inflation with $V_{\mathrm{sr}}\cong {\mu }^3\phi$. The “TT(res)” regions give the (one- and two-sigma) likelihood contours for the temperature 2-point function. The “TTT(res)” regions give $f_{\mathrm{res}}=200$, 20, 2. The region to the left of each horizontal line is ruled out by observational constraints on $f_{\mathrm{NL}}^{\mathrm{equil}}$, for values of the coupling $\alpha =0.04$, 0.2, 1 (see Eq. (1)). The Figure has been adapted from 29 by adding the exclusion regions from $f_{\mathrm{NL}}^{\mathrm{equil}}$.

Figure 4

The left panel shows the inverse decay non-Gaussianity as a function of the inverse of the inflaton-gauge field coupling [see Eq. (1)]. The value shown corresponds to modes that left the horizon 60 e-foldings before the end of inflation. The WMAP limit is obtained from the 95% C. L. WMAP [56] bound on equilateral non-Gaussianity, and from the fact that the shape of inverse decay non-Gaussianity has a cosine of 0.94 with the equilateral template [43]. The right panel shows values of $n_s$ and $r$ for the same range of inflaton-gauge field couplings. These values are compared with the 68% C. L. and 95% C. L. limits given in 56. Both panels show results for linear ($p=1$) and quadratic ($p=2$) slow-roll inflaton potentials.

Figure 5

${\Omega }_{\mathrm{GW}}{h}^2$ as function of the frequency $f$, for $N=60$ e-foldings of observable inflation, a linear slow-roll inflaton potential, and ${\xi }_{\mathrm{CMB}}=0$, 2.33, 2.66 (the value of $\xi$ when the large-scale CMB modes left the horizon). For reference we also show the expected sensitivity of LISA, Advanced LIGO/Virgo and Einstein Telescope (at their most sensitive frequency).

Figure 6

Region in the $\{N_{\mathrm{CMB}},{\xi }_{\mathrm{CMB}}\}$ plane (values assumed by these quantities when the large-scale CMB modes left the horizon) for which the gravity wave signal is detectable at Advanced LIGO/Virgo and Einstein Telescope. The left and right panel refer to a linear and quadratic inflaton potential, respectively.