Scale-dependent gravitational waves from a rolling axion

TL;DR

The authors investigate an inflationary scenario in which a rolling axion-like field $\sigma$ couples to a U(1) gauge field via $\frac{\alpha}{4f}\,\sigma F\tilde{F}$ and sources one helicity of the gauge quanta. This sourced sector amplifies tensor modes and, to a lesser extent, scalar modes, producing a localized bump in the scalar and tensor power spectra and higher-point correlators around the horizon exit during the roll, controlled by $ξ_*$ and the roll width $δ$ (with $ΔN \simeq 1/δ$). They derive the perturbation spectra: ${\cal P}_ζ^{(1)}(k) \simeq [ε_φ {\cal P}_ζ^{(0)}(k)]^2 f_{2,ζ}(k/k_*, ξ_*, δ)$ and ${\cal P}_λ^{(1)}(k) \simeq [ε_φ {\cal P}_ζ^{(0)}(k)]^2 f_{2,λ}(k/k_*, ξ_*, δ)$, and similarly for the bispectra with $f_{3,ζ}$ and $f_{3,λ}$; notably only the $+$ helicity is efficiently sourced. A key result is that, for suitable choices of $k_*$, the sourced tensor signal can be observable in CMB $B$-modes without spoiling TT data, thanks to the localized peak and the transient rolling, while permitting parity-violating TB and potentially large BBB non-Gaussian signatures. The authors also analyze the non-Gaussianity of the sourced perturbations and assess observational prospects for Planck-like and cosmic-variance–limited experiments, highlighting distinctive localized signatures as tests of this mechanism.

Abstract

We consider a model in which a pseudo-scalar field $σ$ rolls for some e-folds during inflation, sourcing one helicity of a gauge field. These fields are only gravitationally coupled to the inflaton, and therefore produce scalar and tensor primordial perturbations only through gravitational interactions. These sourced signals are localized on modes that exit the horizon while the roll of $σ$ is significant. We focus our study on cases in which the model can simultaneously produce (i) a large gravitational wave signal, resulting in observable B-modes of the CMB polarizations, and (ii) sufficiently small scalar perturbations, so to be in agreement with the current limits from temperature anisotropies. Different choice of parameters can instead lead to a localized and visible departure from gaussianity in the scalar sector, either at CMB or LSS scales.

Figures (11)

• Figure 1: Comparison of the exact function $f_{2,\,\zeta}$ (green dots) and of the approximate form (red dashed line) given in eq. (\ref{['f23-fit']}), for the two values of $\delta$ that we have studied and for one illustrative choice of $\xi_*$. The function $f_{2,\zeta}$, defined in \ref{['f23-def']}, depicts a bump in the sourced scalar power spectrum, featuring a short period of a relatively fast rolling of $\sigma$ and the production of the gauge field during this stage. A bump feature is also present in the tensor sector. The phenomenological consequences of these localized signal are studied in Subsection \ref{['subsec:phenoresults']}.
• Figure 2: $\xi_*$ dependence of the fitting $f_{2,\zeta}$, $x^c_{2,\zeta}$ and $\sigma_{2,\zeta}$ entering in (\ref{['f23-fit']}), for $\delta = 0.2$ (an analogous agreement is obtained in the $\delta = 0.5$ case, and for th other $\left\{ i,\, j \right\}$ functions). The red dots denotes the values obtained by evaluating the power spectrum at $\xi_* = \left\{ 3 ,\, 3.5 ,\, 4 ,\, 4.5 ,\, 5 ,\, 5.5 ,\, 6 ,\, 6.5,\,7 \right\}$. The solid lines are the polynomial fits reported in the first row of Table \ref{['tab:fij-d02']}.
• Figure 3: Black-solid lines: tensor-to-scalar ratio (\ref{['r-tot']}). Orange dashed (respectively, blue dotted) lines: ratio between the sourced and the vacuum tensor (respectively, scalar) power spectrum. All ratios are evaluated at the peak of the sourced GW power spectrum.
• Figure 4: Solid lines: Largest value of $\xi_*$ (controlling the amount of produced quanta) allowed by the WMAP TT data, obtained as explained in the text, as a function of $\epsilon_\phi$, and for different values of $k_*$ (controlling the scale of the bump of the sourced modes, see the next figure). Dashed lines: ratio of ${\cal P}_\zeta^{(1)} / {\cal P}_\zeta^{(0)}$ at the peak of the GW bump.
• Figure 5: Temperature-temperature CMB power spectrum. The final WMAP data Bennett:2012zjaHinshaw:2012aka are compared against the theoretical curves, evaluated for $\epsilon_\phi = 10^{-5}$ and for $\delta = 0.2$ (left panel) and $\delta = 0.5$ (right panel). In each panel we show the theoretical curves for three different values of $k_*$ (corresponding to three different locations of the peak of the sourced signal) and for the limiting value $\xi_* = \xi_{*,{\rm limit}}$, obtained as explained in the text.