Primordial gravitational waves for universality classes of pseudoscalar inflation

TL;DR

The paper investigates primordial gravitational waves produced when a pseudoscalar inflaton couples to abelian gauge fields via $L_ ext{int}=\frac{\alpha}{4\Lambda}\,\phi F_{\mu\nu}\tilde F^{\mu\nu}$, introducing a tachyonic gauge-field instability characterized by $\xi=\frac{\alpha|\dot\phi|}{2\Lambda H}$. By classifying single-field slow-roll inflation models with $\epsilon_\phi\simeq\epsilon_V\simeq\frac{\beta_p}{N^p}$ into universality classes labeled by $p$, the authors derive analytic expressions for the scalar and tensor spectra and identify three dynamical regimes (A, B, C) as $\xi$ evolves, including a maximal end-of-inflation bound on $\xi$. Numerical studies of representative models (notably Starobinsky with $p=2$) show that gauge-field production can yield a sizable, potentially detectable stochastic GW background in the frequency bands of LISA/eLISA and advanced LIGO, while remaining consistent with CMB constraints (e.g., $n_s$, $r$, and $\xi_{\rm CMB}<2.5$) and PBH and $N_{\rm eff}$ bounds; the results also highlight how multiple gauge fields and reheating affect the spectra. The work highlights a promising, multi-messenger avenue to constrain inflationary microphysics and guides future observations by linking a universal inflation framework to concrete GW signatures across frequencies.

Abstract

Current bounds from the polarization of the CMB predict the scale-invariant gravitational wave (GW) background of inflation to be out of reach for upcoming GW interferometers. This prospect dramatically changes if the inflaton is a pseudoscalar, in which case its generic coupling to any abelian gauge field provides a new source of GWs, directly related to the dynamics of inflation. This opens up new ways of probing the scalar potential responsible for cosmic inflation. Dividing inflation models into universality classes, we analyze the possible observational signatures. One of the most promising scenarios is Starobinsky inflation, which may lead to observational signatures both in direct GW detection as well as in upcoming CMB detectors. In this case, the complementarity between the CMB and direct GW detection, as well as the possibility of a multi-frequency analysis with upcoming ground and space based GW interferometers, may provide a first clue to the microphysics of inflation.

Figures (10)

• Figure 1: Schematic view of the evolution of the inflaton field $\phi$ (left panel) and the parameter $\xi$ controlling the influence of the gauge fields (right panel) as a function of the number of e-folds of inflation.
• Figure 2: Schematic view of the gravitational wave spectrum for two different values of $p$ in Eq. \ref{['eq:Nparameterization']} and two different values of the inflaton - gauge field coupling $\alpha/\Lambda$.
• Figure 3: Evolution of inflaton field $\phi$ as a function of $N$ and $f$ (see Eq .\ref{['eq:Nf']}) for the Starobinsky model with (solid line) and without (dashed line) the non-minimal interaction with the gauge fields. We show the evolution for the case with $\alpha /\Lambda \sim 75$, $\gamma~=~0.3$, $V_0 \simeq 1.525 \cdot 10^{-9}$.
• Figure 4: Evolution of the parameter $\xi$ governing the strength of the gauge interactions for models with different values of $p$ as defined in Eq. \ref{['eq:Nparameterization']}. The parameters for the Starobinsky model are as in Fig. \ref{['fig:phi_comparison_staro']}, the parameters for the other models are listed in App. \ref{['sec:Appendix']}.
• Figure 5: Power spectrum of scalar perturbations for all the models with the same parameters and color code of Fig. \ref{['fig:xi_all']}. The upper horizontal line estimates the PBH bound, the lower one indicates the COBE normalization.