Gravitational waves at interferometer scales and primordial black holes in axion inflation

TL;DR

This work investigates inflationary gravitational waves sourced by gauge-field amplification in axion-inflation models and assesses their detectability by terrestrial and space interferometers as well as pulsar timing arrays. It shows that PBH constraints on amplified scalar perturbations typically limit the observable GW signal, but can be relaxed through (i) modifying the inflaton potential to weaken PBH production after the relevant scales exit, (ii) introducing a second rolling field to localize the effect, or (iii) employing multiple gauge fields to boost tensor modes relative to scalars. The study finds that LISA and PTA probes can uncover a distinctive, chiral, and nearly non-Gaussian stochastic GW background without overproducing PBHs, while AdvLIGO prospects are more constrained in the simplest setups. It also discusses a PBH-merger channel where PBHs formed from enhanced perturbations could seed present black holes and produce detectable GW across multiple bands, linking early-universe particle production to current observations.

Abstract

We study the prospects of detection at terrestrial and space interferometers, as well as at pulsar timing array experiments, of a stochastic gravitational wave background which can be produced in models of axion inflation. This potential signal, and the development of these experiments, open a new window on inflation on scales much smaller than those currently probed with Cosmic Microwave Background and Large Scale Structure measurements. The sourced signal generated in axion inflation is an ideal candidate for such searches, since it naturally grows at small scales, and it has specific properties (chirality and non-gaussianity) that can distinguish it from an astrophysical background. We study under which conditions such a signal can be produced at an observable level, without the simultaneous overproduction of scalar perturbations in excess of what is allowed by the primordial black hole limits. We also explore the possibility that scalar perturbations generated in a modified version of this model may provide a distribution of primordial black holes compatible with the current bounds, that can act as a seeds of the present black holes in the universe.

Figures (10)

• Figure 1: Left panel: Limits on the rescaled black hole fraction $\tilde{\beta}$ as a function of the black hole mass, as discussed in the text. Right panel: Same limits, written as a bound on the primordial scalar density perturbations as a function of number of e-folds before the end of inflation, assuming a constant Hubble rate $H = 10^{13} \, {\rm GeV}$ during inflation, and a $\chi^2$ statistics of the scalar perturbations (see Appendix \ref{['app:zetaPBH']}).
• Figure 2: LEFT PANEL: Scalar power spectrum in axion inflation for a linear inflaton potential, in the approximation (\ref{['Pz2']}). The coupling to gauge fields is chosen as large as allowed by the PHB bounds shown in the figure; this gives $\xi_{\rm CMB} \mathrel{\hbox{$<$$\sim$}} 1.66$ at $60$ e-folds before the end of inflation. RIGHT PANEL: Corresponding GW signal for the same model and parameters as in the left panel. The points on the theoretical line labelled by "$30$", "$20$", and "$10$", correspond to modes that, respectively, left the horizon $30, 20,$ and $10$ e-folds before the end of inflation.
• Figure 3: The solid line shows the inflaton potential (\ref{['modified-Vphi']}) spanned by the inflation from $N=60$ to $N=5$, with parameters leading to the spectra of Figure \ref{['fig:mod-lin-spectra']}. The two arrows indicate the position of the two transition regions (the potential is linear both at $\phi < \phi_1$ and $\phi > \phi_2$, but with a different slope). The dotted lines shows an unmodified linear inflaton potential.
• Figure 4: As in Figure \ref{['fig:lin-1p66']}, but with a larger coupling of the inflaton to the gauge field, and with the modified inflaton potential (\ref{['modified-Vphi']}). The solid lines are the spectra obtained in this case (the corresponding potential is shown in the solid line of Figure \ref{['fig:modpot']}). The dashed lines show how the spectra would continue at small scales if the instead the inflaton potential remained linear at all values (corresponding to the dashed line in Figure \ref{['fig:modpot']}).
• Figure 5: Scalar and tensor signals for a linear inflation potential. The solid lines show the signal if ${\cal N} = 6$ gauge fields are amplified. For comparison, the dashed lines show the signal when $1$ gauge field is amplified.