Constraints on primordial density perturbations from induced gravitational waves

TL;DR

This work shows that second-order gravitational waves generated during a radiation-dominated early universe encode information about primordial density perturbations on ultra-small scales. By relating the present GW energy density $\Omega_{\mathrm{GW},0}(k)$ to the scalar power via $\Omega_{\mathrm{GW},0}(k)=F_{\mathrm{rad}}\Omega_{\gamma,0}\Delta_{\mathcal{R}}^{4}(k)$, the authors translate bounds from BBN, CMB, and gravitational-wave detectors into upper limits on $\Delta_{\mathcal{R}}^{2}(k)$ and the effective tilt $\overline{n}_s$. Current constraints from LIGO/Virgo and cosmology are relatively weak but improve for higher frequencies, while future detectors like LISA, BBO, DECIGO and pulsar timing arrays could tighten limits substantially, potentially down to $\Delta_{\mathcal{R}}^{2}\sim10^{-7}$ and $\overline{n}_s\lesssim1.1$ for small scales. The results rely on a standard, radiation-dominated expansion history; deviations from this history could modify the bounds, making this a powerful probe of early-universe physics and the origin of structure.

Abstract

We consider the stochastic background of gravitational waves produced during the radiation-dominated hot big bang as a constraint on the primordial density perturbation on comoving length scales much smaller than those directly probed by the cosmic microwave background or large-scale structure. We place weak upper bounds on the primordial density perturbation from current data. Future detectors such as BBO and DECIGO will place much stronger constraints on the primordial density perturbation on small scales.

Figures (1)

• Figure 1: Constraints on the primordial density perturbation, $\Delta_{\cal R}^2$, obtained from gravitational waves produced during the radiation era, using Eq. (\ref{['hr1']}). Black lines denote current constraints from gravitational waves detectors and BBN. Green lines denote constraints expected from future gravitational waves detectors. Diagonal lines show the bounds on $\Delta_{\cal R}^2$ obtained using Eq. (\ref{['OmegaGWdelta']}) for wavenumbers $k_p>k$. WMAP gives a direct measurement (shown in red) of the primordial density perturbation on very low frequencies.