[Paper Review] Imprints of Primordial Non-Gaussianity on Gravitational Wave Spectrum

Caner Ünal|arXiv (Cornell University)|Nov 22, 2018

Cosmology and Gravitation Theories4 citations

TL;DR

This paper demonstrates that primordial non-Gaussianity in scalar curvature fluctuations—even when subdominant—can source a dominant gravitational wave (GW) background via second-order effects during radiation domination. Next-generation GW detectors (e.g., LISA, DECIGO, CE, ET) can probe local non-Gaussianity parameters as low as $f_{\rm NL} \sim 0.5$, surpassing the sensitivity of upcoming CMB experiments, offering a powerful probe of small-scale primordial physics independent of primordial black hole (PBH) abundance.

ABSTRACT

Although Cosmic Microwave Background and Large Scale Structure probe the largest scales of our universe with ever increasing precision, our knowledge about the smaller scales is still very limited other than the bounds on Primordial Black Holes. We show that the statistical properties of the small scale quantum fluctuations can be probed via the stochastic gravitational wave background, which is induced as the scalar modes re-enter the horizon. We found that even if scalar curvature fluctuations have a subdominant non-Gaussian component, these non-Gaussian perturbations can source a dominant portion of the induced GWs. Moreover, the GWs sourced by non-Gaussian scalar fluctuations peaks at a higher frequency and this can result in distinctive observational signatures. We found that the sensitive next-generation-interferometers, which will/could reach $Ω_{GW}h^2 \sim 10^{-15}$ (such as PTA-SKA, LISA, DECIGO, BBO, CE, ET), can probe $f_{NL} \sim 0.5$ which is even better than the predictions of the next generation CMB experiments. If the induced GW background is detected, but not the signatures arising from the non-Gaussian component, $ζ= ζ_G + f_{ m NL} \, ζ_G^{2}$, this translates into bounds on $f_{ m NL}$ depending on the amplitude and the width of the GW signal. If the induced GW background is not detected at all, this translates into bounds on scalar fluctuations. The results are independent from the fact that whether PBH are DM or completely negligible part of the current energy density.

Motivation & Objective

• To investigate whether subdominant primordial non-Gaussianity in scalar fluctuations can leave detectable imprints on the stochastic gravitational wave (GW) background.
• To determine the detectability of induced GWs sourced by non-Gaussian scalar perturbations using next-generation interferometric and pulsar timing array experiments.
• To establish constraints on primordial non-Gaussianity and scalar fluctuation amplitudes independent of whether primordial black holes (PBHs) constitute dark matter.
• To clarify the frequency dependence and spectral shape of induced GWs from non-Gaussian scalar modes, especially in comparison to Gaussian contributions.

Proposed method

• Modeling primordial curvature perturbations as a sum of Gaussian and local-type non-Gaussian components: $\zeta = \zeta_G + f_{\rm NL} \zeta_G^2$, with $f_{\rm NL}$ as the non-Gaussianity parameter.
• Computing the second-order tensor mode power spectrum using the source term $\mathcal{S}_{\lambda,\mathbf{k}}$ derived from first-order scalar fluctuations in a radiation-dominated background.
• Solving the mode equation for tensor perturbations: $h''_{\lambda,\mathbf{k}} + 2\mathcal{H} h'_{\lambda,\mathbf{k}} + \mathbf{k}^2 h_{\lambda,\mathbf{k}} = 2\mathcal{S}_{\lambda,\mathbf{k}}$, with $\mathcal{H}$ as the conformal Hubble parameter.
• Evaluating the energy density spectrum of induced GWs, $\Omega_{\rm GW}(k)$, and converting it to the frequency domain for comparison with observational sensitivities.
• Assessing detectability using projected sensitivities of next-generation GW experiments, including PTA-SKA, LISA, DECIGO, BBO, CE, and ET, with $\Omega_{\rm GW} h^2 \sim 10^{-15}$.
• Deriving bounds on $f_{\rm NL}$ and scalar fluctuation amplitudes from non-detection of the induced GW background, independent of PBH formation.

Experimental results

Research questions

• RQ1 Can a subdominant non-Gaussian component in primordial scalar fluctuations generate a dominant gravitational wave background through second-order effects?
• RQ2 What is the frequency dependence of the induced GW spectrum sourced by non-Gaussian scalar fluctuations, and how does it differ from the Gaussian case?
• RQ3 Can next-generation gravitational wave detectors such as LISA, DECIGO, and CE probe primordial non-Gaussianity at levels below $f_{\rm NL} \sim 1$, surpassing the sensitivity of next-generation CMB experiments?
• RQ4 How do constraints on $f_{\rm NL}$ and scalar fluctuation amplitudes depend on the non-detection of the induced GW background?
• RQ5 Are the results on non-Gaussianity detection via induced GWs robust to assumptions about primordial black hole (PBH) abundance as dark matter?

Key findings

• Even a subdominant non-Gaussian component in primordial scalar fluctuations can source a dominant portion of the induced gravitational wave background due to second-order coupling effects.
• The gravitational wave spectrum sourced by non-Gaussian scalar fluctuations peaks at a higher frequency than the Gaussian component, offering a distinctive observational signature.
• Next-generation interferometric GW detectors (e.g., LISA, DECIGO, BBO, CE, ET) can probe $f_{\rm NL} \sim 0.5$, which is more sensitive than predictions from next-generation CMB experiments.
• Non-detection of the induced GW background translates into strong bounds on the amplitude of scalar fluctuations, orders of magnitude stronger than those from primordial black hole (PBH) constraints.
• The results are independent of whether PBHs constitute a significant fraction of dark matter or are negligible, making the method a robust probe of small-scale primordial physics.
• The induced GW background from modes re-entering during radiation domination can be detected in the nHz and mHz bands, corresponding to PBH masses of $\sim 10M_\odot$ and $\sim 10^{-12}M_\odot$, respectively, which are probed by PTA-SKA and LISA.