[Paper Review] Scalar induced gravity waves from ultra slow-roll Galileon inflation

Sayantan Choudhury, Ahaskar Karde+2 more|arXiv (Cornell University)|Aug 18, 2023

Cosmology and Gravitation Theories4 citations

TL;DR

This paper proposes that scalar-induced gravitational waves (SIGWs) generated during an ultra-slow-roll (USR) phase in Galileon inflation can explain the NANOGrav 15-year low-frequency gravitational wave signal. Leveraging the non-renormalization theorem of Galileon theory, the model controls large fluctuations at phase transitions, producing a SIGW spectrum with peak amplitude $\Omega_{\rm GW}h^{2} \sim \mathcal{O}(10^{-6})$ across $10^{-9}\,{\rm Hz} \sim 10^{7}\,{\rm Hz}$, consistent with LISA, BBO, DECIGO, and HLVK sensitivities, while enabling a broad primordial black hole mass range from $\mathcal{O}(1\,M_\odot)$ to $10^{-18}\,M_\odot$. The one-loop corrected scalar power spectrum preserves this behavior under transition scale shifts.

ABSTRACT

We consider the production of secondary gravity waves in Galileon inflation with an ultra-slow roll (USR) phase and show that the spectrum of scalar-induced gravitational waves (SIGWs) in this case is consistent with the recent NANOGrav 15-year data and with sensitivities of other ground and space-based missions, LISA, BBO, DECIGO, CE, ET, HLVK (consists of aLIGO, aVirgo, and KAGRA), and HLV(03). Thanks to the non-renormalization property of Galileon theory, the amplitude of the large fluctuation is controllable at the sharp transitions between SR and USR regions. We show that the behaviour of the GW spectrum, when one-loop effects are included in the scalar power spectrum, is preserved under a shift of the sharp transition scale with peak amplitude $Ω_{ m GW}h^2\sim {\cal O}(10^{-6})$, and hence it can cover a wide range of frequencies within ${\cal O}(10^{-9}{ m Hz} - 10^{7}{ m Hz})$. An analysis of the allowed mass range for primordial black holes (PBHs) is also performed, where we find that mass values ranging from ${\cal O}(1M_{\odot} - 10^{-18}M_{\odot})$ can be generated over the corresponding allowed range of low and high frequencies.

Motivation & Objective

• To explain the NANOGrav 15-year low-frequency gravitational wave signal via scalar-induced gravitational waves (SIGWs) in a Galileon inflation model.
• To investigate the role of an ultra-slow-roll (USR) phase in generating large scalar perturbations that seed SIGWs.
• To assess the consistency of the SIGW spectrum with ground- and space-based observatories, including LISA, BBO, DECIGO, and HLVK.
• To analyze the allowed mass range for primordial black holes (PBHs) formed from the same large-scale scalar fluctuations.
• To examine the robustness of the SIGW spectrum under one-loop corrections to the scalar power spectrum, leveraging the non-renormalization theorem of Galileon theory.

Proposed method

• Modeling Galileon inflation with a sharp transition from slow-roll (SR) to ultra-slow-roll (USR) phases, where large scalar fluctuations are generated.
• Applying the non-renormalization theorem of Galileon theory to ensure radiative stability of correlation functions and control amplitude of large fluctuations at phase transitions.
• Computing the one-loop corrected scalar power spectrum using third-order action and mode solutions across three phases: SR, USR, and post-USR (SRII).
• Deriving the transfer function and coupling coefficients for second-order gravitational wave production from scalar perturbations in radiation- and matter-dominated eras.
• Using the one-loop corrected scalar power spectrum to compute the dimensionless energy density spectrum of scalar-induced gravitational waves, $\Omega_{\rm GW}(k)$, via the full nonlinear evolution of the system.
• Evaluating the SIGW amplitude across a wide frequency band by integrating over the full range of scales, including the effects of phase transition scale shifts.

Experimental results

Research questions

• RQ1 Can scalar-induced gravitational waves from Galileon inflation with an ultra-slow-roll phase reproduce the NANOGrav 15-year data?
• RQ2 How does the one-loop corrected scalar power spectrum affect the amplitude and shape of the induced gravitational wave spectrum?
• RQ3 What is the frequency range over which the SIGW spectrum remains observable and consistent with future missions like LISA, BBO, DECIGO, and HLVK?
• RQ4 What mass range of primordial black holes (PBHs) can be produced from the same scalar fluctuations that generate SIGWs?
• RQ5 Does the non-renormalization property of Galileon theory preserve the SIGW spectrum under shifts in the transition scale between SR and USR phases?

Key findings

• The scalar-induced gravitational wave (SIGW) spectrum from Galileon inflation with an ultra-slow-roll phase achieves a peak amplitude of $\Omega_{\rm GW}h^{2} \sim \mathcal{O}(10^{-6})$, matching the NANOGrav 15-year data.
• The SIGW spectrum spans a broad frequency range from $10^{-9}\,{\rm Hz}$ to $10^{7}\,{\rm Hz}$, making it detectable by multiple future experiments including LISA, BBO, DECIGO, and HLVK.
• The one-loop corrected scalar power spectrum preserves the SIGW amplitude and shape under shifts in the sharp transition scale between slow-roll and ultra-slow-roll phases.
• The model generates primordial black holes (PBHs) with masses ranging from $\mathcal{O}(1\,M_\odot)$ to $10^{-18}\,M_\odot)$, covering both stellar and sub-stellar mass regimes.
• The non-renormalization theorem of Galileon theory ensures that radiative corrections do not destabilize the large scalar fluctuations, enabling a controlled and stable SIGW production mechanism.
• The full analytical framework, including phase-dependent mode solutions and coupling coefficients, confirms the robustness of the SIGW spectrum across all relevant cosmological eras.