The Third Order Scalar Induced Gravitational Waves

Abstract

Since the gravitational waves were detected by LIGO and Virgo, it has been promising that lots of information about the primordial Universe could be learned by further observations on stochastic gravitational waves background. The studies on gravitational waves induced by primordial curvature perturbations are of great interest. The aim of this paper is to investigate the third order induced gravitational waves. Based on the theory of cosmological perturbations, the first order scalar induces the second order scalar, vector and tensor perturbations. At the next iteration, the first order scalar, the second order scalar, vector and tensor perturbations all induce the third order tensor perturbations. We present the energy density spectrum of the third order gravitational waves for a monochromatic primordial power spectrum. The shape of the energy density spectrum of the third order gravitational waves is different from that of the second order scalar induced gravitational waves. And it is found that the third order gravitational waves sourced by the second order scalar perturbations dominate the energy density spectrum.

33 pages, 4 figures

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• Constraints On Scalar-Induced Gravitational Waves Up To Third Order From Joint Analysis of BBN, CMB, And PTA Data
• Bayesian Implications for the Primordial Black Holes from NANOGrav's Pulsar-Timing Data Using the Scalar-Induced Gravitational Waves
• Missing one-loop contributions in secondary gravitational waves
• Gravitational waves from primordial scalar and tensor perturbations
• Primordial black holes and third order scalar induced gravitational waves
• Impact of the free-streaming neutrinos to the second order induced gravitational waves
• Scalar induced gravitational waves from Chern-Simons gravity during inflation era
• Gravitational waves in ultra-slow-roll and their anisotropy at two loops
• Scalar induced gravitational waves in chiral scalar-tensor theory of gravity
• Multiple peaks in gravitational waves induced from primordial curvature perturbations with non-Gaussianity
• Non-linear corrections of overlap reduction functions for pulsar timing arrays
• Primordial gravitational waves and curvature perturbations induced energy density perturbation
• Scalar-induced gravitational waves in spatially covariant gravity
• Inflationary $\alpha$-Attractor Models with Singular Derivative of Potential
• Covariant transverse-traceless projection for secondary gravitational waves