Analytic solutions of scalar perturbations induced by scalar perturbations

Abstract

We study scalar perturbations induced by scalar perturbations through the non-linear interaction appearing at second order in perturbations. We derive analytic solutions of the induced scalar perturbations in a perfect fluid. In particular, we consider the perturbations in a radiation-dominated era and a matter-dominated era. With the analytic solutions, we also discuss the power spectra of the induced perturbations.

37 pages, 7 figures, v2: version published in JCAP, paragraph structure changed

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• Missing one-loop contributions in secondary gravitational waves
• The Third Order Scalar Induced Gravitational Waves
• Gravitational waves from primordial scalar and tensor perturbations
• Primordial black holes and third order scalar induced gravitational waves
• Spectral Distortion Anisotropy from Inflation for Primordial Black Holes
• Sudden braking and turning with a two-field potential bump: primordial black hole formation
• Induced gravitational waves from statistically anisotropic scalar perturbations
• Cosmological Standard Timers from Unstable Primordial Relics
• Primordial gravitational waves and curvature perturbations induced energy density perturbation