On the Gauge Invariance of Scalar Induced Gravitational Waves: Gauge Fixings Considered

Abstract

The energy density spectrum is an observable of gravitational waves. Divergence has appeared in the energy density spectra of the scalar induced gravitational waves for different gauge fixings. To resolve the discrepancy, we investigate the gauge invariance of the scalar induced gravitational waves. It is shown that the gauge invariant induced gravitational waves can be obtained by subtracting the fictitious tensor perturbations via introducing the counter term composed of the first order scalar perturbations. The kernel function uniquely determines the energy density spectrum of the scalar induced gravitational waves. We explicitly calculate the gauge invariant kernel functions in the Newtonian gauge and the uniform density gauge, respectively. The discrepancy between the energy density spectra upon the Newtonian gauge and the uniform density gauge is shown to be eliminated in the gauge invariant framework. In fact, the gauge invariant approach is also available to other kinds of gauge fixings.

9 pages, 5 figures, sequal to arXiv: 2009.11994 [gr-qc]

References in corpus (7)

• Gravitational Wave Spectrum Induced by Primordial Scalar Perturbations
• The cosmological gravitational wave background from primordial density perturbations
• Gauge Independence of Induced Gravitational Waves
• Gauge-invariant Formulation of the Second-order Cosmological Perturbations
• Gauge transformation of scalar induced gravitational waves
• Gauge transformation of scalar induced tensor perturbation during matter domination
• Gauge Invariant Second Order Gravitational Waves

Cited by in corpus (12)

• The Gravitational-Wave Physics II: Progress
• NANOGrav results and LIGO-Virgo primordial black holes in axion-like curvaton model
• Approximate gauge independence of the induced gravitational wave spectrum
• Gravitational Waves from Density Perturbations in an Early Matter Domination Era
• Double-peaked inflation model: Scalar induced gravitational waves and primordial-black-hole suppression from primordial non-Gaussianity
• Primordial black holes and gravitational waves induced by exponential-tailed perturbations
• Gauge transformation of scalar induced tensor perturbation during matter domination
• The Third Order Scalar Induced Gravitational Waves
• Circularly polarized scalar induced gravitational waves from the Chern-Simons modified gravity
• On the gauge dependence of scalar induced secondary gravitational waves during radiation and matter domination eras
• Gauge-dependence of Scalar Induced Gravitational Waves
• Inflationary $\alpha$-Attractor Models with Singular Derivative of Potential