Note on gauge invariance of second order cosmological perturbations

Abstract

We study the gauge invariant cosmological perturbations up to second order. We show that there are infinite families of gauge invariant variables at both of the first and second orders. The conversion formulae among different families are shown to be described by a finite number of bases that are gauge invariant. For the second order cosmological perturbations induced by the first order scalar perturbations, we explicitly represent the equations of motion of them in terms of the gauge invariant Newtonian, synchronous and hybrid variables, respectively.

v1: 31 pages. v2: Publised in Chinese Physics C

References in corpus (14)

• Gravitational Wave Spectrum Induced by Primordial Scalar Perturbations
• The cosmological gravitational wave background from primordial density perturbations
• Second-order Gauge Invariant Cosmological Perturbation Theory: -- Einstein equations in terms of gauge invariant variables --
• Non-gaussianity from the second-order cosmological perturbation
• Constraints on the induced gravitational wave background from primordial black holes
• Observable Spectra of Induced Gravitational Waves from Inflation
• Gauge Independence of Induced Gravitational Waves
• Scalar Induced Gravitational Waves in Different Gauges
• Gauge-invariant Formulation of the Second-order Cosmological Perturbations
• Constraints on Scalar and Tensor spectra from $N_{eff}$
• Impact of anisotropic stress of free-streaming particles on gravitational waves induced by cosmological density perturbations
• Prospects for probing ultralight primordial black holes using the stochastic gravitational-wave background induced by primordial curvature perturbations
• Gauge-invariant approach to the parametrized post-Newtonian formalism
• Recursive structure in the definitions of gauge-invariant variables for any order perturbations

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• Circularly polarized scalar induced gravitational waves from the Chern-Simons modified gravity
• Impact of the free-streaming neutrinos to the second order induced gravitational waves
• On the gauge dependence of scalar induced secondary gravitational waves during radiation and matter domination eras
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• Inflationary $\alpha$-Attractor Models with Singular Derivative of Potential
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