Cosmological nonlinear density and velocity power spectra including nonlinear vector and tensor modes

Abstract

We present the leading order non-linear density and velocity power spectra in the complete form; previous studies have omitted the vector- and tensor-type perturbations simultaneously excited by the scalar-type perturbation in nonlinear order. These additional contributions are comparable to the scalar-type purely relativistic perturbations, and thus negligible in the current paradigm of concordance cosmology: i.e., concerning density and velocity perturbations of the pressureless matter in perturbation regime well inside of matter-dominated epoch, we show that pure Einstein's gravity contributions appearing from the third order are entirely negligible (five orders of magnitude smaller than the Newtonian contributions) in all scales. We thus prove that Newtonian perturbation theory is quite reliable in calculating the amplitude of matter fluctuations even in the precision era of cosmology. Therefore, besides the ones imprinted as the initial condition generated in the earlier phase, the other relativistic effect relevant for interpreting observational data must be the projection effect that occurs when mapping galaxies on to the observed coordinate.

13 pages, 2 figures, the version accepted to be published in MNRAS

References in corpus (14)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Gravitational Wave Spectrum Induced by Primordial Scalar Perturbations
• The cosmological gravitational wave background from primordial density perturbations
• New Perspective on Galaxy Clustering as a Cosmological Probe: General Relativistic Effects
• Beyond the Linear-Order Relativistic Effect in Galaxy Clustering: Second-Order Gauge-Invariant Formalism
• Observed galaxy number counts on the lightcone up to second order: I. Main result
• Generation of gravitational waves during early structure formation between cosmic inflation and reheating
• Relativistic Effect in Galaxy Clustering
• Observed galaxy number counts on the lightcone up to second order: II. Derivation
• Large-Scale Structure Observables in General Relativity
• Einstein's signature in cosmological large-scale structure
• Cosmic Shear from Scalar-Induced Gravitational Waves
• Fully nonlinear and exact perturbations of the Friedmann world model: Non-flat background
• Third-order cosmological perturbations of zero-pressure multi-component fluids: Pure general relativistic nonlinear effects

Cited by in corpus (7)

• A general relativistic signature in the galaxy bispectrum: the local effects of observing on the lightcone
• Relativistic cosmological large scale structures at one-loop
• Large-Scale Tides in General Relativity
• Second-order cosmological perturbations. IV. Produced by scalar-tensor and tensor-tensor couplings during the radiation dominated stage
• Axion as a cold dark matter candidate: Analysis to third order perturbation for classical axion
• Second-order cosmological perturbations produced by scalar-scalar coupling during inflation stage
• Large scale structures: from inflation to today: a brief report