Gauge-invariant formulation of second-order cosmological perturbations
TLDR
Gauge-invariant treatments of the second-order cosmological perturbation in a four dimensional homogeneous isotropic universe filled with the perfect fluid are completely formulated without any gauge fixing in this paper.Abstract:
Gauge-invariant treatments of the second-order cosmological perturbation in a four dimensional homogeneous isotropic universe filled with the perfect fluid are completely formulated without any gauge fixing. We derive all components of the Einstein equations in the case where the first order vector and tensor modes are negligible. These equations imply that the tensor and the vector mode of the second-order metric perturbations may be generated by the scalar-scalar mode coupling of the linear order perturbations as the result of the nonlinear effects of the Einstein equations.read more
Citations
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Second-Order Gauge Invariant Cosmological Perturbation Theory— Einstein Equations in Terms of Gauge Invariant Variables —
TL;DR: In this article, the second-order gauge invariant cosmological perturbation theory in a four-dimensional homogeneous isotropic universe was formulated and all the components of the Einstein equations in the case that the first-order vector and tensor modes are negligible.
Journal ArticleDOI
Gravitational waves from an early matter era
Hooshyar Assadullahi,David Wands +1 more
TL;DR: In this paper, relativistic perturbation theory was used to give analytic estimates of the tensor perturbations generated at second order by linear density perturbants, and it was shown that large enhancement factors with respect to the naive second-order estimate are possible due to the growth of density perturbs on sub-Hubble scales.
Journal ArticleDOI
Non-linear perturbations of cosmological scalar fields
TL;DR: In this article, a covariant formalism for studying non-linear perturbations of scalar fields is presented, which is very close to that of the analogous equations obtained in the linear theory, but their equations are fully nonlinear and exact.
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Nonlinear perturbations of cosmological scalar fields
David Langlois,Filippo Vernizzi +1 more
TL;DR: In this article, a covariant formalism for studying nonlinear perturbations of scalar fields is presented, which is very close to the analogous equations obtained in the linear theory, but their equations are fully nonlinear and exact.
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Constraints on primordial density perturbations from induced gravitational waves
Hooshyar Assadullahi,David Wands +1 more
TL;DR: In this article, the stochastic background of gravitational waves produced during the radiation-dominated hot big bang was considered as a constraint on the primordial density perturbation on comoving length scales much smaller than those directly probed by the cosmic microwave background or large-scale structure.
References
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First year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Preliminary maps and basic results
Charles L. Bennett,Mark Halpern,Gary Hinshaw,N. Jarosik,Alan J. Kogut,Michele Limon,Michele Limon,S. S. Meyer,Lyman A. Page,David N. Spergel,Gregory S. Tucker,Gregory S. Tucker,Gregory S. Tucker,Edward J. Wollack,Edward L. Wright,Cris W. Barnes,M. R. Greason,Robert S. Hill,Eiichiro Komatsu,M. R. Nolta,N. Odegard,Hiranya V. Peiris,Licia Verde,Janet Weiland +23 more
TL;DR: In this paper, the authors present full sky microwave maps in five frequency bands (23 to 94 GHz) from the WMAP first year sky survey, which are consistent with the 7 in. full-width at half-maximum (FWHM) Cosmic Background Explorer (COBE) maps.
Journal ArticleDOI
First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results
Charles L. Bennett,Mark Halpern,Gary Hinshaw,N. Jarosik,Alan J. Kogut,Michele Limon,Michele Limon,S. S. Meyer,Lyman A. Page,David N. Spergel,Gregory S. Tucker,Edward J. Wollack,Edward L. Wright,Cris W. Barnes,M. R. Greason,Robert S. Hill,Eiichiro Komatsu,M. R. Nolta,N. Odegard,H. V. Peirs,Licia Verde,Janet Weiland +21 more
Abstract: We present full sky microwave maps in five bands (23 to 94 GHz) from the WMAP first year sky survey. Calibration errors are 1 per mode to l=658. The temperature-polarization cross-power spectrum reveals both acoustic features and a large angle correlation from reionization. The optical depth of reionization is 0.17 +/- 0.04, which implies a reionization epoch of 180+220-80 Myr (95% CL) after the Big Bang at a redshift of 20+10-9 (95% CL) for a range of ionization scenarios. This early reionization is incompatible with the presence of a significant warm dark matter density. The age of the best-fit universe is 13.7 +/- 0.2 Gyr old. Decoupling was 379+8-7 kyr after the Big Bang at a redshift of 1089 +/- 1. The thickness of the decoupling surface was dz=195 +/- 2. The matter density is Omega_m h^2 = 0.135 +0.008 -0.009, the baryon density is Omega_b h^2 = 0.0224 +/- 0.0009, and the total mass-energy of the universe is Omega_tot = 1.02 +/- 0.02. The spectral index of scalar fluctuations is fit as n_s = 0.93 +/- 0.03 at wavenumber k_0 = 0.05 Mpc^-1, with a running index slope of dn_s/d ln k = -0.031 +0.016 -0.018 in the best-fit model. This flat universe model is composed of 4.4% baryons, 22% dark matter and 73% dark energy. The dark energy equation of state is limited to w<-0.78 (95% CL). Inflation theory is supported with n_s~1, Omega_tot~1, Gaussian random phases of the CMB anisotropy, and superhorizon fluctuations. An admixture of isocurvature modes does not improve the fit. The tensor-to-scalar ratio is r(k_0=0.002 Mpc^-1)<0.90 (95% CL).
Journal ArticleDOI
Non-Gaussian features of primordial fluctuations in single field inflationary models
TL;DR: In this article, the three point correlation functions for primordial scalar and tensor fluctuations in single field inflationary models were computed in the slow roll limit, where the answer is given terms of the two usual slow roll parameters.
Book
Theory of Cosmological Perturbations
TL;DR: In this paper, the authors present in a manifestly gauge-invariant form the theory of classical linear gravitational perturbations in part I, and a quantum theory of cosmological perturbation in part II.
Journal ArticleDOI
Gauge Invariant Cosmological Perturbations
TL;DR: The physical interpretation of perturbations of homogeneous, isotropic cosmological models in the early Universe, when the perturbation is larger than the particle horizon, is clarified by defining a complete set of gauge-invariant variables as discussed by the authors.