Article

# Gauge invariant Boltzmann equation and the fluid limit

Classical and Quantum Gravity (Impact Factor: 3.56). 07/2007; DOI: 10.1088/0264-9381/24/24/001

Source: arXiv

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**ABSTRACT:**In this paper, we introduce a new approach to a treatment of the gravitational effects (redshift, time delay and lensing) on the observed cosmic microwave background (CMB) anisotropies based on the Boltzmann equation. From the Liouville's theorem in curved spacetime, the intensity of photons is conserved along a photon geodesic when non-gravitational scatterings are absent. Motivated by this fact, we derive a second-order line-of-sight formula by integrating the Boltzmann equation along a perturbed geodesic (curve) instead of a background geodesic (line). In this approach, the separation of the gravitational and intrinsic effects are manifest. This approach can be considered as a generalization of the remapping approach of CMB lensing, where all the gravitational effects can be treated on the same footing.Journal of Cosmology and Astroparticle Physics 09/2014; 2014(10). · 6.04 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We give a concise, self-contained introduction to perturbation theory in cosmology at linear and second orders, striking a balance between mathematical rigour and usability. In particular, we discuss gauge issues and the active and passive approaches to calculating gauge transformations. We also construct gauge-invariant variables, including the second-order tensor perturbation on uniform curvature hypersurfaces.Classical and Quantum Gravity 01/2008; 25. · 3.56 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We estimate the B-polarisation induced in the Cosmic Microwave Background by the non-linear evolution of density perturbations. Using the second-order Boltzmann code SONG, our analysis incorporates, for the first time, all physical effects at recombination. We also include novel contributions from the redshift part of the Boltzmann equation and from the bolometric definition of the temperature in the presence of polarisation. The remaining line-of-sight terms (lensing and time-delay) have previously been studied and must be calculated non-perturbatively. The intrinsic B-mode polarisation is present independent of the initial conditions and might contaminate the signal from primordial gravitational waves. We find this contamination to be comparable to a primordial tensor-to-scalar ratio of $r\simeq10^{-7}$ at the angular scale $\ell\simeq100\,$, where the primordial signal peaks, and $r\simeq 5 \cdot 10^{-5}$ at $\ell\simeq700\,$, where the intrinsic signal peaks. Therefore, we conclude that the intrinsic B-polarisation from second-order effects is not likely to contaminate future searches of primordial gravitational waves.Journal of Cosmology and Astroparticle Physics 01/2014; 2014(07). · 6.04 Impact Factor

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