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:**We develop a new, efficient code for solving the second-order Einstein-Boltzmann equations, and use it to estimate the intrinsic CMB non-Gaussianity arising from the non-linear evolution of density perturbations. The full calculation involves contributions from recombination and less tractable contributions from terms integrated along the line of sight. We investigate the bias that this intrinsic bispectrum implies for searches of primordial non-Gaussianity. We find that the inclusion or omission of certain line of sight terms can make a large impact. When including all physical effects but lensing and time-delay, we find that the local-type f_nl would be biased by f_nl ~ 0.5, below the expected sensitivity of the Planck satellite. The speed of our code allows us to confirm the robustness of our results with respect to a number of numerical parameters.Journal of Cosmology and Astroparticle Physics 02/2013; 2013(04). · 6.04 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 - [Show abstract] [Hide abstract]

**ABSTRACT:**In the context of cosmological perturbation theory, we derive the second order Boltzmann equation describing the evolution of the distribution function of radiation without a specific gauge choice. The essential steps in deriving the Boltzmann equation are revisited and extended given this more general framework: i) the polarisation of light is incorporated in this formalism by using a tensor-valued distribution function; ii) the importance of a choice of the tetrad field to define the local inertial frame in the description of the distribution function is emphasized; iii) we perform a separation between temperature and spectral distortion, both for the intensity and for polarisation for the first time; iv) the gauge dependence of all perturbed quantities that enter the Boltzmann equation is derived, and this enables us to check the correctness of the perturbed Boltzmann equation by explicitly showing its gauge-invariance for both intensity and polarization. We finally discuss several implications of the gauge dependence for the observed temperature.Classical and Quantum Gravity 04/2013; 30(16). · 3.56 Impact Factor

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