Gauge invariant Boltzmann equation and the fluid limit

Classical and Quantum Gravity (Impact Factor: 3.1). 07/2007; 24(24). DOI: 10.1088/0264-9381/24/24/001
Source: arXiv

ABSTRACT This article investigates the collisionless Boltzmann equation up to second order in the cosmological perturbations. It describes the gauge dependence of the distribution function and the construction of a gauge invariant distribution function and brightness, and then derives the gauge invariant fluid limit.

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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). DOI:10.1088/1475-7516/2014/10/051 · 5.88 Impact Factor
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    ABSTRACT: [Abridged version] A huge theoretical and experimental effort is being made by cosmologists and particle physicists to gain insight of the mechanism of generation of the primordial cosmological fluctuations, which remains still largely unknown. The bispectrum of the cosmic microwave background (CMB) has been recognised as a powerful probe of this mechanism, as it is sensitive to the non-Gaussian features in the seed fluctuations. To access this information, however, it is crucial to model the non-linear evolution of the CMB between the formation of the initial fluctuations and its observation, which results in the emergence of an intrinsic bispectrum. In this thesis we quantify the intrinsic bispectrum and compute the bias it induces on the primordial signal. To do so, we develop $\text{SONG}$, an efficient code for solving the second-order Einstein-Boltzmann equations, and use it to estimate the CMB non-Gaussianity arising from the non-linear evolution of density perturbations. The full calculation involves contributions from recombination and less tractable ones from terms integrated along the line of sight. We investigate the bias that the 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 contamination from the intrinsic bispectrum leads to a small bias in the estimates of non-Gaussianity, which is good news for the prospect of using CMB data to probe primordial non-Gaussianity. The intrinsic non-Gaussianity can be searched for directly, using the predicted signal as a template; our calculations suggest this signal is just beyond what is possible with the Planck CMB survey, with a signal-to-noise rising to unity only for an angular resolution of $\ell_\text{max}=3000$.
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    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). DOI:10.1088/1475-7516/2014/07/011 · 5.88 Impact Factor


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