Year-end Sale % OFF 
Abstract
We develop the transport operator formalism, a new line-of-sight integration framework to calculate the anisotropies of the Cosmic Microwave Background (CMB) at the linear and non-linear level. This formalism utilises a transformation operator that removes all inhomogeneous propagation effects acting on the photon distribution function, thus achieving a split between perturbative collisional effects at recombination and non-perturbative line-of-sight effects at later times. The former can be computed in the framework of standard cosmological perturbation theory with a second-order Boltzmann code such as SONG, while the latter can be treated within a separate perturbative scheme allowing the use of non-linear Newtonian potentials. We thus provide a consistent framework to compute all physical effects contained in the Boltzmann equation and to combine the standard remapping approach with Boltzmann codes at any order in perturbation theory, without assuming that all sources are localised at recombination.
Highlights
We develop the transport operator formalism, a new line-of-sight integration framework to calculate the anisotropies of the Cosmic Microwave Background (CMB) at the linear and non-linear level
For our choice of initial conditions, the operator J −1(η) singles out the effects of space-time on the distribution function around recombination, while J (η0) describes the non-trivial structure of space-time and its effect on the distribution function after recombination 2. This formalism allows to identify the residual terms of the propagation effects to any order in perturbation theory; these terms can be implemented in CMB codes like SONG by modifying the collision term
In this paper we introduced the transport operator formalism, a new framework to compute the non-linear CMB anisotropies
Summary
Before dealing with the propagation terms in the full Boltzmann equation we analyse the collision-free transport of a distribution function that is given at some initial time. We will derive a transformation that removes all the inhomogeneous transport terms from the Boltzmann equation This transformation is described by an operator J acting on the distribution function:. The transformed distribution function evolves as in a unperturbed Universe, while all the complications of the non-linear transport are encoded in J Whether this is viable in practise depends on the complexity to find an operator J that satisfies the equation of motion [D, J ] + τ J = 0. This is due to the derivative ∂d contained in the source τ It may either act on Jb or be part of the differential basis contributing to the component of J with one additional index, generating the two equations at the second order. We shall see that we can add collisions in a natural way
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
