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We study the Sunyaev-Zeldovich effect for clusters of galaxies. We explore the relativistic corrections to the Kompaneets equation in terms of two different expansion approximation schemes, namely, the Fokker-Planck expansion approximation and delta function expansion approximation. We show that two expansion approximation formalisms are equivalent under the Thomson approximation, which is extremely good approximation for the CMB photon energies. This will clarify the situation for existing theoretical methods to analyse observation data.
High-precision constraints on primordial non-Gaussianity (PNG) will significantly improve our understanding of the physics of the early universe. Among all the subtleties in using large scale structure observables to constrain PNG, accounting for rel
We derive a `Kompaneets equation for neutrinos, which describes how the distribution function of neutrinos interacting with matter deviates from a Fermi-Dirac distribution with zero chemical potential. To this end, we expand the collision integral in
Relativistic corrections are estimated for classical Cepheids and the Tip of the Red Giant Branch (TRGB stars), to enable future unbiased 1% measurements of Hubbles constant, $H_0$. We considered four effects: $K-$corrections, time-dilation, the appa
The thermal Sunyaev-Zeldovich (tSZ) effect is produced by the interaction of cosmic microwave background (CMB) photons with the hot (a few keV) and diffuse gas of electrons inside galaxy clusters integrated along the line of sight. This effect produc
In low-density or high-temperature plasmas, Compton scattering is the dominant process responsible for energy transport. Kompaneets in 1957 derived a non-linear degenerate parabolic equation for the photon energy distribution. In this paper we consid