Last updated
All hermitian matrix can be decomposed into the Pauli basis. This decomposition is fundamental in quantum mechanics and quantum information theory, as it allows the representation of quantum states and operators in a standardized form, facilitating analysis and computation.
Changes in the Stokes parameter of the CMB due to distortions along the line-of-sight can be written as We have considered general line-of-sight distortions in the CMB. These distortions can be described by 11 fields and their effect on CMB polarization is given by Eqn. (1). We show that these fields correspond to various known instrumental systematics and cosmological signals. Example of cosmological signals include rotation of plane of polarization due to magnetic fields or parity violating physics, screening effects of the patchy reionization, lensing of CMB by the large-scale structure. Instrumental systematics include gain fluctuation, differential gain, pointing, beam ellipticity, differential beam ellipticity, detector rotation.
patchy reionization can cause an uneven screening effect on photons, particularly those from the Cosmic Microwave Background (CMB). Reionization refers to the period in the early universe when the first stars and galaxies formed and emitted enough radiation to ionize the neutral hydrogen that filled the universe. This process did not happen uniformly across space, leading to a patchy or uneven reionization.
As photons from the CMB pass through the universe, they interact with the free electrons produced during reionization. This interaction can scatter the photons, altering their paths and the observed properties of the CMB. In regions where reionization occurred earlier or was more complete, there would be more free electrons to scatter photons, leading to a stronger screening effect. Conversely, in regions where reionization was delayed or incomplete, there would be fewer free electrons, resulting in a weaker screening effect.
This uneven screening effect can introduce anisotropies (variations) in the CMB that are not due to the initial conditions of the universe but rather to the distribution and timing of reionization. These anisotropies provide valuable information about the process of reionization, including its timeline and spatial variation. By studying these effects, astronomers can gain insights into the formation of the first stars and galaxies and the evolution of the universe during this critical period.
The study of the uneven screening effect due to patchy reionization is a complex and active area of research. It involves sophisticated models and observations, including data from CMB experiments and surveys of distant galaxies and quasars that can help map the history of reionization across the sky.
