Abstract
Reionization of the cosmic neutral hydrogen by the first stars in the
Universe is an inhomogeneous process which produces spatial fluctuations in
free electron density. These fluctuations lead to observable signatures in
cosmological probes like the cosmic microwave background (CMB). We explore the
effect of the electron density fluctuations on CMB using photon-conserving
semi-numerical simulations of reionization named SCRIPT. We show that
the amplitude of the kinematic Sunyaev-Zeldovich (kSZ) and $B$-mode
polarization signal depends on the electron density fluctuations along with the
dependence on mid-point and extent of the reionization history. Motivated by
this finding, we provide new scaling relations for the amplitude of kSZ and
$B$-mode polarization signal which can capture the effects arising from the
mean optical depth, width of reionization, and spatial fluctuations in the
electron density. We show that the amplitude of the kSZ and $B$-mode
polarization signal exhibits different dependency on the width of reionization
and spatial fluctuations, and hence a joint study of these CMB probes will be
able to break the degeneracy. By combining external datasets from 21~cm
measurements, the degeneracy can be further lifted by directly exploring the
sizes of the ionized regions.
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