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The linear perturbation theory of inhomogeneous reionization (LPTR) has beendeveloped as an analytical tool for predicting the global ionized fraction andlarge-scale power spectrum of ionized density fluctuations during reionization.In the original formulation of the LPTR, the ionization balance and radiativetransfer equations are linearized and solved in Fourier space. However, theLPTR's approximation to the full solution of the radiative transfer equation isnot straightforward to interpret, since the latter is most intuitivelyconceptualized in position space. To bridge the gap between the LPTR and thelanguage of numerical radiative transfer, we present a new, equivalent,position-space formulation of the LPTR that clarifies the approximations itmakes and facilitates its interpretation. We offer a comparison between theLPTR and the excursion-set model of reionization (ESMR), and demonstrate thebuilt-in capability of the LPTR to explore a wide range of reionizationscenarios, and to go beyond the ESMR in exploring scenarios involving X-rays.

The Linear Perturbation Theory of Reionization in Position-Space: Cosmological Radiative Transfer Along the Light-Cone