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Quarkly

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- TL;DR Summary
- Trying to perform the actual calculations of D. Hu and M. White that will reproduce their work on analysing the CMB Damping Tail.

The formula for the Damping Tail in the CMB BAO analysis generally has the form:

$$\mathcal{D} (k)=\int_{0}^{\eta_0}\dot\tau e^{-\left[\frac {k}{k_D(\eta)} \right]^2}d\eta $$I can’t make sense of this. ##\dot\tau## is the Thompson (Differential) Opacity; the product of electron density, cross section and scale factor:$$\dot\tau(\eta)=n_e\sigma_Ta$$At η = 0 (t = 0), the electron density is infinite (how are there even electrons at this energy level?) and the scale factor is zero. How are we supposed to perform this integration when the Thompson Opacity is so obviously indeterminate at the lower limit of integration?

$$\mathcal{D} (k)=\int_{0}^{\eta_0}\dot\tau e^{-\left[\frac {k}{k_D(\eta)} \right]^2}d\eta $$I can’t make sense of this. ##\dot\tau## is the Thompson (Differential) Opacity; the product of electron density, cross section and scale factor:$$\dot\tau(\eta)=n_e\sigma_Ta$$At η = 0 (t = 0), the electron density is infinite (how are there even electrons at this energy level?) and the scale factor is zero. How are we supposed to perform this integration when the Thompson Opacity is so obviously indeterminate at the lower limit of integration?

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