Introduction to Cosmology Ryden · Problem 8.1

The Cosmic Microwave Background

Physics — Astrophysics · recombination-temperature-baryon-photon-ratio

Problem

The purpose of this problem is to determine how changing the value of the baryon-to-photon ratio, η\eta, affects the recombination temperature in the early universe. Plot the fractional ionization XX as a function of temperature, in the range 3000 K <T<< T < 4500 K; first make the plot assuming η=4×10−10\eta = 4 \times 10^{-10}, then assuming η=8×10−10\eta = 8 \times 10^{-10}. How much does this change in η\eta affect the computed value of the recombination temperature TrecT_{\rm rec}, if we define TrecT_{\rm rec} as the temperature at which X=12X = \frac{1}{2}?

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