Cosmology – Theory

Recombination
Large Scale Structure
Window Function
Transfer Function
References

Recombination

In this section define our notation with respect to the recombination module, more details in [1]. We refer to the total number of hydrogen nucleus (ionized or not) as

nHn np, (1)

where np is the number or protons. We refer to the hydrogen atoms as nH and ionized hydrogen as nH+ and therefore nH + nH+ = nHn. In the same way for the helium the number of helium nuclei is nHen and the single and double ionized as nHe+ and nHe++ respectively.

We also we the helium primordial abundance as the ratio of the helium mass to the total baryonic mass, i.e.,

Y p = nHenmHe (nHenmHe + nHnmH), (2)

where mH and mHe are the hydrogen and helium mass.

The element abundances are define as the ratio of the element by the total number of protons:

Xf = nf np, (3)

where f = (e,H,H+,He,He+,He++) and (e) represent the free electrons. These fractions have the following properties:

XH + XH+ = 1, (4) XHe + XHe+ + XHe++ = XHen, (5) XHen mp mHe Y p 1 Y p. (6)

We also define the number of free electrons as ne. Assuming a neutral universe we have

Xe = XH+ + XHe+ + 2XHe++. (7)