Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 310 / 2 / d

Table of contents
- Solution d

Solution

Write the neutrino degeneracy parameter as

ξ_{ν} = μ_{ν} / T_{ν}

. Requiring one degenerate species not to exceed today's critical density gives

\frac{ξ _{ν}^{4} T _{ν}^{4}}{8 π ^{2}} \leq 6 \times 1 0^{4} T^{4} .

Using

T / T_{ν} = (11/4)^{1/3}

,

ξ_{ν} \leq (48 π^{2} \times 1 0^{4})^{1/4} (\frac{11}{4})^{1/3} ≃ 65 .

Several equally degenerate species would strengthen the bound by the fourth root of their number.

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version