Hubble Parameter

  • #1

Homework Statement


For a κ=0 universe with no cosmological constant, show that H(z)=H0(1+z)3/2


Homework Equations


Friedmann equation: H2=[itex]\frac{8*\pi*g}{3c^2}[/itex]-[itex]\frac{κc^2}{r^2}[/itex]*[itex]\frac{1}{a(t)^2}[/itex]


The Attempt at a Solution


I know that R(z)=R0/(1+z) but I do not know where this comes from. Following this, I should be able to take a density ρ(z)=ρ(now)*(1+z)^3 and input it into the Friedman equation but I am not sure how to proceed
 

Answers and Replies

  • #2
cepheid
Staff Emeritus
Science Advisor
Gold Member
5,192
38
The Friedmann equation should be ##H^2 = \frac{8\pi G}{3}\rho##, where rho is the total mass density of the universe (in this case considered to be entirely due to matter). You can ignore the second term with kappa entirely, since it's zero (flat universe). You are correct that you can write ##\rho = \rho_0 (1+z)^3 ## for ordinary matter. The trick now is figuring out how to rewrite the ##(8\pi G)/3## pre-factor in terms of something else. Hint: what is the expression for the critical density?
 

Related Threads on Hubble Parameter

  • Last Post
Replies
1
Views
621
Replies
2
Views
2K
Replies
1
Views
1K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
2
Views
2K
Replies
1
Views
908
Replies
1
Views
785
  • Last Post
Replies
10
Views
3K
Top