0
$\begingroup$

So I have the equation (derived from the Friedman equations with $a(t_0)=1$ and the powers of $a(t)$ quoted)$$H^2 = H_0^2\left(\frac{\Omega_{R_0}}{a^4(t)}+\frac{\Omega_{M_0}}{a^3(t)}+\Omega_{\Lambda_0}+\frac{1-\Omega_0}{a^2(t)}\right)$$

Where the "$0$" subscript denotes the value of the quantities at the initial time $t_0$, the subscripts $R_0$, $M_0$, $\Lambda_0$ denote the density parameter of radiation, matter and dark energy respectively and $\Omega$ is the total density parameter.

It says that for $\Omega_{M_0}=1$, it follows that $\Omega_{R_0}=\Omega_{\Lambda_0}=0$.

How exactly does this follow? I think that I might be missing something here because I'm not entirely sure I understand how this is so straight forward.

$\endgroup$
2
$\begingroup$

They're imposing spatial flatness. $\Omega_0 = \Omega_{R_0} + \Omega_{M_0} + \Omega_{\Lambda_0}$. The curvature parameter $\Omega_k = 1 - \Omega_0$. Space is flat when $\Omega_k=0$, thus $\Omega_{R_0} + \Omega_{M_0} + \Omega_{\Lambda_0} = 1$. You can relax the flatness requirement, though, in the more general case, though all observations, so far, are consistent with $\Omega_k=0$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.