Difference between revisions of "Composite Models"

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(Problem 3: no solution)
(pr1: link to previous section)
 
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The particle horizon $L_p$ at the current moment $t_0$ is (see \ref{LpDp})
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The particle horizon $L_p$ at the current moment $t_0$ is (see [[Simple_Math#LpDp|this relation]])
 
\[L_p =\lim\limits_{t_e \to 0} D_p (t_e ,t_0)\]   
 
\[L_p =\lim\limits_{t_e \to 0} D_p (t_e ,t_0)\]   
 
The proper distance can be written as
 
The proper distance can be written as

Latest revision as of 16:40, 9 October 2013

Problem 1

Consider a flat universe with several components $\rho=\sum_i \rho_i$, each with density $\rho_i$ and partial pressure $p_i$ being related by the linear state equation $p_i =w_i \rho_i$. Find the particle horizon at present time $t_0$.

Problem 2

Suppose we know the current material composition of the Universe $\Omega_{i0}$, $w_i$ and its expansion rate as function of redshift $H(z)$. Find the particle horizon $L_p (z)$ and the event horizon $L_p (z)$ (i.e the distances to the respective surfaces along the surface $t=const$) at the time that corresponds to current observations with redshift $z$.

Problem 3

When are $L_p$ and $L_e$ equal? It is interesting to know whether both horizons might have or not the same values, and if so, how often this could happen.

Problem 4

Find the particle and event horizons for any redshift $z$ in the standard cosmological model -- $\Lambda$CDM.

Problem 5

Express the particle $L_p (z)$ and event $L_e (z)$ horizons in $\Lambda$CDM through the hyper-geometric function.