Cosmological epoch of matter-radiation equality

In summary, the conversation discusses calculating the redshift when the matter and radiation densities are equal, given the values of Ω_m and Ω_R. The relevant equations and an attempt at a solution are provided, but it is noted that the values given may not be for the actual universe. A sudden realization is also mentioned, leading to a revised calculation of 1+z≈311000.
  • #1
gboff21
50
0

Homework Statement


If Ω_0m=0.25 and Ω_0R=7.4*10^-5 calculate the redshift when the two densities Ω_m and Ω_R are equal.

Relevant Equations
1+z=1/a
[itex]\Omega = \frac{rho}{rho_{crit}}[/itex]
[itex]\rho_{0,crit} = \frac{3 H_{0}^{2}}{8 \pi G}[/itex]

The attempt at a solution

convert matter density: [itex]\epsilon_{0,m} = \rho_{0,m} c^{2} = \Omega_{m,0} \rho_{crit,0} c^{2}[/itex]

sub in for critical density: [itex]\epsilon_{0,m} = \Omega_{m,0} \frac{3 H_{0}^{2}}{8 \pi G} c^{2}[/itex]

calculate ratio of matter to radiation: [itex]\frac{\epsilon_{R}}{\epsilon{M}} = \frac{\Omega_{R,0}}{\Omega{M,0}} \frac{8 \pi G c^{2}}{3 H_{0}^{2}}[/itex]

and as [itex]\epsilon_{R} \propto 1/a^{4}[/itex] and [itex]\epsilon_{M} \propto 1/a^{3}[/itex] and ρ0/a^3 = ρ

[itex]\frac{\epsilon_{R}}{\epsilon{M}} = \frac{\epsilon_{0,R}}{\epsilon{0,M}} 1/a[/itex]

put [itex]\frac{\epsilon_{R}}{\epsilon{M}} = 1[/itex] so

[itex]1 = \frac{\Omega_{M,0}}{\Omega{R,0}} \frac{3 H_{0}^{2}}{8 \pi G c^{2}} (1+z)[/itex]

This comes out as 1+z = 3.215*10^-6
and so gives a negative redshift!

Now I have either done something terribly wrong or the Omegas given are for an arbitrary universe in which the equality epoch has yet to occur!Thanks
 
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  • #2
Sudden realisation (maybe):

Is it because
(ϵR)(ϵM) = (ϵ_0,R) (ϵ_0,M) a
not

(ϵR)(ϵM) = (ϵ_0,R) (ϵ_0,M) 1/a??

1+z≈311000?
 

FAQ: Cosmological epoch of matter-radiation equality

What is the cosmological epoch of matter-radiation equality?

The cosmological epoch of matter-radiation equality is a period in the early universe when the density of matter and the density of radiation were equal. This happened approximately 380,000 years after the Big Bang, when the universe was about 0.01% of its current age.

What caused the transition from radiation-dominated to matter-dominated universe?

The transition from radiation-dominated to matter-dominated universe occurred during the cosmological epoch of matter-radiation equality. As the universe expanded and cooled, the energy of radiation decreased, while the density of matter remained constant. Eventually, the density of matter became greater than the density of radiation, causing the transition.

How did the cosmological epoch of matter-radiation equality affect the formation of structures in the universe?

The cosmological epoch of matter-radiation equality was a crucial period for the formation of structures in the universe. During this time, the slight variations in matter density started to grow and eventually led to the formation of galaxies and other large-scale structures we see in the universe today.

How is the cosmological epoch of matter-radiation equality related to the cosmic microwave background radiation?

The cosmic microwave background radiation is the leftover glow from the early universe, and it is a direct result of the cosmological epoch of matter-radiation equality. As the universe cooled after this epoch, the radiation became less energetic and expanded, leaving behind a faint glow that can still be observed today.

Are there any current experiments or observations studying the cosmological epoch of matter-radiation equality?

Yes, there are many ongoing experiments and observations studying the cosmological epoch of matter-radiation equality. These include studies of the cosmic microwave background radiation, as well as experiments such as the Large Hadron Collider, which aims to recreate the conditions of the early universe and shed light on this important epoch.

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