At what redshift does the density of M > density of DM

[Phil1093]

Here is the problem link picture http://i.imgur.com/0BtcXJk.png

I know that omega=density/critical density
so I know I can find the value of all of those.
DE is dark energy and M is matter (I'm pretty sure).

I assume I have to sub that formula into equation 1, and then rearrange it to create a greater than sign somehow. I think I might have to involve Hubble's constant = a'/a too, to get rid of the (a0/a)^3I really don't know what to do after that. Any help would be great thanks

 

[Buzz Bloom]

Here is the problem link picture http://i.imgur.com/0BtcXJk.png

Hi Phil:

Take a look at https://en.wikipedia.org/wiki/Lambda-CDM_model , under "Cosmic expansion history", the 6th equation. What this tells you is that the sum of the Ωs under the squareroot is always = 1.

From the two equations in the PNG you cited, you should be able to calculate the value for w, which is probably 1.
From the first equation in the PNG, you should see that k = 0 and Ω_k = 0.

You also need to calculate H(a) since that is the value of H you need to use in calculating ρ_c for the value of a that will satisfy
ρ_M = ρ_DE. Also keep in mind that ρ_DE is a constant (doesn't vary with a).BTW, the title of this thread doesn't match the problem in the PNG.

I hope this is helpful,

Regards,
Buzz

 

[Phil1093]

Hi Phil:

Take a look at https://en.wikipedia.org/wiki/Lambda-CDM_model , under "Cosmic expansion history", the 6th equation. What this tells you is that the sum of the Ωs under the squareroot is always = 1.

From the two equations in the PNG you cited, you should be able to calculate the value for w, which is probably 1.
From the first equation in the PNG, you should see that k = 0 and Ω_k = 0.

You also need to calculate H(a) since that is the value of H you need to use in calculating ρ_c for the value of a that will satisfy
ρ_M = ρ_DE. Also keep in mind that ρ_DE is a constant (doesn't vary with a).BTW, the title of this thread doesn't match the problem in the PNG.

I hope this is helpful,

Regards,
Buzz

Thanks, I think I understand it, I have worked out H(a) too. I'm just stuck on how to make ρ_M = ρ_DE. As well as the formulae that associates the scale factor with z.

Thanks
Regards
Phil1093

 

[Phil1093]

Hi Phil:

Take a look at https://en.wikipedia.org/wiki/Lambda-CDM_model , under "Cosmic expansion history", the 6th equation. What this tells you is that the sum of the Ωs under the squareroot is always = 1.

From the two equations in the PNG you cited, you should be able to calculate the value for w, which is probably 1.
From the first equation in the PNG, you should see that k = 0 and Ω_k = 0.

You also need to calculate H(a) since that is the value of H you need to use in calculating ρ_c for the value of a that will satisfy
ρ_M = ρ_DE. Also keep in mind that ρ_DE is a constant (doesn't vary with a).BTW, the title of this thread doesn't match the problem in the PNG.

I hope this is helpful,

Regards,
Buzz

you can ignore my previous reply, I think I have it. Thank you

 

[Phil1093]

Hi Phil:

Take a look at https://en.wikipedia.org/wiki/Lambda-CDM_model , under "Cosmic expansion history", the 6th equation. What this tells you is that the sum of the Ωs under the squareroot is always = 1.

From the two equations in the PNG you cited, you should be able to calculate the value for w, which is probably 1.
From the first equation in the PNG, you should see that k = 0 and Ω_k = 0.

You also need to calculate H(a) since that is the value of H you need to use in calculating ρ_c for the value of a that will satisfy
ρ_M = ρ_DE. Also keep in mind that ρ_DE is a constant (doesn't vary with a).BTW, the title of this thread doesn't match the problem in the PNG.

I hope this is helpful,

Regards,
Buzz

I worked out the answer for z to be around 0.33, does that sound about right?

 

[Buzz Bloom]

I worked out the answer for z to be around 0.33, does that sound about right?

Hi Phil:

Yes.

There is a simpler way to get the answer than using all my hints. I thought having you look at a broader picture would be helpful preparation for what the course is likely to cover later.

The value of a you want corresponds to ρ_DE = ρ_M = ρ_M0 / a³.

Regards,
Buzz