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

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1. Oct 14, 2015

### 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)^3

I really don't know what to do after that. Any help would be great thanks

Last edited by a moderator: Oct 14, 2015
2. Oct 14, 2015

### Buzz Bloom

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 Ωk = 0.

You also need to calculate H(a) since that is the value of H you need to use in calculating ρc for the value of a that will satisfy
ρM = ρDE. Also keep in mind that ρDE is a constant (doesn't vary with a).

BTW, the title of this thread doesn't match the problem in the PNG.

Regards,
Buzz

3. Oct 14, 2015

### Phil1093

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

Thanks
Regards
Phil1093

4. Oct 14, 2015

### Phil1093

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

5. Oct 14, 2015

### Phil1093

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

6. Oct 15, 2015

### Buzz Bloom

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 ρDE = ρM = ρM0 / a3.

Regards,
Buzz