Throughout this question, assume that the universe the universe only contains matter and a possible cosmological constant. use the definition of the density parameter to show that at any epoch we can write the matter density as constant-ω0h0 given that in any realistic cosmology s2mat ~ 1 at early times, compute the hubble parameter at decoupling (zdec 1000) as a fraction of its present value. as the only important characteristic scale in the young universe, the hubble length ch gives the characteristic scale of the first peak in the microwave background. in a spatially-flat cosmology with a cosmological constant, the present physical distance to an object with z »> 1 is given approximately by 0 [if you wish, you can verify this approximation by numerical integration along the lines of problem a2.4.] by considering the angular diameter distance, demonstrate that the angle subtended by the hubble length at decoupling is approximately inde- pendent of s2o in spatially-flat cosmologies, and compute its value in degrees. this demonstrates that the peak position is nearly independent of 2a for spatially-flat geometries, the approximations being the formula for aoto above and the assump- tion that the universe is perfectly matter dominated at last-scattering.

learn it on the intertant so you can solve

u can delete ur account.

1. go on google and write

2 open this and click on your profile pic and if your profile is not appearing, then u have to log in.

3. when u click on your profile pic, there appears four options on the top.

4. click on the 1st option and scroll down and go at the bottom.

5. click on edit profile.

6. there appears a option 'prefernces' and at that option at the right side , 'edit' is written.

7. click on the edit option.

8. there is a option " i want to delete my account" and click on that.

hope this u

and ur welcm

: )

so here is the information for current research:

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-resources of geothermal energy range from the shallow ground to hot water and hot rock found a few miles beneath the earth's surface, and down even deeper to the extremely high temperatures of molten rock called magma

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-geothermal heat pumps can tap into this resource to heat and cool buildings

-a geothermal heat pump system consists of a heat pump, an air delivery system (ductwork), and a heat exchanger-a system of pipes buried in the shallow ground near the building

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