At the time of the last scattering epoch (redshift z~1000)...?

Question

a) What was the avg density of normal matter if today it is about 3 x 10^31 kg/l
b) how large a sphere would have contained 10^11 solar masses, about as much normal mater as a galaxy today?

rhsaunder is right, it is meant to be negative

Answer 1

I don't have answers to either of these, but wish to point out a possible error in the statement of the problem. Consider the claimed current density: is there a missing minus sign in the exponent? If not, something is definitely weird.

Answer 2

I only do part b)

The figure I have for average density is 10^-18 kg per cubic metre at the time of recombination. This is not done according to your question (that is: I did not do the calculation; I looked it up in a book)

One solar mass = 1.9891 x 10^30 kg (let's call it 2 x 10^30 kg).

10^11 solar masses is therefore 2 x 10^41 kg.

The volume needed, at the density given above, is
2 x 10^41 / 10^-18 = 2 x 10^59 cubic metres.

The volume of a sphere of radius r is
(4/3)*pi*r^3

To enclose a volume of 2x10^59 m^3, a sphere would need a radius of CUBEROOT((1.5/pi)*10^59) = CUBEROOT(47.7x10^57) = 3.6x10^19 m = 3800 light-years (approximately, since I've done a lot of rounding).

Of course, check my calculations before using the result.