What is the ratio of mass of the universe to its volume and how this number is calculated by the astronomers. My non professional attempt calculated from the Hubble redshift gave me (6.0+/-0.5)x10^{-27} kg/m^3 and I'd like to know how far it is from the real number. Thanks in advance.

The latest estimates have the average baryonic matter density at ~4.2x10^-28 kg/m^3. If you also throw in dark matter, which amounts to a factor of ~5x greater, one finds a total matter density about 2.6x10^-27 kg/m^3.

The latter is smaller than your estimate by about a factor of 2.3.

The numbers are arrived at both theoretically (GR, Friedmann-Walker-Robertson equations) and observationally (baryon surveys, dark matter surveys, Cosmic Microwave Background fluctuations, etc).

The critical matter density (now) is calculated as: 3H_o^2/(8*pi*G), where H_o is the "local" Hubble parameter.

My exact result is H_o^2/(4*pi*G) so density which you call "critical" (meaning what?), is 3/2 of mine. So why the density of the universe can't be just 1.5 of "critical" density? What would it mean for the universe?

The problem is that I don't have any free parameters to play with so if density is not 1.5 of "critical" then the theory that I'm testing can't be true.

Without knowing the full size of the Universe, how can we calculate its density?

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Noclevername,

One can measure the density of air without having the slightest idea of the
atmosphere's size.

I can determine whether the density of an object is greater or less than
the density of water just by tossing it into some water and seeing whether
it sinks or floats. This isn't an option with the Universe, of course...

-- Jeff, in Minneapolis

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We don't need the full size since if the principle of conservation of energy were true and the universe were static the density would be H_o^2/(4*pi*G*) (and dH/dt=-H_0^2/2). Unfortunately an assumption of validity of the principle of conservation of energy produces density 1.5 times bigger than "critical" (whatever it means) and apparently 2.3 times bigger than what is observed. So if estimated density is exactly right the principle of conservation of energy is wrong and the universe is expanding, as I was already told by many astronomers, prof. John Baez (a mathematical physicists), and all the mathematical physicists at my university. I still have doubts though since each observation has its standard deviation that makes it uncertain. So I'd like to know what is the standard deviation of estimated density, to calculate the probability that the universe is expanding, which I assume, was never done, as I never found it in the literature. That's why I need an advice of an astronomer, and I'm glad that there is such a place where I can get it.

You can say your estimate is that which comes about by universal energy conservation and a static state (whatever they mean), but that's a little different from demonstrating. I for one won't take your word on it.

However, since you asked, the measurements of the fluctuations in the CMB put the most stringent error bars on the baryonic and total matter densities. The uncertainties in the latter are less than +/-15% (from the 2003 WMAP data release; the error bars are about a factor of 2 smaller now in the recently released 2008 data). You can start here, and then go here.

I read a good article recently on the density of the universe. Let me look, if I can find it I'll edit this post for the reference.

Ok, got it, try here:

http://en.wikipedia.org/wiki/Density_parameter

Do you mean that the total matter density of the universe is (2.6+/-7.5%)x10^{-27}kg/m^3, and so that consequently the probability of the total matter density being 6.0x10^{-27}kg/m^3 (and consequently the universe not expanding) is much less than 1ppM and even 1ppB?

Basically, it is a conclusive evidence that the universe is expanding and the energy isn't conserved since to produce H_o=70 km/s/Mpc in non expanding universe with conservation of energy the universe would have to have density 6x10^{-27}kg/m^3 and evidently it has much less. And since a negative result is also a result I just have to change the title of my PhD work to "The conclusive proof of non conservation of energy in the universe based on astrophysical data".

If you don't want to take my word for the above, check http://geocities.com/jim_jastrzebski/sci/3270.htm

I would look with suspicion at all current estimates. In my lifetime, which luckily does not reach back to Einstein's original papers, I have seen serious values for density, assigning the critical density equal to 1, that have ranged from less than .5 to more than 3. Esthetically, it would be nice if it was 1, but I think it's still wait and see. And the value shapes so much of the rest of cosmology . . .

So you advise me to wait with the final conclusion of my PhD work? I still have 3 to 4 years to finish it and I need the density to be exaxtly 1.5 of "critical" to prove that conservation of energy exists also in cosmology (and as a byproduct that the universe isn't expanding). But is there any hope that astronomers find the missing 56% of the universe in just 4 years while they insist now that their accuracy is better than 8%?

You may be the one we're waiting for! Keep going. Use the best research you can find on the density. If the pieces all fit together, you've got a good case.

Ah, it is in a popular science publication, but there is a recent article in Discover (?) about a universe with variable density on cosmological scales.

It's about 9.9 × 10-30 grams per cubic cm, which comes to about 1 hydrogen atom per every 4 cubic yards.

We couldn't hit anything if we tried!

Well, we did manage the Moon, Mars, Venus, and a few other bodies in our neck of the woods, including a tiny, speeding comet. I'll bet the guy who aimed that one was from Kentucky...

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Answer I've always liked best:

Mostly vacuum with a few contaminants...

You must mean the density of part of universe, then, as density is mass divided by volume. And we don't know the universe's volume.

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"Distance doesn’t matter much in space, where if you just start a thing off with the right kind of shove, sooner or later it will get where you want it to go." -Frederik Pohl, Mining the Oort

Mass divided by volume. Which can probably be estimated from a sample, for one thing.

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I'll fix that.

Then when the OP asks "What is the ratio of mass of the universe to its volume"; it should probably be pointed out somewhere in the reply that we have only half of the data needed to actually calculate that. I'm just sayin'.

__________________
"If this were play'd upon a stage now, I could condemn it as an improbable fiction."
Shakespeare, Twelfth Night
Illuminati's Razor-The most complicatedly evil answer is usually the most correct answer. - Fazor
"Every book is a children's book if the kid can read." - Mitch Hedberg
"Distance doesn’t matter much in space, where if you just start a thing off with the right kind of shove, sooner or later it will get where you want it to go." -Frederik Pohl, Mining the Oort

I mean the entire visible Universe, adjusted for a common time.

Or divided by. I bet I do that more often than you!

Does that matter?

I don't have any idea what volume of iron meteoroids landed on the
Earth over the last 100 years, but I know that the density of all those
meteoroids is very close to 7.

-- Jeff, in Minneapolis

__________________
http://www.FreeMars.org/jeff/

"The other planets?
Well, they just happen to be there, but the point of rockets is to explore them!"
-- Kai Yeves

So just the visible parts, then. As I said, "part of".


Yes, that goof has been addressed.
Only if you want any accuracy in the answer.
Straw man. If no one actually told you the composition of objects, could you still say you knew their density without checking? That's closer to the situation we have with regards to the Universe.

__________________
"If this were play'd upon a stage now, I could condemn it as an improbable fiction."
Shakespeare, Twelfth Night
Illuminati's Razor-The most complicatedly evil answer is usually the most correct answer. - Fazor
"Every book is a children's book if the kid can read." - Mitch Hedberg
"Distance doesn’t matter much in space, where if you just start a thing off with the right kind of shove, sooner or later it will get where you want it to go." -Frederik Pohl, Mining the Oort