Mass of the Universe: What's the Real Number?

[sWozzAres]

I have heard various figures, but what is the mass of the universe and what is the margin of error?

Also, since dark matter and dark energy seem hypothetical, shouldn't this be included as part of the margin of error?

 

[phinds]

First, you should be careful about your terminology. "The universe" is of completely unknown size, thus there is no answer to your question.

If you are talking about the "observable universe" then there is an answer, although I don't know what it is.

No, the dark things are not part of the margin of error. Just because we don't know what they ARE does not mean that we don't know what they DO and you are asking about what they do.

 

[sWozzAres]

it should be obvious from context that I mean observable universe! :)

"Both popular and professional research articles in cosmology often use the term "universe" to mean "observable universe". This can be justified on the grounds that we can never know anything by direct experimentation about any part of the universe that is causally disconnected from us, although many credible theories require a total universe much larger than the observable universe"
http://en.wikipedia.org/wiki/Observable_universe

However, I can see that point 3 is valid, certainly for dark matter but the reason behind my question is that I heard that the mass of the universe has a "fudge factor" built into it to account for dark energy and I wanted to know more about this.

 

[cepheid]

There is no need for a "fudge factor." Although we don't have much of a sense of what dark matter is, and even less so for dark energy, we do have a very good idea of how much of each of these constituents there is (per unit volume).

http://spaceinimages.esa.int/Images/2013/03/Planck_cosmic_recipe

These pie charts show how much each constituent contributes to the total "energy budget" of the universe. We can measure these ratios really well for the following reason: the best theory we have that governs the expansion and evolution of the universe as a whole is General Relativity (GR). GR says that there are a whole bunch of things about the universe that depend on its mass-energy content, including its expansion rate and its geometry. So, through observations that allow us to measure the expansion rate, geometry, and other things, we can measure precisely this breakdown of the mass-energy content of the universe by constituent. The parameters in the pie chart, are Ω_de = 0.73, Ω_dm = 0.22, and Ω_b =0.05. These are the density parameters for dark energy, dark matter, and ordinary (atomic or "baryonic") matter respectively. The density parameter for each one is the ratio of its density to a critical density that is required to keep the universe flat (Euclidean, i.e. no spatial curvature). E.g.: Ω_dm = ρ_dm/ρ_cr, where ρ_cr is the critical density. So, the fact that these density parameters add up to 1 tells you that the total energy density of the universe is very close to critical, and therefore the geometry of the universe is close to flat. This is an observed/measured result.

Anyway, if you know the density parameter of each component, you know its density relative to the critical density. So, if you know value of the critical density, then you can get the density of each component in absolute terms (since you know the ratio). Once you know the density of each component, you can compute the total mass/energy that is present due to each component simply by multiplying its density by the volume of the observable universe. Note that I don't bother distinguishing too much between mass density and energy density here, since cosmologists like to use a unit system in which c = 1 and it doesn't matter.

Density parameters:
http://hyperphysics.phy-astr.gsu.edu/hbase/astro/denpar.html

The value of the critical density (today) is given at the bottom.

 

[Trenton]

Cephid,

I actually came onto the site to see if I could find any good explanations of why interstellar gas is not considered to be responsible for the bulk of a galaxy's mass, leading to the requirement of 'dark matter' - when your submission about both dark matter and dark energy caught my eye.

I have read the supplied hyperphysics link but I was hoping for a more detailed analysis, in particular, how the values are derived from GR.

I am mainly interested in following the logic of the 'established' thinking on this, so that among other things, I understand why it is thought that the expansion of the universe is driven by a form of energy.

Without this understanding I feel the temptation to believe that since space contracts under the influence of the stress-energy tensor, the expansion is due to a collapsing stress-energy tensor. The only thing I can think of that effectively excludes this is the notion that the big bang singularity has no time or space outside it but I have never found a formal proof of this.

Any good reading material you can recommend would be much appriciated ...

 

[marcus]

Hi Trenton,
neutral hydrogen is resonant to a certain microwave frequency---wavelength 21 centimeters.
http://en.wikipedia.org/wiki/Hydrogen_line
There are gas clouds in our galaxy and radio astronomers have mapped them. Densities can be estimated etc.
Cepheid and others may supply more complete and detailed info but that's part of the answer to your question.
Ordinary gas and dust clouds indeed are there but do not account for enough mass to obviate dark matter.

 

[Trenton]

I had thought that while the 21 cm line measurments were good for spotting clouds of gas they were not accurate at measuring the mass of such clouds - and that for measuring density of extreamly diffuse gas they were hopelessly inaccurate. I take it this is not the case?

Nor did I think the luminosity models were that good. They work well for counting up mass in visible spectrum non collapsed stars but not as far as I know, for brown dwarfs or neuton stars - But obviously, any inaccuracies of this model would be less of a concern.

Anyway I guess that does answer the question of why it is thought that dark matter must exist!

 

[phinds]

Ordinary gas and dust clouds indeed are there but do not account for enough mass to obviate dark matter.

Marcus, that's the first time in probably 20 years that I have seen the word "obviate" used correctly.

 

[Chronos]

Measuring the actual mass of the observable universe is frightfully difficult. Measuring the global mass density is much less difficult, and that is what cosmologists focus upon. There are billions upon billions of galaxies, not to mention enormous primordial gas clouds to account for. What makes more sense - weigh each one individually, or throw everything on the scale at once? CMB studies are the 'all at once' approach. You divide that result by the volume and - you get the average mass density of the universe. Of course, we use other methods to derive the mass of individual objects. It is, however, a slow process and more of a humor check.

 

[sWozzAres]

Since measuring the mass of the universe is 'frightfully difficult', is it possible that with more accurate techniques, we might discover that the observable universe is contained within it's Schwarzschild radius?

 

[phinds]

Since measuring the mass of the universe is 'frightfully difficult', is it possible that with more accurate techniques, we might discover that the observable universe is contained within it's Schwarzschild radius?

As I recall, there was a post on this forum some time back that said the Schwarzschild radius of the OU is know to be about 10 billion LY. I remember that because I was quite surprised that it wasn't a lot smaller.

 

[gabriel.dac]

Some people believe that the mass of the universe can be... zero. For every positive thing in the universe there is a negative one that cancels it out. So the universe could be a disbalance of... nothing.

It's like... instead of having a 0 you have 1 and -1. In either case you have nothing. This is just a theory, of course.

 

[goldust]

Methinks the universe is infinite.

 

[Jonathan Scott]

Since measuring the mass of the universe is 'frightfully difficult', is it possible that with more accurate techniques, we might discover that the observable universe is contained within it's Schwarzschild radius?

The "Schwarzschild radius" of the observable universe is indeed of the same order of magnitude as its actual radius.

This is related to the Dirac Large Numbers Hypothesis (LNH) and more specifically to the Whitrow-Randall (or Whitrow-Randall-Sciama) relation, which point out some surprising coincidences in cosmology.

The Whitrow-Randall relation says that if you add up the Newtonian gravitational potential decrease due to everything in the universe, in dimensionless units (potential energy per rest energy), that is the sum of Gm/rc^2 for each mass m and distance r, then it appears that the sum is approximately of order 1.

As a rough approximation, if you assume the universe has mass M and effective radius R, and say that the average effect of the distance to each source mass can be approximated by 1/r = 1/kR where k is a constant somewhat less than 1 which depends on the assumed "shape" and hence radial mass distribution of the universe, then one would expect this potential to add up to GM/kRc^2 for the whole universe. If this is a number of order 1, then R is of the same order as 1/k GM/c^2, which is in turn equal to the Schwarzschild radius in the case where k = 0.5.

In Machian gravity theory, the Whitrow-Randall relationship is taken to be constant and defines G in terms of the distribution of the masses in the universe. In GR, this relates to a concept called the "Sum for Inertia" which seems to provide an intuitive explanation for inertia as an inductive effect of the gravitational field, but frustratingly it does not seem possible for it to work exactly, as in GR the gravitational constant G is a universal constant.

 

[Trenton]

A quick note on Gabriel's comments - there is a certain amount of voltage to the zero net universe concept. It has a very deep appeal but I found trying to conceive of a counter balance more mind blowing than GR (which I eventually managed to get my head around). One obvious candidate was the universe's expansion. The problem was I could not advance this theory in any way.

Moving on to the comment by phinds, the figure of 10 billion LY is quoted in Wikipeadia but I don't know the original source of this info. Surely though, if the universe has enough mass to eventually stop expanding and to then contract, it would all have to lie within its own Schwarzschild radius?

I would go further than to describe measuring the mass of the universe as 'frightfully difficult'. You do have to resort to 'throwing everything on the scale at once' as Chronos suggests. But doing this means accepting as fact things that are still conjecture. As compelling as the big bang theory is, I note that the age of 13.6 billion years and the Hubble constant of 72Km/Sec per million parsecs produce an all too convienient result. At a distance of 13.6 billion LY an object will be receeding at c. The troble is there is nothing in GR that says things have to stop there. If we are in a BH spacetime moves inward faster than light.

On the other subject of dark matter I shall reserve judgement. Yes I accept that observations strongly suggest we need dark matter to make up the galactic mass deficit. But although observation must be the paramount driver of theory it is worth asking how good are our observations. WIMPS and axions are reasonable theories but not compelling ones. What is compelling is the case for better telescopes. I am more tempted by the idea that there are very large numbers of brown dwarfs than I am by WIMPS but better telescopes could also find WIMPS. It does not look like tanks of fluid in disused mines are coming up trumps. But ultra accurate measurements of mass aquisition rates of neutron stars might do the trick.

 

[gabriel.dac]

A quick note on Gabriel's comments - there is a certain amount of voltage to the zero net universe concept. It has a very deep appeal but I found trying to conceive of a counter balance more mind blowing than GR (which I eventually managed to get my head around). One obvious candidate was the universe's expansion. The problem was I could not advance this theory in any way.

I find the Zero Energy Universe theory pretty easy to understand. It is easier to understand than GR and the string theory, at least for me.

According to GR, E=mc^2. So there is a relation between mass and energy. All mass known is positive. Some people consider gravity a negative energy, so they would cancel out. I don't know much about this theory, but it certainly makes sense

 

[Trenton]

String theory is weird but GR is, when properly explained, quite straightforward. There is a lot in GR that will be of interest to zero net energy theorists.

On the dark matter front my last entry inolved a joke that went a bit awry. Not point explaining it now though. However a question to consider. This stuff can't be moving any faster than about 250Km/sec otherwise it would escape the galaxy. Since it does not interact with light it is not repelled from stars by radiation pressure like ordinary interstellar gas is. Over time (easiliy within a billion years) all the dark matter would end up in stars since these have far higher escape velocities than 250Km/sec. This would seem to put the missing mass theory back to square one.

 

[Trenton]

I am not qualified to say but anything involving more than 3 spatial dimensions plus time sounds like someone has been watching too much Dr Who. Worse than this string theorists are divided into two camps. One says there are 10 dimensions, the other says 11. Presumably the camp that says 10 watch Dr Who straight. The other watch it while on LSD.

They are not strings anyway. They are hedgehogs. All particles are really energy and energy must move at c. The photon moves in a straight line at c while the particle oscillates in and out at c. The wave function for this looks like a hedgehog. Google 'hedgehog space' and you will see what I mean.

 

[phinds]

I am not qualified to say but anything involving more than 3 spatial dimensions plus time sounds like someone has been watching too much Dr Who. Worse than this string theorists are divided into two camps. One says there are 10 dimensions, the other says 11. Presumably the camp that says 10 watch Dr Who straight. The other watch it while on LSD.

 

[Chronos]

The majority of galaxies are too distant to submit to traditional methods of mass measurement [e.g. virial theorem]. We have since developed more advanced techniques, including gravitational lensing and the sunyaev-zel'dovich effect, but, these methods have their own limitations and are not always usable. So, we are stuck with 'big picture' methods to achieve any meaningful degree of precision.

 

[Chronos]

I wanted to mention that the existence of dark matter was first noticed by Fritz Zwicky, who was using virial theorem to estimate the mass of the coma cluster and found an immense discrepancy between that and the apparent mass suggested by luminosity. That remains one of the most compelling arguments favoring the existence of dark matter. Of course now we have the bullet cluster, which also looks pretty strong. Alternative explanations include MACHO's, which have been convincingly excluded based on lensing studies, and MOND [an alternative to Newtonian gravity]. It too has been largely ruled out, or at least so complex as to be dismissed on the grounds of Occam's razor. Albeit, a small number of devoted MOND adherents still remain among us.

 

[gabriel.dac]

I am not qualified to say but anything involving more than 3 spatial dimensions plus time sounds like someone has been watching too much Dr Who. Worse than this string theorists are divided into two camps. One says there are 10 dimensions, the other says 11. Presumably the camp that says 10 watch Dr Who straight. The other watch it while on LSD.

Both agree that there are 10 spatial dimensions. But some of them consider time to be a dimension as well, so, 11 dimensions.

And I see no reason why time cannot be a dimension as well.

 

[Hornbein]

Marcus, that's the first time in probably 20 years that I have seen the word "obviate" used correctly.

Perspicuity obviates perspicacity.

 

[Trenton]

For the record I am firmly non-MOND. I remain just about 'open' on the subject of dark matter although I really am baffled as to why nobody seems to think it would all end up in the stars - therby negating its 'purpose' which is to account for missing mass.

The only way it could avoid this fate is to be mutually repulsive at close distances rather than be inverse square. Is such a repulsive force in the dark matter hypothesis? I have not heard as such.

 

[Jonathan Scott]

There are of course two aspects of MOND: the observation than an empirical formula seems to be ridiculously successful at explaining and predicting rotation rates for galaxies, and various theories which attempt to explain why that formula works so well (most of which have difficulty in achieving internal consistency, let alone consistency with other factors).

Even if you don't like the MOND-based theories (which is a perfectly sensible position to take), the MOND empirical formula is still such a surprisingly strong result that regardless of your preferred theory you still have the interesting puzzle of explaining why MOND seems to work, for example why Dark Matter happens to distribute itself in a way that is apparently determined by the distribution of the luminous content, even for galaxies with very different structure.

 

[Trenton]

I was aware of MOND's formula being successful at matching observed galactic rotation. And of course, it should never be forgotten that science is all about formulating theories that match observations. But it lacks consistency as you say and for me that is a very big hurdle to overcome.

But dark matter is far from clean cut either. Unless there is mutual repulsion between particles of dark matter that worked at close range only, the dark matter theory would fail to explain the galactic rotation. It would all end up in stars and be a zero sum game.

Although neither can be ruled out (at least by the likes of me), both theories have issues when shaving with Occam. This is why I think it is worth examining the possibility that our luminosity/matter models are wrong. It is possible that the missing mass is largely due to so called MACHOs but it is hard to believe that for every star there are four or five neutron stars or BHs. Likewise it is hard to believe that there are hundreds of brown dwarfs per star.

The interstella gas has to be the place to look for the bulk of the missing mass. How well would hydrogen sat at or close to 2.7K emit at the 21cm wavelength? Do we know and if so how do we know this? Maybe now Voyager has passed the heliosphere we might get some answers regarding the abundance of charged particles at least.

I am clutching at straws to a certain extent but I don't see any harm in tightening up the models even if it still leaves us with a mass deficit.

 

[Drakkith]

But dark matter is far from clean cut either. Unless there is mutual repulsion between particles of dark matter that worked at close range only, the dark matter theory would fail to explain the galactic rotation. It would all end up in stars and be a zero sum game.

How so? Without a way to shed energy and momentum, dark matter cannot clump together like normal matter can.

 

[kurros]

...although I really am baffled as to why nobody seems to think it would all end up in the stars - therby negating its 'purpose' which is to account for missing mass.

If dark matter is a WIMP then some of it WILL be captured by stars. This kind of dark matter usually self-annihilates, so people are looking for things like excess neutrinos coming from the sun due to such annihilations.

However, as Drakkith says, the cross-section for these interactions is really small, so only a small fraction of dark matter can be captured this way. Not to mention it has to pass through the sun to scatter and be captured in the first place, and stars are pretty small compared to the amount of empty space out there. Most WIMP dark matter is expected to just perpetually slosh back and forth in big halos around the galaxies. Like a big non-interacting gas.

 

[Chronos]

For the record I am firmly non-MOND. I remain just about 'open' on the subject of dark matter although I really am baffled as to why nobody seems to think it would all end up in the stars - therby negating its 'purpose' which is to account for missing mass.

The only way it could avoid this fate is to be mutually repulsive at close distances rather than be inverse square. Is such a repulsive force in the dark matter hypothesis? I have not heard as such.

Dark matter is virtually collisionless, even with itself, hence it does not clump in stars, or pretty much anything else. It tends to be most abundant in halos because it continuously yo-yo's in and out of the galaxy, and that is where it's velocity is minimal.

 

[yogi]

Embellishing upon the idea of Mach's Principle as the synergistic consequence of each mass contributing to all the others, then one can get a rough estimate of the mass as [(4pi)R^2]kgm/meters^2
where R is the Hubble radius. Using R = 1.3 x 10^26 meters this leads to a little over 10^53 kgm This assumes a two sphere model of the universe with all the matter energy concentrated on the surface. For a 3 sphere the total would be higher by a factor of 6/5. This only works if all the matter energy is ordinary