# Mass of the U

1. Apr 7, 2005

### wolram

How can we estimate the mass of the Universe if we can only see
the part that is within our horizon?

2. Apr 7, 2005

### mapper

I imagine cause we are only estimating whats known to us. Its an educated guess.

3. Apr 7, 2005

### Chronos

Based on the current rate of expansion, the critical mass density of the universe is about 1.06E-29 grams per cc [roughly 6 hydrogen atoms per cubic meter]. Our best measurements indicate the universe is flat, hence extremely close, if not exactly at the critical density. To get the total mass of the universe, you need only multiply the average density by the volume. If you assume, as most do, that to be the Hubble volume, you arrive at a total mass of around 6E52 kg.

4. Apr 7, 2005

### SpaceTiger

Staff Emeritus
Or perhaps, more precisely, what's knowable to us. This is basically the correct answer, though. The mass of the "universe" usually refers to the mass of the observable universe and that has a definite size.

5. Apr 7, 2005

### Crosson

Figures for the total mass of the universe are infered from the expansion rate of the universe.

6. Apr 7, 2005

### SpaceTiger

Staff Emeritus
You need more than that. Hubble's constant is part of the problem, but the full formula (for a flat universe) is:

$$M=\frac{4}{3}\pi r_p^3 \rho$$

$$r_p=\int_0^{t_0} \frac{c}{a}dt$$

$$\rho = \Omega_M \rho_{crit}=\frac{3\Omega_M H_0^2}{8\pi G}$$

where rp is the particle horizon, $$\rho_{crit}$$ is the critical density, $$\Omega_M$$ is the matter density parameter, and $$H_0$$ is Hubble's constant.

In other words, you need Hubble's Constant, omega matter, and the dependence of the scale factor on time, something which itself depends on the other density parameters (such as dark energy). We have good measurements of these things from WMAP, but it's not as simple as you seem to be suggesting.

7. Apr 8, 2005

### hellfire

If we want to compute the mass of the universe which is knowable to us, we should restrict to a size which is empirically proven (at least with some assumptions). For example, based on Neil Cornish work searching for intersections of circles in the CMB, we could assume the universe is at least 24 Gly in diameter (comoving distance). This is less than 46 Gly in radius (comoving distance) for the particle horizon in the standard model. Thus, we should use 12 Gly as the ‘known’ radius, but not more. However, this makes actually no sensible difference, since we do not expect to know the mass with such an accuracy. I assume that only orders of magnitude are relevant.

Last edited: Apr 8, 2005
8. Apr 8, 2005

### SpaceTiger

Staff Emeritus
If it weren't for this last point, I imagine we could get into a long and healthy debate on the issue, but the measurements really are too crude for it to be worth it. I have a lot of trust in the standard model beyond the CMB, though certainly not all the way to t=0, as my equations above would indicate. The point was mainly to illustrate what was needed for the calculation. To get the answer that you're suggesting, one need only change the lower limit of the integral to the time of recombination.

9. Apr 8, 2005

### hellfire

You are right if we were sure that there is no matching at all between any of all possible circles which can be drawn in the CMB. In such a case, we would reach the comoving distance at which the last scattering surface is located without noticing any topological effect and we could take this as the known radius (actually 45.5 Gly for z = 1100, instead of 46.3 Gly for the particle horizon). However, this is not the case, as it seams that Cornish did only put some minimum constrainst on possible matchings of circles obtaining 12 Gly for the radius. I agree with you that it is and interesting theoretical discussion, but it is not relevant for the calculations givent the current data.

10. Apr 8, 2005

### SpaceTiger

Staff Emeritus
:tongue2:

If the topology is non-trivial on those scales, I'll eat my hat.

Last edited: Apr 8, 2005
11. Apr 8, 2005

### wolram

By Space Tiger.

In other words, you need Hubble's Constant, omega matter, and the dependence of the scale factor on time, something which itself depends on the other density parameters (such as dark energy).

Dark energy, seems such a thorn in the side, is there a model that comes
even close without it?

12. Apr 8, 2005

### SpaceTiger

Staff Emeritus
I would say no, but it depends on who you ask. There's one about super-horizon modes that's been making the rounds on astro-ph, but it's too early to say anything definitive about it.

13. Apr 8, 2005

### wolram

http://arxiv.org/abs/gr-qc/0503099

A quick search of arxiv has come up with this paper

A new model of the observed universe, using solutions to the full Einstein equations, is developed on the basis of the suggestion of Kolb, Matarrese, Notari and Riotto [hep-th/0503117] that our observable universe is an underdense bubble in a spatially flat bulk universe. It is argued that on the basis of Mach's principle, that true cosmic time is set by the bulk universe. With this understanding a systematic reanalysis of all observed quantities in cosmology is required. I provide such a reanalysis by giving an exact model of the universe depending on two measured parameters: the present density parameter, Omega_0, and the Hubble constant, H_0. The observable universe is not accelerating. Nonetheless, due to systematic factors in the luminosity distance relation the inferred luminosity distances will very closely mimic models with a cosmological constant, in accord with the evidence of distant type Ia supernovae. The measured Hubble constant is found to differ from the present physical Hubble parameter by a systematic offset. The predicted age of the universe agrees well with observation. For a universe with only baryonic matter, the expansion age can easily account for structure formation at large redshifts. It is also predicted that the low multipole (large angle) anomalies seen in the cosmic microwave background anisotropy spectrum might be resolved by the new model.

14. Apr 8, 2005

### SpaceTiger

Staff Emeritus
There are a lot more and they all take different sides. Look for recent papers that have Kolb as an author or reference his recent work.

15. Apr 8, 2005

### Chronos

The Kolb et al paper [http://www.arxiv.org/abs/hep-th/0503117] has drawn a great deal of attention [there is a related thread on Wiltshire & Kolb on the string board]. Kolb has been taking a pretty fierce beating, for the most part.

16. Apr 8, 2005

### wolram

By Chronos

The Kolb et al paper [http://www.arxiv.org/abs/hep-th/0503117] has drawn a great deal of attention [there is a related thread on Wiltshire & Kolb on the string board]. Kolb has been taking a pretty fierce beating, for the most part.

I think that any paper that attempts to do away with dark energy is worth
a look at, it seems to me that it is," bandage", for a theory that does not
quite work, how can it be that our U is made of 75% of stuff we know
nothing about, and how can we make predictions about any thing if all this
mass is just not there? Kolb may be wrong, but no more than a theory with
a huge unknown chunk thrown in to make it work i guess a theory like
that would not pass peer review now.

17. Apr 8, 2005

### Chronos

Nobody is going to be happy with dark energy, or dark matter, until we know what it is and how it came to be. As distasteful as it is to insert huge chunks of 'unknowns' into the equation of state, there just has not been a better alternative to date. While it is possible our basic theories are either wrong or have gaping holes. People like Kolb continue exploring that possibility, and they do this knowing full well, and expecting their peers to jump all over it. Science is a cruel mistress.

18. Apr 8, 2005

### turbo

So true. The standard model needs both dark energy and dark matter (in monstrous quantities!)to keep it from self-destructing. The universe is complex, but it must arise from simple consistent rules. The implications of the possibility that rules of the universe can change or even smoothly evolve include non-homogeneity, non-uniformity, and prehaps inadequate time for life to evolve. Let's pretend that the rules of the universe are relatively stable, and that they are the same here for me as they are for you.

Perhaps there is a model by which light loses energy through its interaction with the EM fields through which it passes, negating the need for DE, because the universe is NOT expanding at all. Perhaps that same model can model gravitation on galactic and cluster scales better than GR, and can explain the optical effects of "gravitational' redshift without the need for DM. Would you even entertain considering the relevance of such a model? I have constructed such a model, and it is logically consistant throughout, with no wierd constants, infinities, etc.

Last edited: Apr 8, 2005
19. Apr 9, 2005

### Chronos

I would not seriously entertain such a model. It rubs against the grain of QED - another theory that is not imminently imperiled. It is well known that the vacuum polarization effect alters the 1/r-nature strength of Coulomb's law by a factor of 0.1% at a distance scale of the electron-Compton wavelength. The VP effect is based in the response of the vacuum to field strength inhomogenities and interpreted as a dielectric particle-hole (electron-positron) photon polarizibility. Due to its limited range, VP potential can only be detected in the vicinity of the atomic nucleus. The VP effect does not violate the superposition of electromagnetic fields, hence anomalous, and unobserved interactions, such as photon-photon scattering, or photon-electromagnetic field interactions are highly improbable.

20. Apr 9, 2005

### wolram

http://xxx.sf.nchc.gov.tw/PS_cache/gr-qc/pdf/0503/0503107.pdf