# Critical density and observable mass

1. Jan 22, 2012

### jimjohnson

Please comment on my assumptions and results, this has confused me for some time. Thanks

The following is an attempt to reconcile the critical density of the universe with the amount of observable matter as represented by number of stars.

Assumptions for critical density: Hubble constant (H) = 72 km/sec/Mpc or 2.34 x e-18/sec; volume of universe = 9.22 x e84 cm3; cosmological constant = 7.12 x e-30 (from Brian Greene’s Hidden Reality, page 337); and ratio of matter (baryonic) to dark matter is 1 to 5. majority of baryonic matter exists as stars.

Calculation of mass based on critical density : critical density = 3 x H2/(8 x pie x G) = 9.81 x e-30 gm/cm3; density of matter and dark matter = 2.69 x e-30 gm/cm3 (9.81 x e-30 minus 7.12 x e-30); density of matter = .45 x e-30 gm/cm3 (ratio of 1 to 5); mass of both matter and dark matter = 2.47 x e55gm (volume x density); mass of dark matter = 20.6 x e54 gm; and mass of matter = 4.1 x e54 gm.

Assumptions for number of stars: number of galaxies = e11; number of stars per galaxy = 5 x e10; average mass of star = .6 x e33 gm (.3 x sun’s mass).

Calculation of matter based on number of stars: matter = 5.4 x e54 gm.

Thus, using these assumptions the results are reasonably close, 4.1 to 5.4 x e54 gm for matter. When dark matter is included, 2.47 x e55 gm, the result is also close to the e55 gm, which is based on CMB splotches size (stated in Hidden Reality, page 275).
Jim Johnson, Jan 22, 2012

2. Jan 22, 2012

### mathman

The main problem with your analysis is that you left out the contribution of dark energy. When added into the total, the sum will equal the critical density.

I haven't checked your calculations, but the ratio of total matter density to the critical density looks about right (~ 27%).

3. Jan 22, 2012

### jimjohnson

Mathman, thanks for your response. I was starting to think my analysis of total energy in the universe was of no interest.
Anyway, I did include dark energy, it is the cosmolgical constant. Thus, the equation, I should have included, is as follows (interms of mass rather than density):
Critical density (90.4 x e54 gm) = matter (4.1 x e54 gm) + dark matter (20.6 x e54 gm) + dark energy (65.7 x e54 gm).
There are so many different assumptions and partial explainations concerning the total energy, I wanted to attempt a clarification.

4. Jan 22, 2012

### salvestrom

Working on the basis that the critical density is about 5.5 hydrogen atoms per cubic meter I convereted this to an equal mass of Higgs Boson, using a low end value of 115GeV. The result was 1 Higgs particle per 21 cubic meters. This seemed odd, as it if wasn't enough. Something to do with an imbalance. Wouldn't there be quite a large number of particles or are they all non-existant virtual particles? I read a paper that talked about demonstrating how H-Bosons could decay into dark matter. It had some oddities: chiefly that they took the Hubble Constant as 100 and used the maths to calculate the Higgs as having a mass in the range of 70GeV.

If space is full of energy doesn't that give it a mass. Not literall, but it can be included in the same way that dark energy is. Actually, that brings up a question. How do they add in the mass-energy of a photon? Do they treat that as part of the 4% 'ordinary' matter?

Oh, and please don't respond with comments about how I might as well have converted the density to gold atoms... although I now wonder how much gold that would even be... but gold isn't a fundamental particle for giving mass. That is what makes me curious...

If the Higgs field is always 'on' so to speak... how would that figure into a mass calculation of the universe.

I'll stop now. =D

I once asked my physics teacher how big an explosion it would take to knock the earth out of orbit. I'm imagining the same look on your faces reading this as he had. He did however tell me that such an explosion would probably blow the planet in half.

Last edited: Jan 22, 2012
5. Jan 23, 2012

### jimjohnson

If the critical density (9.8 x e-30 gm/cm3, based on H of 72), is divided by the mass of a proton (1.7 x e-24 gm) the result is 5.76 atoms/m3 or 5.76 x e-6 atoms/cm3. Thus, your quote for density is about the same. Converting the critical density mass/cm3 to total mass results in 90.4 x e54 gm.
The CMB total energy is 3.9 x e72 erg (energy density x volume or 4.2 x e-13 erg/cm3 x 9.2 x e84 cm3). Converting this to mass results in .43 x e52 gm. Thus, the critical density mass is in the range of e5 times larger than the mass/energy of the CMB.
I do not know how to calclate the Higgs energy.