Critical density and total observable mass

[jimjohnson]

Assuming a Hubble constant of 74.3 km/sec/Mpc, the critical density is about E-29 gm/cm3. To calculate observable matter based on 5% of this density (the other 95% is dark matter and dark energy), a volume has to be used. But which volume, the one with a 13.7 billion light year radius or the approximate 45 billion light year radius of the expanded universe?
The two results vary by 39 times, 4.6 x E54 gm or 1.8 x E56 gm.

 

[jimjohnson]

After pondering this, I think the answer should be to use the volume based on the 13.7 billion year radius. Since matter density dilutes with expansion, it is more logical to assume the amount of mass is based on the 13.7 billion year radius.Then, matter density would be 39 times less at the larger radius. Sound correct?

 

[ibysaiyan]

After pondering this, I think the answer should be to use the volume based on the 13.7 billion year radius. Since matter density dilutes with expansion, it is more logical to assume the amount of mass is based on the 13.7 billion year radius.Then, matter density would be 39 times less at the larger radius. Sound correct?

Here's a guess.. since Hubble's constant can be defined : (dR/dt) /[itex]R_{0}[/itex] so it'd make sense to take into account the volume of the universe corresponding to hubble's time ( although Hubble's time is a misleading way of finding the age of the universe) . Just a thought . I don't see anything wrong with your logic . I maybe wrong wait for other ( more experienced users) to post.

 

[jimjohnson]

I have two conflicting sources.
The first says use the larger volume: http://en.wikipedia.org/wiki/Observable_universe
The second says use the "present event horizon" which is the smaller volume: NASA, Ask the Astrophysicst, Feb 11 ,1998 by Jim Lochner
Other input? Thanks.

 

[pmacias]

I would like to clarify that the critical density is the density of matter required for the universe to eventually reach a state of equilibrium, where the expansion rate is balanced by the gravitational pull of matter. This density is estimated to be around 10^-29 grams per cubic centimeter, which is a very small amount of matter per unit volume.

In order to calculate the observable matter based on 5% of this density, we need to consider the volume of the universe. However, it is important to note that the universe is constantly expanding, and its size changes over time. Therefore, the volume we consider for this calculation will also affect the results.

The two volumes mentioned in the content, one with a radius of 13.7 billion light years and the other with a radius of approximately 45 billion light years, represent different stages of the universe's expansion. The first one represents the size of the observable universe at its current age, while the second one represents the size of the universe at the time of recombination, when the first atoms were formed.

Hence, the results obtained using these two volumes will vary significantly, as mentioned in the content. It is important to understand that these calculations are based on certain assumptions and models, and they may change as we gather more data and refine our understanding of the universe.

In conclusion, as scientists, we must be open to the fact that our understanding of the universe is constantly evolving, and we must continue to explore and gather data to improve our calculations and models. The results obtained using different volumes should be interpreted with caution and should not be seen as definitive answers.