Critical density and total observable mass

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Discussion Overview

The discussion centers on the calculation of observable mass in the universe based on critical density, specifically addressing which volume to use: the 13.7 billion light year radius or the 45 billion light year radius of the expanded universe. The conversation explores implications of these choices on the estimated mass of observable matter.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant calculates the critical density to be about E-29 gm/cm3 and notes that using different volumes leads to significantly different mass estimates (4.6 x E54 gm vs. 1.8 x E56 gm).
  • Another participant suggests that the volume based on the 13.7 billion year radius should be used, arguing that matter density dilutes with expansion, making this choice more logical.
  • A third participant echoes the previous suggestion about using the 13.7 billion year radius and introduces a thought about Hubble's constant and its relation to the volume of the universe, while acknowledging potential flaws in their reasoning.
  • One participant presents conflicting sources regarding which volume to use, citing a Wikipedia article that supports the larger volume and a NASA source advocating for the smaller volume, seeking further input.

Areas of Agreement / Disagreement

Participants express differing views on which volume to use for calculating observable mass, with no consensus reached on the correct approach. Multiple competing perspectives remain in the discussion.

Contextual Notes

Participants reference different sources and interpretations regarding the volumes, indicating a lack of resolution on the definitions and implications of the volumes in question.

jimjohnson
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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.
 
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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?
 
jimjohnson said:
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) /R_{0} 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.
 
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.
 

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