How is the Expansion of the Universe Related to Recession Velocity?

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SUMMARY

The discussion centers on the expansion of the universe as described by the Lambda-CDM model, which asserts that the universe will continue to expand indefinitely without collapsing. Participants emphasize the importance of specifying parameters such as time and distance when discussing the expansion factor of the universe. The critical density and its relation to the Friedmann equation are also highlighted, with a specific example indicating that the ratio of critical radius to current radius (Rc/Ro) is 6.00, based on a density of 1.2. The conversation underscores the necessity of clear problem statements in cosmological inquiries.

PREREQUISITES
  • Understanding of the Lambda-CDM model in cosmology
  • Familiarity with the Friedmann equations
  • Knowledge of critical density and its implications
  • Basic grasp of recession velocity and proper motion concepts
NEXT STEPS
  • Study the Friedmann equations in detail, focusing on their applications in cosmology
  • Research the implications of critical density on the universe's expansion
  • Explore the relationship between the Hubble parameter and recession velocity
  • Examine case studies involving the Lambda-CDM model and its predictions
USEFUL FOR

Astronomers, cosmologists, physics students, and anyone interested in understanding the dynamics of the universe's expansion and the underlying mathematical models.

jjson775
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Homework Statement
The average density of the universe is 1.2 pc. How many times larger will the universe become before it begins to collapse? That is, by what factor will the distance between remote galaxies increase in the future?
Relevant Equations
See below
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According to our current cosmological model, the Lambda-CDM model which fits the data quite well, the universe will never "begin to collapse" It will continue expanding forever.
 
jjson775 said:
By what factor will the distance between remote galaxies increase in the future?
Google is your friend. You should learn how to use it.
What is the rate at which the universe is expanding?
82.4 kilometers per second per megaparsec
 
Neither one of these replies help me with the problem as stated. I need to find R in terms of p(rho) sub c.
 
jjson775 said:
Neither one of these replies help me with the problem as stated. I need to find R in terms of p(rho) sub c.
You asked by how much the will expand before it begins to collapse. It will never begin to collapse. Then you asked by what factor the universe will expand in the future, but you didn't specify when in the future. So the problem is unanswerable as stated.
 
jjson775 said:
Homework Statement:: The average density of the universe is 1.2 pc. How many times larger will the universe become before it begins to collapse? That is, by what factor will the distance between remote galaxies increase in the future?
Relevant Equations:: See below

View attachment 276402
What version of the Friedmann equation are you working with here?
 
phyzguy said:
According to our current cosmological model, the Lambda-CDM model which fits the data quite well, the universe will never "begin to collapse" It will continue expanding forever.
The problem statement specifies a density greater than the critical density.
 
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phyzguy said:
You asked by how much the will expand before it begins to collapse. It will never begin to collapse. Then you asked by what factor the universe will expand in the future, but you didn't specify when in the future. So the problem is unanswerable as stated.
He ALSO didn't specify how far away he is talking about, which matters since the expansion "factor", as I envision him to be thinking of it, depends on distance as well as how far into the future. I don' t think he understands the answer in post #3.
 
haruspex said:
The problem statement specifies a density greater than the critical density.
Ah. I missed that point. Well then, does that make it a well posed problem?
 
  • #10
phyzguy said:
Ah. I missed that point. Well then, does that make it a well posed problem?
I think we need to see the specific Friedmann equation under consideration.
 
  • #11
Rc = critical radius where kinetic energy of escaping galaxy = 0. Can be calculated from critical density formula given above.
Ro = radius where density = 1.2. I think what I am looking for is Rc/Ro.
The answer in the book is 6.00.
 
  • #12
jjson775 said:
Rc = critical radius where kinetic energy of escaping galaxy = 0. Can be calculated from critical density formula given above.
Ro = radius where density = 1.2. I think what I am looking for is Rc/Ro.
The answer in the book is 6.00.
See the rules for homework:
  • Reproduce the problem statement accurately.
    Type the problem statement exactly as worded. If you're only asking about one part of a long problem it may not be necessary to type up the entire problem, but you need to ensure you've provided the proper context for the sub-problem. If you paraphrase or summarize, make sure you're not changing the meaning or omitting important information. It's very frustrating trying to help with a problem only to discover that critical information is missing.
  • Show us that you've thought about the problem.

Can you say that you've followed either of those guidelines? At best we have a hint of what the problem might be.
 
  • #13
jjson775 said:
kinetic energy of escaping galaxy
"escaping" from what ? Kinetic energy relative to what ?

I think you are confusing recession velocity with proper motion since "escaping" and "kinetic energy" both imply proper motion.
 
  • #14
PeroK said:
See the rules for homework:
  • Reproduce the problem statement accurately.
    Type the problem statement exactly as worded. If you're only asking about one part of a long problem it may not be necessary to type up the entire problem, but you need to ensure you've provided the proper context for the sub-problem. If you paraphrase or summarize, make sure you're not changing the meaning or omitting important information. It's very frustrating trying to help with a problem only to discover that critical information is missing.
  • Show us that you've thought about the problem.

Can you say that you've followed either of those guidelines? At best we have a hint of what the problem might be.
Yes and yes
 
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  • #15
phinds said:
"escaping" from what ? Kinetic energy relative to what ?

I think you are confusing recession velocity with proper motion since "escaping" and "kinetic energy" both imply proper motion.
In my textbook, a large section of the universe is modeled as a sphere. The critical density is derived from the Hubble parameter H and the universal gravitational constant G. See formula above. The derivation considers a galaxy of mass m moving away from the center of the sphere. The kinetic energy of the galaxy is then equated to the potential gravitational energy.
 

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