Is the Friedmann Paradox Solved by the Concordance Model?

  • Context: Graduate 
  • Thread starter Thread starter meteor
  • Start date Start date
  • Tags Tags
    Friedmann Paradox
Click For Summary

Discussion Overview

The discussion revolves around the Friedmann Paradox and its relationship to the Concordance Model in cosmology. Participants explore the implications of the Friedmann equation, particularly focusing on the definitions and units of energy density and mass density, and how these relate to the critical energy density.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents the Friedmann equation and expresses confusion regarding the relationship between the density of energy and critical energy density, noting discrepancies in the formulas.
  • Another participant clarifies that rho represents mass density while rho_crit represents energy density, emphasizing the need for conversion between the two using c^2.
  • Some participants point out that rho includes all forms of energy, not just mass, and suggest that the absence of a lambda term in their interpretation of the Friedmann equation is justified.
  • There is a suggestion that different conventions in literature may lead to variations in the forms of the Friedmann equation, which could explain the observed differences in the formulas.
  • A participant introduces the conversion factor c^2 as a means to reconcile the differences between mass and energy densities.

Areas of Agreement / Disagreement

Participants express differing views on the definitions and roles of rho and rho_crit, with some agreeing that rho encompasses all forms of energy, while others emphasize the distinction between mass and energy densities. The discussion remains unresolved regarding the implications of these definitions on the Friedmann Paradox.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the units of rho and rho_crit, as well as the conventions used in different sources. The relationship between mass density and energy density is not fully resolved, and participants acknowledge potential variations in the Friedmann equation across different contexts.

meteor
Messages
937
Reaction score
0
Please show me how to solve this paradox
cos the Friedmann equation is:
[tex] H^{2}= \frac{8*pi*G*rho}{3}-\frac{k*c^{2}}{R^{2}}[/tex]
but the concordance model says that k=0, so we can eliminate the last term of the equation
then we isolate rho, the density of energy:
[tex] rho=\frac{3*H^{2}}{8*pi*G}[/tex]
but however, the formula for the critical energy density is
[tex] rho_{crit}=\frac{3*H^2*c^2}{8*pi*G}[/tex]
but the concordance model says that rho=rhocrit
but you see that the 2 formulae are not equal, there's an extra c2 in the formula for rhocrit

I can't figure where is the mistake
 
Last edited:
Astronomy news on Phys.org
rho is mass density. rho_crit is energy density (as you wrote it). Mass and energy have different units, and you use c^2 to convert between them.

Most people like to use units such that c=1, and then energy and mass are interchangable. This convention is so common that books are sometimes careless about distinguishing the two.
 
Last edited:
please, take a look to this thread
https://www.physicsforums.com/showthread.php?t=2864
Here's jeff, and I think that he is a knowledgeable person, and says that rho includes all kinds of energy, not only mass

It's not rhocrit but rho, which does in fact - as marcus pointed out - include all forms of energy so there's no need for the lamda term (review the derivation of the FRW equation)
 
Last edited:
meteor said:
please, take a look to this thread
https://www.physicsforums.com/showthread.php?t=2864
Here's jeff, and I think that he is a knowledgeable person, and says that rho includes all kinds of energy, not only mass

That's true. I was being a little sloppy myself. rho includes everything, but the way you wrote it, it has units of mass/volume, whereas rho_crit has units of energy/volume. Wherever you're quoting rho_crit from has a slightly different form for Friedmann's equation than you do, so their answer is different by c^2. This is just a convention. You can choose either mass units or energy units for rho as long as H works out as 1/time in the end.
 
use the conversion c^2=m/e
 

Similar threads

Graduate What is the Friedmann acceleration equation
  • · Replies 1 ·
Replies
1
Views
6K
Graduate Mass density of radiation in Friedmann equation?
  • · Replies 6 ·
Replies
6
Views
3K
Graduate What Describes the Expansion of the Universe?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate What is the Critical Density in the Context of Universe Expansion?
  • · Replies 1 ·
Replies
1
Views
6K
Graduate Anisotropic Universe and Friedmann Equations
  • · Replies 27 ·
Replies
27
Views
5K
Undergrad Does the Friedmann vacuum equation have a linear solution?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Cosmological Scalar Field Density Dilution
  • · Replies 3 ·
Replies
3
Views
3K
Derive and Solve the Lane-Emden Equation for a Polytropic Gas Sphere
  • · Replies 6 ·
Replies
6
Views
3K
Height of a stable droplet on a perfectly wetting surface
  • · Replies 63 ·
3
Replies
63
Views
5K
Undergrad Quadrupole moment tensor calculation for ellipsoid
  • · Replies 3 ·
Replies
3
Views
2K