Friedmann Equation Analysis, expansion of the universe?

In summary, the discussion is about Friedmann's equation and how the right hand side being negative does not necessarily mean that the universe will reach a critical point and then contract. It only means that the expansion of the universe is decelerating. Additionally, it is possible for the acceleration and velocity terms to have different signs. There is evidence that in our current universe, the expansion is accelerating, but this was not always the case.
  • #1
SmcWill
2
0
Friedmann's Eq can be viewed here https://ned.ipac.caltech.edu/level5/March08/Frieman/Equations/paper1x.gif
What I don't get is that all the texts/analyses of Friedmann's equation say that if the right hand side is negative it means that the universe will expand reach a critical point and then contract. But if the right hand side is negative doesn't it mean that a dot, the rate of change of the scaling term, is imaginary? Also I don't understand how this squared term can be negative, or even how we can analyze something from it being negative. Thank you!
 
Space news on Phys.org
  • #2
SmcWill said:
if the right hand side is negative doesn't it mean that a dot, the rate of change of the scaling term, is imaginary?

They mean the RHS of the second Friedmann equation, the one with ##\ddot{a} / a## on the LHS.

Also, you may be misunderstanding the sources you're looking at (links to them would be helpful). The RHS of the second Friedmann equation being negative means the expansion of the universe is decelerating; but that alone doesn't tell you whether the expansion will eventually stop and then turn into contraction. You need more information to determine that.
 
  • #3
I understand that if that equation is negative then the acceleration of the scale constant is concave down. But then doesn't that mean that we must know the sign of a double dot and a dot? For example it tells us that a(t) is concave down. but what if it were a function like this http://www.biology.arizona.edu/biomath/tutorials/functions/images/function_concave_down.gif (the left graph), and is there any evidence that it isn't this way? Also, thank you for your reply that cleared a lot of confusion up.
 
  • #4
SmcWill said:
doesn't that mean that we must know the sign of a double dot and a dot?

No. It is perfectly possible for ##\ddot{a}## to be negative but ##\dot{a}## positive.

SmcWill said:
is there any evidence that it isn't this way?

We know that ##\dot{a}## is positive in our universe now. That's what "the universe is expanding" means, and we have lots of evidence that the universe is expanding.

In our actual universe now, ##\ddot{a}## is also positive. That is what is meant by "the expansion of the universe is accelerating". But that has only been the case for the last few billion years; before that, ##\ddot{a}## was negative, but ##\dot{a}## was still positive (the universe was still expanding--and it has been since the Big Bang).
 

FAQ: Friedmann Equation Analysis, expansion of the universe?

1. What is the Friedmann Equation and how does it relate to the expansion of the universe?

The Friedmann Equation is a mathematical equation used to describe the expansion of the universe in the context of the general theory of relativity. It takes into account factors such as the density and curvature of the universe, and can be used to predict the evolution and fate of the universe.

2. How does the Friedmann Equation account for the observed acceleration of the universe's expansion?

The Friedmann Equation includes a term known as the "cosmological constant" which represents the energy density of empty space. This term can account for the observed acceleration of the universe's expansion, as it implies the existence of a repulsive force that is driving the expansion.

3. Can the Friedmann Equation be used to explain the formation of galaxies and other large-scale structures in the universe?

Yes, the Friedmann Equation can be used to explain the formation of galaxies and other large-scale structures in the universe. It predicts that as the universe expands, small density fluctuations will grow and eventually form clumps of matter, which will eventually form galaxies and other structures.

4. What are some of the assumptions made in the Friedmann Equation analysis?

The Friedmann Equation analysis assumes that the universe is homogeneous and isotropic on large scales, meaning that it looks the same in all directions and at all points in time. It also assumes that the universe is described by the general theory of relativity, and that the matter in the universe is distributed evenly on large scales.

5. How has the Friedmann Equation been tested and validated?

The Friedmann Equation has been tested and validated through various observational data, such as the cosmic microwave background radiation, the large-scale distribution of galaxies, and the observed redshift of distant galaxies. These observations are consistent with the predictions of the Friedmann Equation, providing further evidence for the expansion of the universe.

Similar threads

Back
Top