All Questions
35
questions
1
vote
2
answers
48
views
Viable values for the $K$ parameter in the FLRW metric
The FLWR metric is sometimes given as $$c^2 d\tau^2 = c^2 dt^2 - \frac{a(t)^2}{(1-KX^2)} dX^2. $$
I am not interested in the tangential motion so I set $d \Omega = 0$ although it is of interest in ...
- 6,102
0
votes
1
answer
67
views
If space has a positive curvature, is the expansion of the universe caused by time, not "dark energy"? [closed]
Ok, I will assume that space has a positive curvature, where space is the "surface" of this sphere, and time is the radius from the center, so the universe is a 4D hypersphere. Under these ...
- 403
4
votes
2
answers
170
views
Why isn't the curvature scale in Robertson-Walker metric dynamic?
$$ds^2=-c^2dt^2+a(t)^2 \left[ {dr^2\over1-k{r^2\over R_0^2}}+r^2d\Omega^2 \right]$$
This is the FRW metric, here k=0 for flat space, k=1 for spherical space, k=-1 for hyperbolic space. $R_0$ is the ...
- 619
1
vote
0
answers
33
views
The General form of the Friedmann equation written in another way
Using the general form of the Friedmann equation:
$$H^2 =H_0^2(Ω_{m0}(1+z)^3+Ω_{r0}(1+z)^4+Ω_{k0}(1+z)^2+Ω_Λ)$$
and taking $a_0=1$, How can I derive that the Friedmann can be writing in the following ...
- 11
1
vote
1
answer
373
views
Radius of curvature of the Universe
Is it correct that the radius of curvature scales with the scale factor $R(t) = a(t) R_o$? If so, in an expanding universe, the radius of curvature gets larger and larger, does that make the curvature ...
- 161
0
votes
1
answer
228
views
What is the relationship b/w mass’s effect on the curvature of space vs the expansion of space?
As is well known, General relativity explains that mass and energy bend the curvature of spacetime. Mass energy of different amounts lead to different space time curvatures.
As is also well known, the ...
- 1
0
votes
1
answer
133
views
Shape of the universe as dark energy starts to dominate
We say that the universe has a particular shape (flat, sphere or saddle) depending on what the ratio between the average energy density and the critical energy density is, something we call $\Omega$.
...
2
votes
1
answer
220
views
Can we have positively curved space within negatively curved spacetime?
Thinking about the universe as a whole. One could imagine that the three spatial dimensions each have the same, say positive, curvature, making space spherical, while time is negatively curved, making ...
- 371
0
votes
1
answer
42
views
Solving Equation of Motion during Preheating in Mixed-$R^2$
Recently, I have an interest in Mixed Higgs-$R^2$ inflation and its preheating. However, there are some problems that I faced, one of them is solving the equation of motion in certain papers and ...
1
vote
1
answer
59
views
Curvature sign-changing Friedman models
Isotropy and homogeneity of space leads to the spacetime metric of the form
$$
ds^2=-dt^2+d\sigma_k^2,
$$
where $d\sigma_k^2$ is the metric on one of the standard manifolds (the 3-sphere, Euclidean 3-...
- 421
0
votes
2
answers
60
views
Does the increasing rate of expansion of the universe have any implication on or alter the curvature of the universe?
I'm not really knowledgeable on physics but was curious about this and couldn't find any good answers related to it.
- 3
2
votes
2
answers
124
views
Measuring the Hubble constant in a curved universe
In an article from the University of Chicago, July 17, 2020, it is stated that
"Judging cosmic distances from Earth is hard. So instead, scientists measure the angle in the sky between two ...
- 24.8k
3
votes
4
answers
681
views
How is the curvature term of the Friedmann Equation calculated with the Newtonian derivation?
I'm trying to develop and intuitive understanding of the Friedmann equation. I'm afraid I get lost with the relativistic derivation as it's just a lot of crank-turning. When I derive it from the ...
- 584
0
votes
1
answer
441
views
How do you calculate curvature from the density?
We know that this density results in a flat universe.
$$\rho_c=\frac{3 H^2}{8 \pi G}$$
And we know that if the universe isn't flat, the density as a proportion of critical density can be expressed as ...
- 584
1
vote
1
answer
411
views
Inflation theory and the flatness problem
Recently I have watched videos on how the inflation theory solves some problems that arise from the Big Bang Theory. In particular, I have a few questions regarding the flatness problem and how the ...
- 95