All Questions
Tagged with cosmology metric-tensor
180
questions
5
votes
1
answer
391
views
A true singularity at $t=0$, coordinate independent Big Bang
Consider a flat Robertson-Walker metric.
When we say that there is a singularity at $t=0$, clearly it is a coordinate dependent statement. So it is a "candidate" singularity.
In principle there is ...
user56963
4
votes
2
answers
1k
views
Can hyperbolic space be bounded?
There are many visualisations of hyperbolic geometry using Poincaré disks.
What are their purpose?
Can hyperbolic space be bounded?
Can we endow the disk with the structure described by the FLRW ...
- 43
5
votes
2
answers
468
views
FRW metric and its validity througout the age of the universe
Why do we think that the FRW metric should be valid throughout the entire history of the universe?
- 26.8k
25
votes
2
answers
8k
views
How does the Hubble parameter change with the age of the universe?
How does the Hubble parameter change with the age of the universe?
This question was posted recently, and I had almost finished writing an answer when the question was deleted. Since it's a shame to ...
- 358k
1
vote
0
answers
343
views
How to test that a flat metric represents a global three-torus geometry
When introducing Robertson-Walker metrics, Carroll's suggests that we
consider our spacetime to be $R \times \Sigma$, where $R$ represents the time direction and $\Sigma$ is a maximally symmetric ...
user56963
8
votes
2
answers
1k
views
Non-stationary spacetime
What is an example for a spacetime that is non-stationary that is considered as a description of something in nature?
So far all the spacetimes I encounted have always been stationary (Schwartzschild,...
- 2,024
5
votes
1
answer
353
views
Metric to describe an expanding spacetime from coordinates reflecting the perspective of a local observer
The FLRW metric describes the metric expansion of spacetime from the perspective of comoving coordinates. Given the way this metric is usually formulated, comoving distances stay constant, and the ...
- 243
2
votes
0
answers
148
views
General formula to compute the redshift (first order perturbations)
Consider an expanding universe with the following metric in conformal time/co-moving coordinates:
$$ds^2=a^2\left[-c^2\left(1+\frac{2\phi}{c^2}\right)d\eta^2+\left(1-\frac{2\phi}{c^2}\right)\left(dx^...
- 1,109
2
votes
1
answer
741
views
Cosmological metric with off-diagonal terms?
In the context of Cosmology models, What are examples of metrics with off-diagonal terms?
- 43
3
votes
2
answers
517
views
General expression of the redshift: explanation?
In some papers, authors put the following formula for the cosmological redshift $z$ :
$1+z=\frac{\left(g_{\mu\nu}k^{\mu}u^{\nu}\right)_{S}}{\left(g_{\mu\nu}k^{\mu}u^{\nu}\right)_{O}}$
where :
$S$ ...
- 1,109
2
votes
2
answers
1k
views
Coordinate and conformal transformations of the FRW metric
I'm considering a metric of the following form,
$$ds^2 = \left[F(r,t)-G(r,t)\right]dt^2 - \left[F(r,t)+G(r,t)\right]dr^2 - r^2d\Omega^2$$
with signature $(1,3)$, where $F(r,t)$ and $G(r,t)$ are ...
- 21
2
votes
3
answers
610
views
Metric tensor of expanding universe
Why is the metric tensor of a expanding universe a function of time?
Why is it not a function of distance between the galaxies? I heard this from a lecture.
Can anyone help me understand?
- 598
9
votes
4
answers
700
views
Einstein tensor in Friedmann equations : where is the missing $c^2$?
I would like to demonstrate the several forms of the Friedmann equations WITH the $c^2$ factors. Everything is fine ... apart that I have a missing $c^2$ factor somewhere.
In all the following $\rho$ ...
- 1,109
5
votes
1
answer
2k
views
Cosmology with a negative cosmological constant
Based on the Friedmann equation for a universe with only cosmological constant,
$$\left(\frac{\dot{a}}{a}\right)^2 \sim \Lambda$$
I would expect the scale factor $a(t) \sim e^{-it}$ if $\Lambda < ...
- 2,558
22
votes
3
answers
9k
views
What is meant when it is said that the universe is homogeneous and isotropic?
It is sometimes said that the universe is homogeneous and isotropic. What is meant by each of these descriptions? Are they mutually exclusive, or does one require the other? And what implications rise ...
- 3,439