1
vote
0answers
61 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 ...
4
votes
1answer
126 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 ...
1
vote
0answers
41 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 ...
2
votes
0answers
92 views

General formula to compute the redshift (first order perturbations)

Consider an expanding universe with the following metric in conformal time/co-moving coordinates: ...
2
votes
1answer
161 views

Cosmological metric with off-diagonal terms?

In the context of Cosmology models, What are examples of metrics with off-diagonal terms?
2
votes
1answer
82 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
vote
2answers
267 views

Coordinate and conformal transformations of the FRW metric

I'm considering a metric of the following form (signature $(+,-,-,-)$): $$ds^2 = (F(r,t)-G(r,t))dt^2 - (F(r,t)+G(r,t))dr^2 - r^2(d\Omega)^2$$ where $F(r,t)$ and $G(r,t)$ are arbitrary scalar ...
1
vote
2answers
114 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?
6
votes
2answers
300 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 $\rho$ ...
2
votes
1answer
239 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 < ...
14
votes
3answers
251 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 ...