1
vote
0answers
26 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
87 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
108 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
78 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
247 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
113 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
273 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
207 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
209 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 ...