All Questions
7
questions
0
votes
1
answer
66
views
Name of metric used by Friedmann
In his original paper, Friedmann used the following dynamic and symmetrical metric:
$$\mathrm{d}s^2=a(t)^2\left(\mathrm{d}\chi^2+\sin (\chi)^2\left(\mathrm{d}\theta^2+\sin (\theta)^2 \mathrm{d}\phi^2\...
- 181
0
votes
1
answer
52
views
Common choice in FLRW between dimensionless of scale factor (and coordinates of r lenght dimension) or the contrary
I have an old cosmology book in which the scale factor is expressed in the Roberston-Walker metric as:
$\mathrm{d} s^2=c^2 \mathrm{~d} t^2-R(t)^2 \mathrm{~d} l^2$
with: $\mathrm{d} l^2=\dfrac{\mathrm{...
0
votes
2
answers
113
views
Why is the scaling factor in the Robertson-Walker metric squared?
Not much to add beyond the title. The Robertson-Walker metric solution to the field equations has the form
$$g_{\mu\nu}dx^\mu dx^\nu=-dt^2+a^2(t)\biggl(\frac{dr^2}{1-Kr^2}+r^2(d\theta^2+sin^2\theta \...
- 6,963
3
votes
1
answer
848
views
Friedmann-Robertson-Walker (FRW) metric and scale factor confusion
I'm confused about the different ways of writing the Friedmann-Robertson-Walker (FRW) metric using the normalised and non-normalised scale factor. Peacock, for example, (see equation 3.13) gives
$$c^{...
- 3,059
1
vote
1
answer
87
views
Significance of the sign in the solution to the Friedmann equation
$$\left(\frac{\dot{a}}{a}\right)^2 + \frac{k}{a^2} = \frac{8 \pi G}{3} \rho$$
The Friedmann equation contains a square of the first order derivative of the scale factor $a$ with respect to time. ...
- 1,222
6
votes
1
answer
574
views
Fermi coordinates for a Friedman Robertson Walker metric
I am trying to derive the Fermi normal coordinates formula for a FRW Universe given in Eq. (4) of a paper by Nicolis et al (2008):
$$ds^2\approx -[1-(\dot{H}+H^2)|{\bf x}|^2]dt^2+[1-{1\over 2}H^2|{\...
- 2,094
2
votes
0
answers
262
views
FRW Metric maximally symmetric, derivation, $R=3K$ or $R=6K$ confusion, two different texts
I'm looking at Tod and Hughston Introduction to GR and writing the metric in the two forms;
[1]$$
ds^{2}=dt^{2}-R^{2}(t)(\frac{dr^{2}}{1-kr^{2}}+r^{2}(d\theta^{2}+sin^{2}\theta d\phi^{2}))
$$
[2] $$
...
