All Questions
43
questions
4
votes
3
answers
199
views
Change of variables from FRW metric to Newtonian gauge
My question arises from a physics paper, where they state that if we take the FRW metric as follows, where $t_c$ and $\vec{x}$ are the FRW comoving coordinates:
$$ds^2=-dt_c^2+a^2(t_c)d\vec{x}_c^2$$
...
- 293
0
votes
0
answers
27
views
A question about Friedmann cosmological expansion equation
A recent paper, arXiv:2403.01555, gives the equations for homogeneity and isotropy of an expanding 3-space as expressed in the following
distance interval as $x^i = (t, \chi, \theta, \phi)$ and $x^i + ...
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
0
votes
1
answer
650
views
Klein-Gordon equation in FRW spacetime
The metric for FRW spacetime is $$ds^2=a(n)^2(dn^2 - dx^2)$$ where $dn$ is the conformal time differential form. The Klein Gordon equation in curved spacetime is $$\left(\frac{1}{g^{1/2}}\partial_{\mu}...
user310742
0
votes
0
answers
105
views
Raychaudhuri equation and expansion scalar for constant $a(t)$ FLRW metric
On the Wikipedia page for the Raychaudhuri equation, the expansion scalar $\theta$ is described as the rate of change of volume of a ball of matter with respect to the time of a central, comoving ...
- 323
0
votes
0
answers
45
views
Comoving particle in FRLW metric
I don't know how to describe the motion of a comoving particle in the FRLW metric. I should also find the time that a comoving particle determines using the expression of the FLRW metric. How could I ...
- 1
1
vote
1
answer
72
views
What is the correct gamma factor in FLRW metric in curved spacetime?
Question
What is the correct gamma factor in FLRW metric in curved spacetime?
So I'm quite perplexed my this paper. It seems to be using the Lorentzian gamma factor (equation $3.11$) but for FLRW ...
- 1,389
0
votes
0
answers
89
views
How to prove that Hubble's law is consistent with homogeneity by using a translation?
Assuming that Hubble's law
$$v=H_{0}\,r$$
works for some specific point and that the universe has FLRW metric
$${\displaystyle -c^{2}\mathrm {d} \tau ^{2}=-c^{2}\mathrm {d} t^{2}+{a(t)}^{2}(\mathrm{d}...
- 1,580
2
votes
0
answers
48
views
Does expansion of space over time assume a particular space/time dichotomy?
Regarding the expansion of the Universe, Wikipedia states:
The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe ...
- 222
1
vote
1
answer
135
views
Understanding the Plane Symmetric Metric
I don't understand as to what is the point of having a plane symmetric universe / metric at all? I mean shouldn't any physically sensical cosmological model (e.g. FLRW Model) entail a spherically ...
- 155
1
vote
1
answer
477
views
Distances in cosmology
I want to make sure that I understand the different distance measures is cosmology.
To do that I consider the FLRW metric:
$$ ds^2=dt^2-R(t)^2\left(\frac{dr^2}{1-kr^2}+r^2d\theta^2+r^2\sin^2\theta d\...
user255856
0
votes
2
answers
249
views
Why the FLRW metric was chosen with constant $g_{00}$ time component?
The FLRW metric is used to describe Universe expansion. Why for this purpose time component of the metric is chosen to be constant? Even other metrics which describe inhomogeneous Universe expansion ...
- 15
0
votes
2
answers
193
views
What is $a(t)$ in FRLW metric?
The Friedmann-Lemaitre-Robertson-Walker metric (FLRW metric) is described as:
$$ds^2 = dt^2 - a^2(t) (\frac{d \bar{r}^2}{1-K\bar{r}^2} + \bar{r}^2 d\Omega^2)$$
What does $a(t)$ represent?
I know that ...
- 84
1
vote
0
answers
34
views
Embedding Schwarzschild in FRLW [duplicate]
Does there exist an exact metric in the literature for embedding the Schwarzschild metric in the Friedmann–Lemaître–Robertson–Walker metric? If so, please give a good reference. Thanks.
- 2,155
1
vote
1
answer
59
views
Curvature sign-changing Friedman models
Isotropy and homogeneity of space leads to the spacetime metric of the form
$$
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