All Questions
6
questions
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Why is $h_{\mu\nu}$ not a tensor in the perturbed Universe in cosmological perturbation theory?
In the cosmological perturbation theory course per Hannu Kurki-Suonio (2022) : https://www.mv.helsinki.fi/home/hkurkisu/CosPer.pdf, there is a remark in the text page 5 that puzzles me. The text goes ...
- 1,109
1
vote
1
answer
230
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Raising and lowering indices in line elements - why do we raise and lower them in line elements?
My question refers to Piattella's lecture notes on cosmology. On page 15, the Euclidean line element is defined as
$$
ds^2 = \vert d\mathbf{x}\vert^2 = \delta_{ij}dx^idx^j.
$$
My first question is ...
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-2
votes
1
answer
74
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Write down the components of metric tensor correctly [closed]
this is a FLRW metric and I want to write down the metric tensor from this FLRW metric accurately. Can anyone please help me to do this? Thanks in advance.
\begin{equation}\tag{1}
ds^2 = a^2 ( \tau) [...
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5
votes
1
answer
249
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A question from cosmological perturbation theory
We consider the following scalar perturbation on the FRW metric
$$ds^2=-(1+2\Phi)dt^2+2a(\partial_iB)dx^idt+a^2[(1-2\Psi)\delta_{ij}+2\partial_{ij}E]dx^idx^j,$$
where $\Phi$, $B$, $\Psi$ and $E$ are ...
- 3,691
0
votes
1
answer
127
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Isotropy of 3-space and spacetime metric
The most general spacetime metric is given by $$ds^2=g_{\mu\nu}dx^\mu dx^\nu=c^2dt^2+g_{0i}dtdx^i+g_{ij}dx^i dx^j.$$
Why is the second term said to violate isotropy of 3-space?
It is true that ...
- 26.8k
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 :
$S$ ...
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