I'd like to compare some models of mine against results from WMAP. Is there anywhere I can get the data, l(l+1) Cl / 2pi as a function of l? I see plenty of images of the TT, TE power spectra with error bars on them from WMAP, but can't seem to find the data. Ideally I'd like to plot my models...
Couldn't think of a better place to post this. I'm writing a document in latex that has several very large equations in it. I can split them up so that they take up two or three lines using the \begin{split} command or \begin{align} command, but If I need to split a line that is contained within...
In GR the metric can raise or lower indices, but which index will it raise in this case:
\delta^{ij} \partial_i \xi_j
is it,
\partial^j \xi_j
or,
\partial_i \xi^i
Or are these equal?
just a quick query, I know that,
\nabla_0 A_{\alpha}= \partial_0 A_{\alpha} - \Gamma^{\beta}_{0 \alpha} A_{\beta}
But what does
\nabla^0 A_{\alpha} equal?
aha! got it.
\Gamma^i_{0j} = \frac{a'}{a}\delta^{ij}+\frac{1}{2}g^{i\nu}\partial_0(h_{\nu j}) .
If I expand the last term out,
\frac{1}{2}(\eta^{i\nu}-h^{i\nu})\partial_0(h_{\nu j}) .
Ignore higher order terms (ie h^2), using the metric signiture (+,-,-,-) coupled with the fact that only...
I'm starting to think that the answer I've been given has a typo, and should read \delta^i_j instead of \delta_{ij} .
I've lost the dummy indices as I've summed over v . When v=0 everything equalled zero, so the next index was j (where j = 1,2,3). Is this not the way to proceed?
Also, I...
Not so much a homework problem, more needing help understanding where something comes from. I've attached a jpg file with what I need help on.
I've done a general relativity course at uni but can't seem to work out what should be a very simple problem.