AST4414/5416: Cosmology - Fall 2009 - Social Whiteboard

Welcome to the Cosmology 2009 wiki page. This purpose of this page is primarily to provide a communication tool for students taking the Cosmology course to discuss homework, post links to useful resources, etc. The main course website is still blackboard, though if there is a desire to have some of that information moved over here let me know.

Questions for Chris

If you have questions/comments you want to direct at the instructor (me), I've got this page setup to email me modification notices.

Otherwise the floor is yours...

Open Discussion

Moved from the Questions for Chris page:..

Q: One of the few things that continues to elude me is how the mus, nus, rhos, and sigmas work. Take for instance the calculation of the affine connection in the homework. How does that work. I was okay with g_ij, but the inclusion of the k and the other parameter (I will call it l) throws me. Which parameters are for theta and r, and which are for x and y? Also many of the references I found just use numbers for the metric locations. I am just a little confused on the actual details on how to do this as I have never seen any of this before.

A: There are a couple of different conventions at play here. Weinberg (and others) often reserve the use of greek indices to refer to fully 4-D space-time coordinates, and reserves roman (i,j,k etc) indices to refer to strictly spatial coordinates. I've tried to be consistent with this, but I can't guaranteed that I've always succeeded and if you find a place where I've goofed, point it out to me. So here I use $g_{ij}$ since we're just looking at familiar spatial geometry and not the somewhat more alien Lorentz geometry of relativity.

A second convention is comes into play at times when discussing locally inertial Minkowsi frames. Here it is often the convention to refer to the 0 component as the locally inertial time coordinate, and then refer to the spatial coordinates by generic roman (i,j) indices, or if you're adopting a cartesian coordinate system then $x^{0}=t$; $x^{1}=x$; $x^{2}=y$; $x^{3}=z$.

I haven't used it in the PS 1 assignment, but I've been known to adopt a similar notation for non-cartesian specific coordinates, vis $g_{rr}$ being the radius-radius component of the metric tensor. (i.e. the coefficient that would show up in front of $dr^{2}$ in the equation for the line-element in polar coordinates.) I will be using this notation for the solutions to PS 1 and you may find it convenient as well.

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