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| Cosmology |
1. The loose terminology that the Universe is expanding really means that space is expanding, and this is signalled by an increase in the cosmic scale factor with time. For a closed, finite Universe this is like the increase of the radius, but for an infinite Universe the scale factor should not be interpreted a radius but instead as a measure of the average separation between galaxies.
3. We are not the center. Because of the expansion of spacetime, any galaxy will appear to be the center as we view from it. Thus all distant galaxies will be redshifted, no matter where we view from.
5. Since light can only travel several hundred kilometers in a time of order 1/1000 of a second, flickering on this timescale implies that the energy source for the gamma-ray burst is no more than several hundred kilometers in diameter. If it were larger, there would be insufficient time for a signal to pass through the object and correlate the flickering intensity because of the finite speed of light.
7. The Jeans mass is proportional to the temperature raised to the 3/2 power and inversely proportional to the square root of the number density of particles in the gas. Since density decreases faster than temperature, the Jeans mass will become larger as the Universe evolves, on average. Thus, we may expect that it is harder to make galaxies as time goes on because the average Jeans mass increases, meaning that larger and larger disturbances are required to initiate gravitational contraction.
9. To produce the pair requires 2 x 0.511 = 1.02 MeV. Solving for T = E/k, this gives about 6 x 109 K. Thus, in a gas at six billion degrees an average photon carries enough energy to create an electron-positron pair.