This is the first in a series of lecture notes for Physics 380. These notes are meant to provide a qualitative summary of each course lecture. Their goal is to prevent students, in their rush to take notes on the details of the lectures, from losing sight of the broader picture: how topics fit together, what examples or particular topics show, and the motivations and justifications for steps taken in class.

Lecture 1:

Handouts:

1: Syllabus

Noted course details (help sessions and exam times, etc) from syllabus.

Elaborated on course outline from syllabus. Much of the course will focus on the standard big bang model, which treats our universe as an expanding homogeneous and isotropic space, the Friedmann-Robertson-Walker (FRW) solution to general relativity. In this background the thermodynamics of interacting particles determines the universe's physical history (cosmology). This history is ``standard,'' or well-tested and widely believed, for events going back to about $10^{-2}$ seconds after the initial singularity in the FRW solution, corresponding to particle interactions with a length scale of about $10^{-4}$ angstroms and energy scale of $1\ {\rm GeV}$. Standard cosmology has focused on the time frame required to develop its main observational predictions, the $3^o$ K cosmic microwave background and the formation of light nuclei (big bang nucleosynthesis) -- thus the focus on ``the first three minutes.''

The remainder of the course will focus on extensions of the standard model, which try to explain later evolution (including contemporary and detailed observations) and earlier eras with nonstandard particle interactions. We'll discuss two extended models: an early era of inflation, driven by phase transitions in particle physics; and the new standard model of late-time cosmology, due to multiple recent observations, which notes that our universe currently has accelerating expansion rate, most simply explained by a nonzero cosmological constant $\Lambda$ now dominating the energy density of the universe. The extended models thus extend the standard big bang model, which posits early radiation-dominated expansion followed by later matter-dominated expansion, with an earlier epoch of inflation and a later -- present -- one of $\Lambda$-dominated expansion.

We discussed the course outline, then began with motivations for the standard cosmological model. The nineteenth century, and probably your most recent physics courses, closed with a different ``standard'' cosmological model: that of an infinite, uniform, static universe, whose local interactions obey Newtonian gravity -- producing the observed orbits of planets, moons, asteroids and other occupants of our solar system. Based on these local orbits and the assumption of a fixed distribution of stars, astronomers were able to accurately predict a litany of observational facts: basically, when and where each observed star, nebula, etc could be expected to appear in the sky.

Given such empirical success, we must motivate discarding such a theory. We began discussing the failures of such a model: the conceptual paradoxes of Olbers and Newtonian instability, as well as the observational discovery in 1929 of the Hubble expansion. These paradoxes push us to a nonstatic model of universe, whose spatial expansion is driven by its matter content as dictated by general relativity.

We began with Olbers' paradox: why is the night sky dark? We calculated the apparent flux on earth due to an infinite distribution of stars with uniform density $n$, where each star has luminosity $L$. Our naive calculation gave the unexpected answer that the flux on earth should be infinite; that is, the night sky should be infinitely bright.

We refined the calculation to account for the opaqueness of stars: that is, that we see only the first star on our line of sight, with any more distant stars in that direction being obstructed by the first. We did a crude calculation of the predicted flux, including starlight from (statistically) only the closest stars in the universe along each line of sight. We found a finite, but still qualitatively incorrect answer: we predicted the night sky to have a brightness orders of magnitude greater than that of the sun. Thus both the night sky and day sky would have brightness dominated by starlight, much much greater than the the day sky we actually observe (we know this day brightness to be due to our own sun's light, as the night sky observationally is dark).

We then discussed the hidden assumptions in our calculation and how relaxing them might resolve the paradox. Olbers imagined that including other opaque patches in the universe -- such as dust clouds that absorb incoming starlight -- might fix the problem. However, this turns out to be a temporary (nonstatic) fix: ultimately any such dust clouds heat up and start radiating, recreating the original problem. A second possibility involves our assumption of static stars -- that is, that light received from distant stars, emitted a time $R/c$ ago, was emitted with the same luminosity as light emitted from current stars. Relaxing this static assumption gives the dominant physical effect in reducing the flux seen on earth. For a non-static universe, stars emit light in a time-dependent way; in particular, they only emit light after they are formed. In the homework you see that this cut off on the most distant starlight received (the earliest emitted) is enough to resolve the paradox. A final physical effect comes from the redshifting of starlight in an expanding universe, which reduces its power; this effect turns out to be quantitatively negligible.

We then discussed the second conceptual failure of the infinite static Newtonian picture: its instability to gravitational collapse. We reviewed why a finite uniform Newtonian universe collapses radially toward its center point, then extended the same quantitative analysis to an infinite uniform Newtonian universe. We found that wherever we chose our origin, Newtonian theory predicted a radial collapse toward that origin. Thus our prediction of a physical observable - the motion of stars in the universe -- depends on our choice of coordinate axes.

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