We continued discussion of the quasiNewtonian expanding universe.

We then relaxed our Newtonian assumption a tiny bit, considering both the Newtonian ``matter-dominated'' case, where $\rho$ scales as $r^{-3}$ as we've argued; and a relativistic ``radiation-dominated'' case where $\rho$ scales as $r^{-4}$. We argued for heuristic origins of this case in general relativity, where energy density, and not just mass, triggers gravitational attraction; and showed that photons/ultrarelativistic particles should have energy density scaling as $r^{-4}$.

Having understood its dynamics in terms of scale factor $R$ in the last lecture, we used the dependence of the Hubble ``constant'' $H = \dot{R}/R$ to solve for the time-dependence of the expansion $R(t)$, finding $R \simeq t^{2/n}$, where $\rho \simeq r^{-n}$. We also noted how the actual time elapsed, or age of the universe, was related to $t_o \equiv H^{-1}$, for both cases. This agrees well with the observed age of the universe. Resolution of a recent ``age crisis'' by recalibration of the distances, and hence ages, of the stars in globular clusters illustrates the recurring importance of the cosmological distance ladder in measuring dynamics of our universe.

We noted that our own universe underwent an early radiation-dominated era, when temperatures were high enough to make many particles relativistic. Eventually, however, the more slowly falling $\rho$ of matter came to dominate, and we entered the current matter-dominated era, which expands more rapidly. This picture and dynamics, gleaned from our quasi-Newtonian approach, will survive general relativistic treatment. However, this evolution will be preceded by an inflationary era, and followed by a $\Lambda$-dominated era, neither of which are intelligible in a quasi-Newtonian limit.

We then discussed the cosmological principle (homogeneity and isotropy of the universe) and its range of validity. We then showed how it implies that triangles in the universe must remain similar as they evolve, which implies Hubble's law for uniform expansion or contraction of the universe. This validates the uniform, but time-dependent extension of Hubble's law which we assumed in discussing quasiNewtonian dynamics of the universe.

Hubble's law inevitably leads to large physical recession velocities for distant galaxies, forcing us to consider relativistic dynamics. We thus will begin a review of special relativity next time, at a level foreshadowing some of the general relativistic extensions we will soon need.

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