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Lecture 38 – Cosmology II. How do we describe (and understand) the expansion of the universe, what is happening now, what happened in the remote past, and what will happen in the distant future?. General Relativity. General Relativity and the Universe.
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Lecture 38 – Cosmology II How do we describe (and understand) the expansion of the universe, what is happening now, what happened in the remote past, and what will happen in the distant future? General Relativity
General Relativity and the Universe • General Relativity says that mass bends or warps spacetime (Einstein Field Equations) • Since ordinary space is a part of spacetime, space can be curved as well • Read textbook for further comments on the meaning of “curved space”
An analogy: 2D space on the surface of a balloon. Curvature indicated by non-Euclidean geometry
A physical theory of the universe • Start with Einstein field equations (too tough) • Assume universe approximated by smoothed-out paste, characterized by its mean density • Assume universe is homogeneous • Assume universe is isotropic Cosmological Principle
Friedmann Universe, described by Friedmann equation Friedmann equation an equation for the “cosmic scale factor” a(t). Friedmann equation says how a(t) depends on mean density in the universe, plus other things
Friedmann equation…basis of cosmology a(t), da/dt = a, H0 = (a/a) Friedmann equation K=0…flat, Euclidean space K>0…positive curvature, like sphere K<0…negative curvature, like potato chip
Equation is simple (relatively) to solve if K=0 Then: (a/a0) = (t/t0)2/3 Also an expression for the mean density, which is defined as the critical density In this case, H0 0 as t infinity If the true density in the universe = critical density, K=0
Other possibilities, depending on how density compares with critical density • True density < critical, open universe, H0 > 0 as t infinity. • True density > critical, closed universe, a reaches a maximum, then contraction begins
The “Big Bang” • Friedmann equation predicts a=0 in remote past • This happened 14 Gyr ago if Omega=0 • Happened (2/3)*14 Gyr ago if Omega =1 • At that time, universe infinitely compressed • From that instant on, there was expansion of universe, density drops, temperature drops, like aftermath of explosion • Big Bang
Why age of universe depends on the mean density in Friedmann universe
The Big Bang The Big Bang was not like an explosion, in that it didn’t “explode into nothing”. At the time of the BB, the universe was probably infinite in extent; the scale has gotten bigger with time. Even if it was finite (K>0), it was unbounded
A Reality Check • All of this sounds pretty weird (and it’s about to get weirder), but it isn’t “made up” • We have Hubble’s Law: the universe IS expanding • We have the equations of General Relativity, exhaustively tested in physics experiments • More to come
The Big Bang from the inside out; start at t=0 and see what happens • First few seconds: really weird stuff • First three minutes: whole universe hot and dense as center of Sun. Nuclear reactions everywhere • 700,000 years after BB: universe cools to point where hydrogen atoms combine from protons and electrons, making universe transparent • Few hundred million years after BB: first ghostly protogalaxies • One billion years after BB: birth of the quasars • 5 billion years after BB: galaxies as they are today
