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 equationK=0…flat, Euclidean space

K>0…positive curvature, like sphereK<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