Cosmology II - The nature of the universe What kind of universe do we live in (positive, Negative, or zero curvature)

Example1: space with positive curvature: the surface of a sphere You would have flunked Sophomore geometry

Interesting historical aside Karl Friedrich Gauss thought of this, and sent out surveyors to test if the geometry in Hanover really was Euclidean

The case of zero curvature: Euclidean space

Final case: that of negative curvature: the surface of a saddle

Within the context of General Relativity, all three cases of curvature (positive, negative, zero) are theoretical possibilities. All three possibilities give universes which expand with time The question is: what kind of universe do we live in?

Point to emphasize For all three types of curvature, the solutions of the equation have a(t) increasing. The equations of General Relativity could have predicted Hubble’s Law

How to measure the curvature (or geometry) of our universe Measure angular size of a “rigid rod” as a function of distance (z). Measure the brightness of a “standard candle” as a function of distance (z). Unfortunately, real astronomical objects don’t want to stay constant over cosmological times.

Result of solutions of equations for Friedmann Universe Evolution of universe And its curvature depend On the mean density (1)Density less than critical density: negative curvature and indefinite expansion (2)Density greater than critical density, positive curvature and future contraction

Value of the critical density kg/cubic meter ~ 10 hydrogen atoms/cubic meter Typical density in the interstellar medium is 1 million - 10 million hydrogen atoms/cubic meter Space could be very empty and still have a density greater than critical Say it with equations!

The age of the universe In a Friedmann universe, the age depends on what sort of a(t) we have

A consistency check for cosmological theories: are our estimates for the age of the universe consistent with independent measurements of the age of objects? Age of the Earth Age of globular cluster stars

Connection with textbook: Skip (for now) discussion of cosmological constant and Dark Energy. Will return to later, since they are an important Part of modern cosmology

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

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