Cosmology:

1
Cosmology Mass and Energy I

• by
• Robert Nemiroff
• Michigan Tech U.

2
Physics X About This Course

• Officially "Extraordinary Concepts in Physics"
• Being taught for credit at Michigan Tech
• Light on math, heavy on concepts
• Anyone anywhere is welcome
• No textbook required
• Wikipedia, web links, and lectures only
• Find all the lectures with Google at
• "Starship Asterisk" then "Physics X" 
• http//bb.nightskylive.net/asterisk/viewforum.php?
  f39

3
Mass and Energy in the Universe Overview

•  
•  
• Standard GR cosmology only
• Called Friedmann Robertson-Walker
• It's the most standard GR set of cosmologies
•  
• This lecture is based (mostly) on my paper
•  "Adventures in Friedmann cosmology A detailed
  expansion of the cosmological Friedmann
  equations" by Nemiroff Patla
• 2008AmJPh..76..265N

4
Cosmology Friedmann Equations

•  
•  
• Two Energy equation and Acceleration equation
• Relates two variables
• "a" scale factor for the universe
• "Omega" O the energy density of the universe
• Energy equation is the simplest 
• Uses only the first derivative of "a" (and a)
• Can be complicated if several types of energy
  involved

5
Cosmology Friedmann Equations

•  
•  
• Acceleration equation is more complicated
• Uses second derivative of "a" (and a)
• time part of larger 4-vector
• mathematically equivalent to Energy equation 
• when spatially symmetric in all 3 spatial
  dimensions

6
Cosmology Cosmic Rest Frames

•  
• Every place in the universe has an intrinsic
  "rest frame"
• This seems to violate Special Relativity
• But Friedmann GR solutions establish it
• Defined by rest frame of energy forms in the
  universe
• Cosmic microwave background (main one)
• Matter at rest "with respect to the universe" 
• sees the microwave background the same in every
  direction

7
Cosmology Horizons

• Event Horizon
• Inside, events cannot effect outside
• Particle Horizon
• Also known as "Cosmological Horizon"
• Furthest distance particles can reach you if they
  left at the Big Bang
• Gravitational Horizon
• Furthest distance gravity can reach you

8
Cosmology Scale Factor "a"

• The scale length at any time in a Friedmann
  Robertson Walker (FRW) universe is given by the
  single parameter "a".  
• One way to visualize "a" is as the average
  distance between galaxies.  
• Even when there are no galaxies.
• In an expanding universe, "a" increases with time.

9
Friedmann Equation of Energy Generic Form

• Where
• H (da/dt)/a Hubble's parameter
• G gravitational constant
• ? energy density
• c speed of light
• R un-normalized universe scale factor
• k dimensionless, related to curvature

10
Friedmann Equation different terminology

•  
• Different energy types change differently as the
  universe expands
• The total energy density of the universe includes
  all possible energy types

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Friedmann Equation of EnergyGeneral Form

• Where Ho is H at the present time (z0)

12
Cosmology Perfect Fluids

• A perfect fluid is defined by only two variables
• density ?
• pressure P
•  
• These are presumed defined everywhere in the
  universe to be the same at any given time.  
• This is also called the Cosmological Principle

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Cosmology Perfect Fluids

• w P/ (? c2) tells the type of perfect fluid.
•  
• Each perfect fluid is a different type of energy.
• ? a-3(1w) shows how density changes with w as
  the universe scale factor "a" changes.

14
Cosmology Perfect Fluids
15
Friedmann Cosmology Energy Conservation

• Energy is NOT conserved. 
• Matter dilutes EVERYWHERE in the universe.  So
  energy related to matter decreases.  There is no
  place for this energy to go.

16
Cosmology Gravity attraction or repulsion