Relativity and cosmology for undergraduates

Ka Chun Yu.

Table of contents :
App_B_weighingtheuniverse.pdf……Page 0
The Ancients……Page 4
European Thought Before the 20th Century……Page 6
Early This Century……Page 8
Newtonian Gravity and Mechanics……Page 12
Maxwell and the Ether……Page 13
Inertial and Gravitational Mass……Page 14
Special Relativity……Page 18
Length Contraction……Page 21
Velocity Transformations……Page 22
Relativistic Mass……Page 23
Spacetime……Page 29
Spacetime Continued……Page 33
General Relativity and Curved Space Time……Page 36
Geodesics and Spatial Curvature……Page 40
Curved Space in 3-D……Page 43
Geodesics in Spacetime……Page 46
The Schwarzschild Solution……Page 49
Motion of Particles and Light in the Schwarzschild Metric……Page 50
Deflection of Light by Gravitating Bodies……Page 55
Effective Potentials……Page 57
Effective Potentials in the Schwarzschild Metric……Page 59
Gravitational Collapse and Black Holes……Page 62
Falling Into a Black Hole……Page 67
Evidence for the Existence of Black Holes……Page 68
Massive Black Holes in Galaxies……Page 71
Parallax……Page 78
Standard Candles……Page 79
Cepheid Variables……Page 80
Expansion of the Universe……Page 81
Cosmological Principle……Page 84
Comoving Coordinates……Page 85
Friedmann-Robertson-Walker Metric……Page 86
Redshifts in an Expanding Universe……Page 88
Horizons……Page 90
Luminosity Distance……Page 91
Deceleration Parameter q……Page 92
Cosmic Dynamics……Page 93
Friedmann Equations……Page 96
Critical Density……Page 97
and Flat, Closed, and Open Universes……Page 99
Models with Non-zero……Page 102
Classification of Friedmann Universes……Page 104
The Steady State Model……Page 108
The Effect of Radiation……Page 109
Energy Density of the Universe……Page 112
Baryon/Photon Number……Page 114
Nucleosynthesis in the Big Bang……Page 117
Predictions of Big Bang Nucleosynthesis……Page 119
Comparison with Observations……Page 120
Omega in Baryons……Page 121
Cosmic Problems……Page 122
The Smoothness or Horizon Problem……Page 123
Formation of Small-Scale Problem……Page 124
Flatness Problem……Page 125
Dark Matter……Page 126
Hot Dark Matter: Massive Neutrinos……Page 128
A Solution for Problems with the Big Bang?……Page 152
The Origin of Inflation……Page 155
The Planck Era……Page 157
Inflationary Phase Transition……Page 158
Weighing the Universe……Page 161
Analyzing the Cosmic Microwave Background……Page 164
Basics of Gravitational Lensing……Page 174
Microlensing……Page 176
Weighing the Universe……Page 178