312
Index
P
Parallel displacement, 64–66, 68, 69, 73, 81,
102, 112, 113
P-forms, 55, 90, 91
Planck distribution, 264, 265
Planck scale, 156, 158, 280, 292, 293, 295,
301
Plane waves, 164–166, 168, 171, 174, 184,
187
Poisson’s equation, 120, 163, 164, 243
Polarization, CMB, 165, 169, 170, 175, 180,
185, 250
Power law inflation, 282, 295, 296
PPN parameters, 137, 139
Precession of orbit, 133, 140, 189
Proper length, 9, 10
Proper time, 8, 19, 20, 23, 25–28, 68, 103,
142, 144, 148, 169, 194, 210
Proton, 140, 148, 180, 266, 276–278, 302
Q
Quadrupole formula, 174, 176, 179
Quarks, 195, 265, 275, 277–279, 286
Quotient theorem, 46, 47, 85, 111
R
Radiation era, 249, 265–267, 270–272, 275,
277, 281–283, 288
Rapidity, 11, 12, 25, 26
Redshift z, 250
Ricci, 84, 85, 87, 113, 161, 231
Ricci tensor, 116–119, 123, 126, 140, 157,
161, 231
Riemann, 33, 34, 37, 38, 52, 59, 61, 64, 66,
73, 74, 100, 111, 113, 116, 118, 122,
123, 157, 161, 220, 231
Riemann tensor, 109, 111–116, 121–123,
157, 160, 161, 165, 166
S
Scalar, 18, 38–40, 42, 45, 46, 49, 52–54, 67,
81, 83, 88, 90–92, 116, 118, 123, 157,
161, 165, 185, 194, 196, 220, 231,
284, 297
Scalar field, 83, 279, 284, 285, 296–299, 302
Schwarzschild metric, 128, 135, 140–142,
151, 152, 157, 158, 242
Schwarzschild radius, 128, 139–142, 145,
148–150, 153, 155, 157, 158, 242,
300
Self-parallel curves, 67
Signature, 36, 38, 53, 56, 57, 68, 75, 98, 100,
109, 121, 122, 145, 146, 166
Slow roll, 285, 286
Spacetime, 13, 15, 19, 26, 27, 33, 36, 38,
54, 99, 100, 102, 104–106, 109, 118,
121–123, 129, 145, 150, 165, 183,
200, 257, 276, 280, 293–295, 297
Spectrum of CMB, 205, 250, 264, 279, 286
Steady state universe, 244
Stellar evolution, 148
T
Tangent space, 122
Tangent vector, 67, 68, 74, 86, 89, 146, 147
Tensor, 14, 15, 18, 28, 29, 33, 34, 36, 44–49,
52, 53, 55, 56, 59, 61–63, 65, 66, 81–
88, 90, 92, 109–118, 123, 125, 151,
161, 164, 185, 193, 195–198, 223,
224, 231, 298
Tetrad, 49–52
Tidal forces, 100, 121, 170
Time dilation, 7, 8, 11, 20
Trajectory, 19, 20, 25–28, 38, 68, 77, 98, 104,
147, 157, 258
U
Uncertainty Principle (UP), 154, 155, 293,
300, 302
Universe, 9, 11, 117, 118, 145, 150, 152,
156, 182, 193, 195, 198–201, 203,
205–207, 213, 214, 216, 217, 220,
225–230, 233–245, 247–254, 256–
267, 269, 270, 272, 273, 275–277,
279–282, 284–293, 295, 296, 301,
302
V
Vacuum, 5, 13, 115–117, 123, 128, 154, 164,
171, 198–200, 225, 230, 254–256,
263, 275, 282, 285, 286, 290, 296
Vacuum energy density, 250, 255–257, 284,
299
Vacuum field equations, 117, 125, 129
Vector, 4, 13, 15–24, 33, 38–52, 58–69, 73,
74, 78, 79, 81–92, 95, 102, 106, 109–
113, 146, 161, 164, 165, 184–188,
194
Vector transplantation, 61, 62, 64–66, 73, 74,
102
Volume element, 52–55, 88, 91, 92, 145
Index
P
Parallel displacement, 64–66, 68, 69, 73, 81,
102, 112, 113
P-forms, 55, 90, 91
Planck distribution, 264, 265
Planck scale, 156, 158, 280, 292, 293, 295,
301
Plane waves, 164–166, 168, 171, 174, 184,
187
Poisson’s equation, 120, 163, 164, 243
Polarization, CMB, 165, 169, 170, 175, 180,
185, 250
Power law inflation, 282, 295, 296
PPN parameters, 137, 139
Precession of orbit, 133, 140, 189
Proper length, 9, 10
Proper time, 8, 19, 20, 23, 25–28, 68, 103,
142, 144, 148, 169, 194, 210
Proton, 140, 148, 180, 266, 276–278, 302
Q
Quadrupole formula, 174, 176, 179
Quarks, 195, 265, 275, 277–279, 286
Quotient theorem, 46, 47, 85, 111
R
Radiation era, 249, 265–267, 270–272, 275,
277, 281–283, 288
Rapidity, 11, 12, 25, 26
Redshift z, 250
Ricci, 84, 85, 87, 113, 161, 231
Ricci tensor, 116–119, 123, 126, 140, 157,
161, 231
Riemann, 33, 34, 37, 38, 52, 59, 61, 64, 66,
73, 74, 100, 111, 113, 116, 118, 122,
123, 157, 161, 220, 231
Riemann tensor, 109, 111–116, 121–123,
157, 160, 161, 165, 166
S
Scalar, 18, 38–40, 42, 45, 46, 49, 52–54, 67,
81, 83, 88, 90–92, 116, 118, 123, 157,
161, 165, 185, 194, 196, 220, 231,
284, 297
Scalar field, 83, 279, 284, 285, 296–299, 302
Schwarzschild metric, 128, 135, 140–142,
151, 152, 157, 158, 242
Schwarzschild radius, 128, 139–142, 145,
148–150, 153, 155, 157, 158, 242,
300
Self-parallel curves, 67
Signature, 36, 38, 53, 56, 57, 68, 75, 98, 100,
109, 121, 122, 145, 146, 166
Slow roll, 285, 286
Spacetime, 13, 15, 19, 26, 27, 33, 36, 38,
54, 99, 100, 102, 104–106, 109, 118,
121–123, 129, 145, 150, 165, 183,
200, 257, 276, 280, 293–295, 297
Spectrum of CMB, 205, 250, 264, 279, 286
Steady state universe, 244
Stellar evolution, 148
T
Tangent space, 122
Tangent vector, 67, 68, 74, 86, 89, 146, 147
Tensor, 14, 15, 18, 28, 29, 33, 34, 36, 44–49,
52, 53, 55, 56, 59, 61–63, 65, 66, 81–
88, 90, 92, 109–118, 123, 125, 151,
161, 164, 185, 193, 195–198, 223,
224, 231, 298
Tetrad, 49–52
Tidal forces, 100, 121, 170
Time dilation, 7, 8, 11, 20
Trajectory, 19, 20, 25–28, 38, 68, 77, 98, 104,
147, 157, 258
U
Uncertainty Principle (UP), 154, 155, 293,
300, 302
Universe, 9, 11, 117, 118, 145, 150, 152,
156, 182, 193, 195, 198–201, 203,
205–207, 213, 214, 216, 217, 220,
225–230, 233–245, 247–254, 256–
267, 269, 270, 272, 273, 275–277,
279–282, 284–293, 295, 296, 301,
302
V
Vacuum, 5, 13, 115–117, 123, 128, 154, 164,
171, 198–200, 225, 230, 254–256,
263, 275, 282, 285, 286, 290, 296
Vacuum energy density, 250, 255–257, 284,
299
Vacuum field equations, 117, 125, 129
Vector, 4, 13, 15–24, 33, 38–52, 58–69, 73,
74, 78, 79, 81–92, 95, 102, 106, 109–
113, 146, 161, 164, 165, 184–188,
194
Vector transplantation, 61, 62, 64–66, 73, 74,
102
Volume element, 52–55, 88, 91, 92, 145