Notes on Relativity and Cosmology - Physics Department, UCSB

More documents

Recommendations

Info

306 CHAPTER 10. COSMOLOGY these experiments will either confirm or deny the predictions of inflation in more detail. By the way, it is a rather strange picture of the universe with which we are left. There are several confusing issues. One of them is “where does this vacuum energy come from?” It turns out that there are some reasonable ideas on this subject coming from quantum field theory... However, while they are all reasonable ideas for creating a vacuum energy, they all predict a value that is 10 120 times too large. I will take a moment to state the obvious: 10 120 is an incredibly huge number. A billion is ten to the ninth power, so 10 120 is one billion raised to the thirteenth power. As a result, physicists are always asking, “Why is the cosmological constant so small?” Another issue is that, as we mentioned, Ω Λ and Ω matter do not stay constant in time. They change, and in fact they change in different ways. There is a nice diagram (also from Sean Carroll) showing how they change with time. I’ll hand this out too. What you can see is that, more or less independently of where you start, the universe naturally evolves toward Ω Λ = 1. On the other hand, back at the big bang Ω Λ was almost certainly near zero. So, an interesting question is: “why is Ω Λ only now in the middle ground (Ω Λ = .6), making it’s move between zero and one?” For example, does this argue that the cosmological constant is not really constant, and that there is some new physical principle that keeps it in this middle ground? Otherwise, why should the value of the cosmological constant be such that Ω Λ is just now making it’s debut? It is not clear why Λ should not have a value such that it would have taken over long ago, or such that it would still be way too tiny to notice. 10.5 The Beginning and The End Well, we are nearly finished with our story but we are not yet at the end. We traced the universe back to a time when it was so hot and dense that the nuclei of atoms were just forming. We have seen that there is experimental evidence (in the abundances of Hydrogen and Helium) that the universe actually was this hot and dense in its distant past. Well, if our understanding of physics is right, it must have been even hotter and more dense before. So, what was this like? How hot and dense was it? From the perspective of general relativity, the most natural idea is that the farther back we go, the hotter and denser it was. Looking back in time, we expect that there was a time when it was so hot that protons and neutrons themselves fell apart, and that the universe was full of things called quarks. Farther back still, the universe so hot that our current knowledge of physics is not sufficient to describe it. All kinds of weird things might have happened, like maybe the universe had more than four dimensions back then. Maybe the universe was filled with truly exotic particles. Maybe the universe underwent various periods of inflation followed by relative quiet. Anyway, looking very far back we expect that one would find conditions very similar to those near the singularity of a black hole. This is called the ‘big bang
10.5. THE BEGINNING AND THE END 307 singularity.’ Just as at a black hole, general relativity would break down there and would not accurately describe what was happening. Roughly speaking, we would be in a domain of quantum gravity where, as with a Schwarzschild black hole, our now familiar notions of space and time may completely fall apart. It may or may not make sense to even ask what came ‘before.’ Isn’t that a good place to end our story?
Page 1:
Notes on Relativit
Page 4 and 5:
4 CONTENTS 2.3 Homework Problems .
Page 6 and 7:
6 CONTENTS 8 General Relativity and
Page 8 and 9:
8 CONTENTS
Page 10 and 11:
10 CONTENTS While I have worked to
Page 12 and 13:
12 CONTENTS way you deal with almos
Page 14 and 15:
14 CONTENTS but this does not mean
Page 16 and 17:
16 CONTENTS 0.3 Coursework and Grad
Page 18 and 19:
18 CONTENTS d) include references t
Page 20 and 21:
20 CONTENTS However, your challenge
Page 22 and 23:
22 CONTENTS 0.4 Some Suggestions fo
Page 24 and 25:
24 CONTENTS Course Calendar The fol
Page 26 and 27:
26 CHAPTER 1. SPACE, TIME, AND NEWT
Page 28 and 29:
Page 30 and 31:
Page 32 and 33:
Page 34 and 35:
Page 36 and 37:
Page 38 and 39:
Page 40 and 41:
Page 42 and 43:
Page 44 and 45:
44 CHAPTER 2. MAXWELL, E&M, AND THE
Page 46 and 47:
Page 48 and 49:
Page 50 and 51:
Page 52 and 53:
Page 54 and 55:
Page 56 and 57:
56 CHAPTER 3. EINSTEIN AND INERTIAL
Page 58 and 59:
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
Page 78 and 79:
Page 80 and 81:
Page 82 and 83:
Page 84 and 85:
Page 86 and 87:
86 CHAPTER 4. MINKOWSKIAN GEOMETRY
Page 88 and 89:
Page 90 and 91:
Page 92 and 93:
Page 94 and 95:
Page 96 and 97:
Page 98 and 99:
Page 100 and 101:
Page 102 and 103:
Page 104 and 105:
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
Page 112 and 113:
Page 114 and 115:
Page 116 and 117:
Page 118 and 119:
Page 120 and 121:
Page 122 and 123:
122 CHAPTER 5. ACCELERATING REFEREN
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
Page 130 and 131:
Page 132 and 133:
Page 134 and 135:
Page 136 and 137:
Page 138 and 139:
Page 140 and 141:
Page 142 and 143:
Page 144 and 145:
144 CHAPTER 6. DYNAMICS: ENERGY AND
Page 146 and 147:
Page 148 and 149:
Page 150 and 151:
Page 152 and 153:
Page 154 and 155:
Page 156 and 157:
Page 158 and 159:
Page 160 and 161:
Page 162 and 163:
Page 164 and 165:
Page 166 and 167:
Page 168 and 169:
168 CHAPTER 7. RELATIVITY AND THE G
Page 170 and 171:
Page 172 and 173:
Page 174 and 175:
Page 176 and 177:
Page 178 and 179:
Page 180 and 181:
Page 182 and 183:
Page 184 and 185:
Page 186 and 187:
Page 188 and 189:
Page 190 and 191:
Page 192 and 193:
Page 194 and 195:
194 CHAPTER 8. GENERAL RELATIVITY A
Page 196 and 197:
Page 198 and 199:
Page 200 and 201:
Page 202 and 203:
Page 204 and 205:
Page 206 and 207:
Page 208 and 209:
Page 210 and 211:
Page 212 and 213:
Page 214 and 215:
Page 216 and 217:
Page 218 and 219:
Page 220 and 221:
Page 222 and 223:
Page 224 and 225:
Page 226 and 227:
Page 228 and 229:
228 CHAPTER 9. BLACK HOLES of gravi
Page 230 and 231:
230 CHAPTER 9. BLACK HOLES However,
Page 232 and 233:
232 CHAPTER 9. BLACK HOLES require
Page 234 and 235:
234 CHAPTER 9. BLACK HOLES √ dr r
Page 236 and 237:
236 CHAPTER 9. BLACK HOLES Future I
Page 238 and 239:
238 CHAPTER 9. BLACK HOLES r = R s
Page 240 and 241:
240 CHAPTER 9. BLACK HOLES r < R s
Page 242 and 243:
242 CHAPTER 9. BLACK HOLES this: Fi
Page 244 and 245:
244 CHAPTER 9. BLACK HOLES Well, ou
Page 246 and 247:
246 CHAPTER 9. BLACK HOLES finite p
Page 248 and 249:
248 CHAPTER 9. BLACK HOLES r = R s
Page 250 and 251:
250 CHAPTER 9. BLACK HOLES Now that
Page 252 and 253:
252 CHAPTER 9. BLACK HOLES the firs
Page 254 and 255:
254 CHAPTER 9. BLACK HOLES through
Page 256 and 257: 256 CHAPTER 9. BLACK HOLES this lin
Page 258 and 259: 258 CHAPTER 9. BLACK HOLES Believe
Page 260 and 261: 260 CHAPTER 9. BLACK HOLES you tie
Page 262 and 263: 262 CHAPTER 9. BLACK HOLES universe
Page 264 and 265: 264 CHAPTER 9. BLACK HOLES way that
Page 266 and 267: 266 CHAPTER 9. BLACK HOLES Now, an
Page 268 and 269: 268 CHAPTER 9. BLACK HOLES 9.6 Blac
Page 270 and 271: 270 CHAPTER 9. BLACK HOLES The poin
Page 272 and 273: 272 CHAPTER 9. BLACK HOLES r = 0 r
Page 274 and 275: 274 CHAPTER 9. BLACK HOLES In this
Page 276 and 277: 276 CHAPTER 9. BLACK HOLES Some of
Page 278 and 279: 278 CHAPTER 9. BLACK HOLES (c) In t
Page 280 and 281: 280 CHAPTER 9. BLACK HOLES r = R s
Page 282 and 283: 282 CHAPTER 9. BLACK HOLES (c) What
Page 284 and 285: 284 CHAPTER 10. COSMOLOGY Well, the
Page 286 and 287: 286 CHAPTER 10. COSMOLOGY 3. The th
Page 288 and 289: 288 CHAPTER 10. COSMOLOGY a a = 1 T
Page 290 and 291: 290 CHAPTER 10. COSMOLOGY -1 -2 0 1
Page 292 and 293: 292 CHAPTER 10. COSMOLOGY ( ) 2 3 d
Page 294 and 295: 294 CHAPTER 10. COSMOLOGY Since P =
Page 296 and 297: 296 CHAPTER 10. COSMOLOGY 10.4 Obse
Page 298 and 299: 298 CHAPTER 10. COSMOLOGY 10.4.2 On
Page 300 and 301: 300 CHAPTER 10. COSMOLOGY these tin
Page 302 and 303: 302 CHAPTER 10. COSMOLOGY Infinite
Page 304 and 305: 304 CHAPTER 10. COSMOLOGY clumped t
show all

Notes on Relativity and Cosmology - Physics Department, UCSB

Create successful ePaper yourself

Delete template?

Save as template?