Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

De sitter space - de Sitter–Schwarzschild metric


Published on

In general relativity, the de Sitter–Schwarzschild solution describes a black hole in a causal patch of de Sitter space. Unlike a flat-space black hole, there is a largest possible de Sitter black hole, which is the Nariai spacetime.

Published in: Technology
  • Be the first to comment

  • Be the first to like this

De sitter space - de Sitter–Schwarzschild metric

  1. 1. The Origin of the Universe and the Arrow of Time Sean Carroll, Caltech How can we make sense of our unnatural-looking universe?
  2. 2. The single most surprising thing about the universe: things change. Eggs break, ice cubes melt, stars emit radiation, we record memories of the past. And it all happens in a consistent “direction” (from the past to the future) throughout the universe: the arrow of time.
  3. 3. Why does time have a direction? It’s not a feature of the microscopic laws of physics. Those work equally well forwards or backwards in time; they are “invariant under time reversal” (t ® -t, pi ® -pi).
  4. 4. Today’s take-home messages: 1. The origin of time’s arrow is cosmological. 2. We don’t understand why. 3. We might need to consider what happened before the Big Bang. 4. This is not just recreational theology.
  5. 5. Everyone knows why there is an arrow of time: entropy. The 2nd Law of Thermodynamics says that entropy tends to increase (in closed systems) as a function of time. Not invariant under time reversal! Alan Guth’s office
  6. 6. phase space sets of macroscopically indistinguishable microstates Entropy measures volumes in phase space. Boltzmann: entropy increases because there are more high- entropy states than low-entropy ones.
  7. 7. Entropy increases because there are more ways to be high-entropy than low-entropy. If you start in a low-entropy state, evolving to higher entropy is the most natural thing in the world. But why did the entropy start out so low? A question about initial conditions: the early universe!
  8. 8. The low entropy near the Big Bang is responsible for everything about the arrow of time. Life and death Biological evolution Memory The “flow” of time Without the arrow of time, we would be in thermal equilibrium -- everything static, nothing ever changing. The question is: why aren’t we in thermal equilibrium? [Penrose]
  9. 9. Boltzmann: maybe the multiverse is in thermal equilibrium, and we can explain our local environment by invoking the anthropic principle. “There must then be in the universe, which is in thermal equilibrium as a whole and therefore dead, here and there relatively small regions of the size of our galaxy (which we call worlds), which during the relatively short time of eons deviate significantly from thermal equilibrium. Among these worlds the state probability increases as often as it decreases.” (1895) Maybe the observable universe is just a thermal fluctuation.
  10. 10. Boltzmann wasn’t the first to suggest this scenario. “For surely the atoms did not hold council, assigning order to each, flexing their keen minds with questions of place and motion and who goes where. But shuffled and jumbled in many ways, in the course of endless time they are buffeted, driven along, chancing upon all motions, combinations. At last they fall into such an arrangement as would create this universe…” -- Lucretius, De Rerum Natura, c. 50 BC.
  11. 11. Sir Arthur Eddington explained why we cannot be a thermal fluctuation. “A universe containing mathematical physicists will at any assigned date be in the state of maximum disorganization which is not inconsistent with the existence of such creatures.” (1931) Fluctuations are rare, and large fluctuations are very rare: P ~ e-DS. This scenario predicts that we should be the minimum possible fluctuations -- “Boltzmann Brains.”
  12. 12. Skeptical voices are important.
  13. 13. History of the Actual Universe • Empty de Sitter space, with rL ~ (10-3 eV)4. • Focused incoming radiation forms a white hole. • Over many many years, the white hole grows to billions of M3 via incoming low-energy photons. • Other white holes come into the horizon to form a homogeneous, contracting distribution. • White holes lose mass by ejecting matter. • Matter occasionally implodes into stars. • Stars receive inwardly-directed radiation, using the energy to convert heavy elements to lighter ones. • Stars disperse into gas, which smoothes out over the universe. • Gas continues to contract all the way to a Big Crunch.
  14. 14. We don’t have a general formula for entropy, but we do understand some special cases. Thermal gas (early universe): Black holes (today): de Sitter space: (future universe)
  15. 15. Entropy goes up as the universe expands -- the 2nd law works! Consider our comoving patch. early universe S ~ Sthermal ~ 1088 today S ~ SBH ~ 10100 future S ~ SdS ~ 10120 time It goes without saying that we are not in equilibrium. Entropy today is much smaller than it could be. All because it was extremely small in the early universe.
  16. 16. Does inflation help? Well, no. We tell the following fairy tale. The early universe was a chaotic, randomly-fluctuating place. But eventually some tiny patch of space came to be dominated by the potential energy of some scalar field. That led to a period of accelerated expansion that smoothed out any perturbations, eventually reheating into the observed Big Bang. The claim is: finding such a potential-dominated patch can’t be that hard, so our universe is (supposedly) natural. time roiling high- energy chaos today inflationary patch
  17. 17. But a “randomly fluctuating” system is most likely to be in a high-entropy configuration. And the entropy of the proto-inflationary patch is extremely low! CMB, BBN S ~ Sthermal ~ 1088 today S ~ SBH ~ 10100 future S ~ SdS ~ 10120 The universe is less likely to inflate than just to look like what we see today. Inflation makes the problem worse. inflation S ~ 1010 - 1015 [Penrose]
  18. 18. Inflation does not: • explain homogeneity, isotropy, or flatness • remove sensitive dependence on initial conditions. On the other hand, inflation does: • produce scale-free primordial density perturbations • create a lot of particles from almost nothing. So inflation is definitely worth salvaging. But it does not remove the need for a theory of initial conditions: it makes that need more urgent than ever!
  19. 19. Two basic scenarios: • The universe has a boundary in time. Presumed in the conventional Big Bang model, but based on classical general relativity. Low entropy is simply imposed at the boundary. • The universe is eternal. Standard quantum mechanics: Quantum gravity must somehow resolve the singularity; the Big Bang was just a phase.
  20. 20. What happened before the Big Bang? Conventional answer: there is no such thing as “before the Big Bang”; space and time didn’t exist. Correct answer: we just don’t know. Classical general relativity predicts a singularity. But classical GR isn’t applicable; we need to use quantum gravity. Black hole evaporation is a clue that singularities might not be absolute boundaries.
  21. 21. Eternal cosmologies are all the rage. conventional eternal inflation pre-Big-Bang cyclic universe loop quantum cosmology “Bouncing” models typically impose low- entropy conditions at the bounce; require substantial fine-tuning. “Ever-growing” models feature an entropy that grows monotonically for all time -- require infinite fine-tuning. [Veneziano] [Steinhardt & Turok] [Vilenkin; Linde] [Bojowald]
  22. 22. We want to spontaneously violate time reversal. How can that happen? Easy. Consider a ball rolling in a potential with no minimum. Every trajectory does the same thing: rolls in from infinity, turns around, and rolls out. Every solution exhibits an “arrow of time” almost everywhere. We want the universe to be like that, except with entropy instead of position. No stable equilibrium. x V (x)
  23. 23. But isn’t empty space perfectly stable? It would be, if it weren’t for vacuum energy. In the presence of vacuum energy, even empty space has a nonzero temperature. In such a space, the quantum fields of which matter is composed will constantly be fluctuating, even though space is “empty.” background space
  24. 24. baby universe background space Quantum fluctuations can produce new universes. (Maybe.) Rarely, but inevitably, fluctuating fields will conspire to create a patch of false vacuum, ready to inflate. A baby universe will pinch off from the background spacetime, expanding and creating more entropy. f V (f) [Farhi, Guth, et al.]
  25. 25. time roiling high- energy chaos today inflationary patch time cold empty de Sitter space today inflationary patch We’re replacing this: with this: Why bother? The point is that cold empty space is not a finely-tuned initial condition; it’s high-entropy, generic, “natural.”
  26. 26. parent universe “Big Bangs” arrows of time arrows of time Crucial bonus: This story can be told in both directions in time. Evolving empty space to the past, we would also see baby-universes created; their arrow of time would be reversed with respect to ours. The multiverse can be perfectly time-symmetric; we just don’t see all of it. [Carroll & Chen]
  27. 27. Why should we care?
  28. 28. Observable remnants of the multiverse: colliding bubbles [Aguirre & Johnson; Chang, Kleban & Levi]
  29. 29. Observable remnants of the multiverse: tilted CMB [Ericksen et al; Hansen et al] [Images courtesy H.K. Eriksen] [Erickcek, Kamionkowski and Carroll] Unmodulated CMB Dipole Power Modulation A pre-inflationary supermode can lead to a hemispherical power modulation in the CMB -- which apparently exists!
  30. 30. Take-home messages The observable universe features a finely- tuned boundary condition in the past, responsible for the arrow of time. Inflation is no help; it just makes the entropy problem worse. Inflation requires a theory of initial conditions. A symmetric universe with unbounded entropy might be the answer. But we can’t really address the problem without understanding quantum gravity. And we can’t understand the multiverse without confronting this problem.