what we (don't) know about the beginning of the universe
TRANSCRIPT
Sean Carroll, Caltech
What We (Don’t) Know Aboutthe Beginning of the Universe
1. What we know about the Big Bang
2. The spacetime viewpoint
3. The quantum viewpoint
What we know about the Big Bang:1. Something Bang-like happened.
standard GR(CDM)
today
allowedhistories
[Carroll & Kaplinghat][Planck]
cosmic background radiation primordial nucleosynthesis
The universe 13.8 billion years ago was hot, dense,expanding very rapidly, and decelerating.
What we know about the Big Bang:2. Classical GR suggests singularities are generic.
Highly symmetric universes tendto have an initial singularity (Lemaître).
More strongly, Hawking’s theorem:compact expanding universes obeyingthe Strong Energy Condition (gravityattracts) always have singularities.
[Donald Menzel, Popular Science, 1932]
But the Strong Energy Condition can be violated. And theorists are happy to consider modifying GR.
What we know about the Big Bang:3. The early universe had extremely low entropy.
time
early universeS ~ Sradiation ~ 1088
todayS ~ SBH ~ 10103
futureS ~ SdS
~ 10123
Of all the states that look macroscopically like our presentuniverse, only a tiny fraction evolved from smooth states.Most were chaotic, Planckian, singular.
space ofstates
“macrostates” = sets of macroscopically
indistinguishable microstates
Boltzmann, 1870s: entropy counts the number of states that look the same macroscopically.
Low initial entropy isan enormous fine-tuning.Calls out for a robustexplanation.
Inflation doesn’t explain why entropy was initially low.
Inflation: if a patch ofspace starts in a false vacuum, it naturally accelerates, createsenergy, smooths out,and reheats into matter and radiation.
But that initial proto-inflationary state is even lower-entropythan the conventional hot big Bang (1 < Sinflation < 1015).
You don’t explain low entropy by positing even lower entropy.
1. What it’s like to have a beginning.
The spacetime viewpoint on the beginning of the universe
size
timesiz
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time
2. Ways of avoiding a beginning
– eternal universes.Bouncing
ReproducingHibernating
Cyclic
size
time
size
time
size
time
What it’s like to have a beginning
Don’t ever say the universe “came into existence.”Sounds like a process within time, rather than thebeginning of time itself.
Rather, there was an initial moment – a time beforewhich there was no other time.
What “caused” the universe?
Wrong question. Rather: is it plausible that the lawsof physics allow for a universe with a beginning?
(Yes.)
Bouncing cosmologiesSmooth out the singularity, either through new degreesof freedom (fields, branes, dimensions), or throughintrinsically quantum effects.
Stringy Bounce[Veneziano]
QuantumCosmology
[Bojowald, Ashtekar,Page, Hartle,
Hawking, Hertog]
de Sitter Bounce[Aguirre, Gratton]
Ekyprotic Bounce[Khoury, Ovrut,
Steinhardt, Turok]
Bouncing cosmologies have an entropy puzzle:
•If entropy grows monotonically, requires infinite fine-tuning.•If entropy has a minimum at the bounce, why?
size
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entro
py
??
Cyclic cosmologiesRepeat the bounce over and over.
[Turok, Steinhardt; Penrose]
Hibernating cosmologiesUniverse is quiescent and quasi-stationary into the eternal past; at some point undergoes a phase transition and begins to expand.
[Brandenberger, Vafa] [Greene, Hinterbichler, Judes, Parikh]
String gas cosmology Primordial degravitation
Both cyclic and hibernating cosmologies have an entropy catastrophe:
•Entropy grows monotonically for all time. Requiresinfinite fine-tuning in the infinite past.
size
time
entro
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[Farhi, Guth, Guven]
Reproducing cosmologies
Imagine a “parent” universe that is itself quiescent and high-entropy.
But through some mechanism it can give birth to newoffspring universes, with initially low entropy.
E.g. spacetime quantum tunneling into disconnected“baby universes.”
size
time
2 largedimensions
Alternatively: spontaneous compactification
1 large dimension,1 compact
2 largedimensions
1 large dimension,1 compact
Six-dimensional de Sitter space w/electromagnetic fieldswill spontaneously nucleate four-dim de Sitter universes.
[Carroll, Johnson, & Randall]
Result: a time-symmetric multiverse
• New universes branch off from the parent universe inboth directions of time. Overall time-symmetric.
• Easier to create new low-entropy universes than high-entropy ones.
• This might explain why our Big Bang had low entropy.
Reproducing cosmologies don’t have an entropy problem!
•Entropy grows without bound toward past and future.•There is a middle point of lowest entropy, but it needn’t be “low” in any objective sense. (Indeed,it can be locally maximal.)
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[Carroll & Chen; see also Barbour, Koslowski & Mercati; Hartle & Hertog; Goldstein, Tomulka & Zanghi; Carroll & Guth]
The quantum viewpoint on the beginning of the universeQuantum theory describes the evolution of quantum states living in a Hilbert space H, obeyingSchrödinger’s equation .
We often start with a classical systemand “quantize” it, yielding a quantumtheory “of” that system. But that’shuman convention, not Nature.
Honest quantum questions areabout what happens to vectorsin Hilbert space, evolving under the Schrödinger equation.
time(?)
Derived/emergent
space
fieldsparticlescausality
light conesmetric collapse/
branching
wave functionsHilbert space
tensor productsentanglement
Hamiltonianinformation
entropy
pointer states
Fundamental
Emergence in QM
locality
Time evolution: the Quantum Eternity Theorem
• Consider a universe described by a quantum state obeying Schrödinger’s equation
with nonzero energy, governed by laws of physics that are independent of time.
• Then: the universe is eternal. (Time t runs from –∞ to +∞.)
[Carroll, 2008, arxiv:0811.3722]
In quantum mechanics, if time is fundamental, it never ends.
Expand the state in energy eigenstates:
Each phase just rotates in a circle; the set of all of them move in a straight line through a torus. No singularities, barriers, etc.
A generic quantum universe lasts forever, withouta beginning or an end.
Recurrence theorem: if Hilbert spaceH is finite-dimensional, states return to their starting points infinitely often.
Problems with an eternal quantum universe: recurrences, fluctuations, Boltzmann brains.
Entropy is usually maximal(equilibrium). Downwardfluctuations are suppressed:
Almost all observers are minimalfluctuations: “Boltzmann brains.”
Possible solution: Hilbert space is infinite-dimensional.There is no recurrence theorem in an infinite-dimensionalHilbert space. Quantum equivalent of an unboundedphase space.
The quantum state has infinite room to grow and change.
This is the kind of quantumtheory that might ultimatelyhave as an emergent classicalspacetime a bouncing orreproductive cosmologies.
Entropy growing without bound in both directions of time.
Alternative: time is emergent, not fundamental
Loophole for Quantum Eternity Theorem: we livein a single energy eigenstate. E.g. .
Seems non-generic, but is exactly what we get byquantizing general relativity: the Wheeler-DeWitt equation for a wave function of spatial three-metrics.
Where does time come from?
[e.g. Hartle, Hawking]
Time can emerge in quantum mechanicsbecause we can superpose different states
[Page & Wootters 1983]
Emergent time: a stationarystate is a superposition;one subsystem serves asan effective “clock.”
t = 1
t = 2
t = 3
Ordinarily: quantum state evolves as time passes.
If Hilbert space is infinite-dimensional, emergent “time” can run forever. No need for a beginning – but there couldbe one.
But if Hilbert space is finite-dimensional, there are only a finite number of possible clock states.
Therefore, time will have a beginning.
hija internal “clock” hija)
semiclassicaltrajectory
superspace = {3-geometries, matter fields}
universe had a beginning
universe may or may not have hada beginning
universe is eternal,with a finiterecurrence time(& Boltzmann brains)
universe is eternal,and need neverexperience recurrence
Was the Big Bang the beginning of the universe?tim
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time
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