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

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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

time

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

py

[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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