The Origin of the Universe

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The Origin of the Universe and the Arrow of Time
Sean Carroll, Caltech
How can we make sense of our unnatural-looking
universe?
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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.
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Why does time have a direction?
Its 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).
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Todays take-home messages

1. The origin of times arrow is cosmological.
2. We dont understand why.
3. We might need to consider what happened before
   the Big Bang.
4. This is not just recreational theology.

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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 Guths office
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Entropy measures volumes in phase space.
phase space
Boltzmann entropy increases because there are
more high- entropy states than low-entropy ones.
sets of macroscopically indistinguishable
microstates
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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!
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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
Penrose
Without the arrow of time, we would be in
thermal equilibrium -- everything static, nothing
ever changing. The question is why arent we
in thermal equilibrium?
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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.
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Boltzmann wasnt 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.
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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-?S. This scenario predicts
that we should be the minimum possible fluctuation
s -- Boltzmann Brains.
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Skeptical voices are important.
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History of the Actual Universe

• Empty de Sitter space, with ?? (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.

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We dont have a general formula for entropy,
but we do understand some special cases. Thermal
gas(early universe) Black holes (today) d
e Sitter space (future universe)
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Entropy goes up as the universe expands --
the 2nd law works! Consider our comoving patch.
time
early universe S Sthermal 1088
today S SBH 10100
future S SdS 10120
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.
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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 cant be that hard, so
our universe is (supposedly) natural.
time
today
roiling high- energy chaos
inflationary patch
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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!
Penrose
inflation S 1010 - 1015
today S SBH 10100
future S SdS 10120
CMB, BBN S Sthermal 1088
The universe is less likely to inflate than just
to look like what we see today. Inflation makes
the problem worse.
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• 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!

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• 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.

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What happened before the Big
Bang? Conventional answer there is no such
thing as before the Big Bang space and time
didnt exist. Correct answer we just dont
know. Classical general relativity predicts a
singularity. But classical GR isnt applicable
we need to use quantum gravity. Black hole
evaporation is a clue that singularities
might not be absolute boundaries.
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Eternal cosmologies are all the rage.
Bouncing models typically impose low- entropy
conditions at the bounce require substantial
fine-tuning.
loop quantum cosmology
pre-Big-Bang
Bojowald
Veneziano
Ever-growing models feature an entropy
that grows monotonically for all time --
require infinite fine-tuning.
conventional eternal inflation
cyclic universe
Steinhardt Turok
Vilenkin Linde
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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.
V (x)
x
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But isnt empty space perfectly stable? It would
be, if it werent 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
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Quantum fluctuations can produce new universes.
(Maybe.)
background space
baby universe
Farhi, Guth, et al.
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.
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Were replacing this with this
Why bother? The point is that cold empty space
is not a finely-tuned initial condition its
high-entropy, generic, natural.
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Crucial bonus This story can be told in both
directions in time.
arrows of time
parent universe
arrows of time
Big Bangs
Carroll Chen
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 dont see all of it.
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Why should we care?
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Observable remnants of the multiverse
colliding bubbles
Aguirre Johnson Chang, Kleban Levi
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Observable remnants of the multiverse tilted
CMB
A pre-inflationary supermode can lead to a
hemispherical power modulation in the CMB --
which apparently exists!
Erickcek, Kamionkowski and Carroll
Ericksen et al Hansen et al
Images courtesy H.K. Eriksen
Unmodulated CMB
Dipole Power Modulation
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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 cant really address the
problem without understanding quantum gravity.
And we cant understand the multiverse without
confronting this problem.