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Return to cosmology
Is inflation in trouble?
Are we cycling back to cycles?
And then what happens to the 2nd law?
Fine-Tuning Inflation
We saw inflation correctly
predict:
1. Flatness of universe
2. Homogeneity of
universe
3. Absence of magnetic
monopoles
4. Many details of the
microwave
background
If you just granted it:
1. The right general sort
of scalar potential
2. Fine-tuned so that
the end of the rapid
inflationary roll is
gentle, not a huge
energy dumping
crash.
Inflation Issues
• Old issue: Parameters have to be fine-tuned to get the sort of
Goldilocks universe in which something could live.
– Can we use anthropic selection to account for that?
– Where do we get the ensemble to select from?
• Birth of new inflating bubbles from old cold flat empty universes?
• Eternal inflation? (see below)
A problem shared by all such anthropic pictures:
• Our universe is much larger and more homogeneous than needed (so far as we
know) to form life. It seems there should be much more net volume of livable
space in smaller universes or smaller livable pockets. Why aren’t we there?
• Have we
– Missed something needed for anthropic selection?
– Missed something major in cosmology?
• This problem was already present for Boltzmann’s anthropic ideas about the origin
of the Second Law (initial low entropy). Why over such a big volume?
A Special Problem for Inflation
• The 1960’s inflationary predictions were confirmed in amazing detail. They
described what would happen to a typical patch of space, if the inflationary form
was tuned to give a soft landing. But these predictions were not correct
theoretically! (according to Steinhardt, Turok,..)
• The fate of a typical starting patch of space is not the typical condition for a
resulting patch,
– Because certain atypical patches inflate much more!
– And quantum fluctuations guarantee that the starting conditions include
those atypical possibilities.
Why the smooth
distribution of matter?
Unless the inflation parameters are tuned
just right, a much lumpier distribution
comes out.
What’s wrong with that?
Still plenty of galaxies.
So why don’t we see a universe like that?
Anthropic Answers?
• “….the anthropic principle assumes we live in a very atypical island with just the
minimal conditions needed to support life. The claim is that the conditions in more
typical islands are incompatible with galaxies or stars or some other prerequisite for
life as we know it. Even though the typical islands occupy more space than ones like
ours, they can be ignored because we are interested only in regions that humans
could potentially inhabit. Unfortunately for this idea, the conditions in our universe
are not minimal—the universe is flatter, smoother and more precisely scale-invariant
than it had to be to support life.” (Steinhardt)
• Is the highly even distribution required for there to be observers (thus reducing to
previous case, with possible anthropic solution)? Not for any known reason. On the
surface, more lumpiness leads to more galaxies and more chance for life.
• Are we missing something about the conditions for life to exist?
• Or is there actually a very different explanation for the homogeneity of the
universe?
Does Inflation Even Help?
Second issue:
Penrose claims it requires much less fine-tuning
to get here without inflation!
Although it’s basically a one-parameter tuning for
inflation (instead of many parameters for many
temperature in different region), the tuning of that
one is exceedingly fine.
Eternal Inflation:
Feature or Bug?
Third issue:
Inflation predicts an infinite collection of postinflation bubbles. What are the predictions for
them?
Every physical possibility is realizedan infinite number of times.
So much for the denominator in calculating the
probability of life starting!
What do we mean by “fraction of universes with
property ….”
What fraction of the integers are even?
How do we calculate what to expect?
An Alternative Cosmology?
Ekpyrotic Models
• Basic claim: there are flattening processes other than inflation, occurring
during a shrinking stage of the universe. In these processes
the atypical lumpy parts shrink more instead of grow more.
So you’re mostly left with smooth parts.
• Requires some sort of cyclic picture.
• Current version: colliding 3-branes in a higher dimensional space.
• Cold flat branes collide, giving a hot flat universe with quantum
fluctuations, similar but not identical to the post-inflation stage.
Is this testable?
Phys. Rev. Lett. 100, 171302 (2008)
Non-Gaussianities in New Ekpyrotic Cosmology
Evgeny I. Buchbinder1, Justin Khoury1, and Burt A. Ovrut2
The new ekpyrotic model is an alternative scenario of the early
Universe which relies on a phase of slow contraction before the big
bang. We calculate the 3-point and 4-point correlation functions of
primordial density perturbations and find a generically large nonGaussian signal, just below the current sensitivity level of cosmic
microwave background experiments. This is in contrast with slow-roll
inflation, which predicts negligible non-Gaussianity. The model is also
distinguishable from alternative inflationary scenarios that can yield
large non-Gaussianity, such as Dirac-Born-Infeld inflation and the
simplest curvatonlike models, through the shape dependence of the
correlation functions. Non-Gaussianity therefore provides a
distinguishing and testable prediction of New Ekpyrotic Cosmology
From 2012: “The data are currently being gathered by the Planck satellite.”
Is this testable?
PHYSICAL REVIEW D 76, 123503 (2007)
New ekpyrotic cosmology
Evgeny I. Buchbinder,1 Justin Khoury,1 and Burt A. Ovrut2
At the level of a cosmological scenario, ‘‘new ekpyrotic
cosmology’’ provides a consistent alternative paradigm to
inflationary cosmology. The two scenarios make distinctive
predictions for the gravitational wave spectrum: the
inflationary spectrum is nearly scale invariant, whereas that
of ekpyrotic cosmology is very blue and, therefore,
unobservable on large scales [8]. Moreover, the generic
prediction of the simplest inflationary models is a significant
gravity wave amplitude, just below the current sensitivity
levels of microwave background experiments [6].
Ekpyrosis, on the other hand, predicts an unobservably
small amplitude. Thus the failure to detect B-mode
polarization in upcoming experiments would place inflation in
an uncomfortable corner [6], while lending support to the
ekpyrotic paradigm.
From 2012: “The data are currently being gathered by the Planck satellite.”
Some Planck Results Are In!
arXiv:1303.5084v1 [astro-ph.CO] 20 Mar 2013
Planck 2013 results. XXIV. Constraints on primordial non-Gaussianity
So inflation- the standard version, wins this round!
We’re waiting for the gravity wave results.
Cycles and Entropy?
• How can any cyclic picture be reconciled with the Second Law?
• Extrapolation of the Second Law to an infinite universe is problematic.
– E.g. in Carroll’s rough picture. The birth of baby universes from big flat
ones increases entropy. But each baby universe is born with very low
entropy. Those that happen to be inflatable become like ours. The rest of
the high-entropy multiverse is not directly visible. Net entropy keeps
increasing, but observable entropy starts over from scratch on each
round.
• If this picture turns out to be consistent with full quantum gravity!
Putting together GR, QM, and entropy
Hawking and beyond
• The entropy of a black hole is known from classical thermodynamics, plus the rule
that whatever comes out doesn't depend on the details of what went in.
• The object falling in never quite forms a black hole, due to the gravitational timeslowing near the (almost) horizon. Instead, it is thought to form a tangle of stringsand the entropy of those strings can be calculated via standard techniques: the log
of the number of possible string states which have the right total mass. It comes
out to be the same entropy which classical thermodynamics attributed to that
much mass disappearing into the black hole!
– This turns out to be generic for quantum gravity, not a specific string result.
• In the long run the stuff evaporates into (mainly) electromagnetic radiation, almost
the same as the ideal thermal radiation predicted by Hawking for quantum
radiation from a fully-formed black hole. However, the detailed evolution from
falling-in to radiating-out obeys the Liouville theorem, i.e. no entropy production in
principle. In practice, the input is thoroughly scrambled.
But here's a problem
From 2012 notes:
“
– In the reference frame of the guy falling in, he crosses the horizon and loses
contact with the outside universe, before disappearing in the singularity. Far in
the outside future includes his Hawking-evaporated self. Is it uniquely
determined by his current self (as in the outside frame) or is it genuinely
random (as per Hawking)? Is all this even self-consistent?
– A paradox?
– I’ll try to get some answers from the experts. ”
– Since then the experts have weighed in.
The Black Hole Information Paradox
We try to put together 3 basic principles
1. Nothing special happens as you cross the horizon
– Since the curvature there isn’t very big the Equivalence Principle should hold.
2. The universe far from the black hole is described by quantum field theory (QFT)
3. The overall time evolution is still just a rotation in the space of quantum states
(“unitary”) and thus obeys the quantum Liouville theorem. One stateone state
– Follows from a mathematical correspondence between a QFT in D-1
dimensions and a QFT+gravity in D dimensions (more later)
– So no global entropy is made or lost.
•
It turns out these aren’t consistent!
The outline of the argument
A particle decays into two particles:
They’re entangled (spins, momentum,…)
(Not quite to scale)
• Hawking radiation is entangled with the black hole.
– Just like any two-particle decay. So what if one of the particles is much bigger?
• After most of the BH entropy has been radiated away, the remaining radiation is
pretty much determined by the previous radiation, i.e. strongly entangled with it.
• So it’s entangled both with the earlier radiation and the leftover BH
• But a fundamental property of QM is that entanglement is monogamous.
• Whoops.
• So it looks like (at least) one of our three assumptions must be wrong.
Aaronson’s Take on Firewalls
http://www.scottaaronson.com/blog/?p=1508
“As I understand it, the issue is actually pretty simple. Do you agree that
(1) the Hawking evaporation process should be unitary, and
(2) the laws of physics should describe the experiences of an infalling observer, not just
those of an observer who stays outside the horizon?
If so, then you seem forced to accept
(3) the interior degrees of freedom should just be some sort of scrambled re-encoding
of the exterior degrees, rather than living in a separate subfactor of Hilbert space
(since otherwise we’d violate unitarity).
But then we get
(4) by applying a suitable unitary transformation to the Hawking radiation of an old
enough black hole before you jump into it, someone ought to be able, in principle, to
completely modify what you experience when you do jump in. Moreover, that person
could be far away from you—an apparent gross violation of locality.”
Susskind goes with (4): The black hole and the remote entangled radiation are not
really separate objects. And suggests that all entangled objects are maybe connected
by spacetime wormholes, which can’t transmit information.