Transcript Document

Overview of Dark Energy Theory
Miao Li
Institute of Theoretical Physics
2009.02.25
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Contents:
1. Weinberg’s classification
2. A new classification
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• Weinberg’s classification
1 Supersymmetry, superstring etc
2 Anthropic principle
3 Self-tuning mechanism
4 Modifying general relativity
5 Quantum cosmology
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1 Supersymmetry etc
The SUSY algebra contains
If SUSY is unbroken, the above leads to
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Apparently, we are not in a unbroken SUSY
world, so naturally
where
is the SUSY breaking scale .
Thus, SUSY doesn’t solve the CC problem.
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An alternative is the non-scale SUGRA.
Assuming K (Kahler potential) and W (superpotential) be functions of a set of scalars.
One can break SUSY and meanwhile make
H=0
But one needs to fine tune K.
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2 Anthropic principle
Weinberg:
Formation of clutsers at z=4 requires
But this result presumes that
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Poll:
Do you believe that the CC is a prediction of the
anthropic principle?
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3 Self-tuning mechanism
To use it to make CC=0, then by some other
mechanism to have a small CC.
Idea: Introducing a scalar to make
depend on this scalar.
No-go theorem:
It is impossible to make CC=0 without making
G=0.
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4 Modifying gravity
Demand
the Einstein equations are modified to
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Conservation of the stress tensor
thus, the Einstein equations with a CC are
recovered.
CC becomes an integration constant, determined
by initial conditions.
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5 Quantum cosmology
Banks and Hawking argued that the wave
function of the universe may be used to
predict CC=0.
Hawking in particular computed in a semiclassical fashion
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Thus, P is highly peaked at CC=0.
Later, Coleman, introducing the idea of baby
universes and the third quantization, obtains
an even more drastic result
By now, we all know that these “predictions”
are falsified by observations!
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A new classification:
1 Symmetry
2 Anthropic principle
3 Self-tuning mechanism
4 Modifying gravity
5 Quantum cosmology
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6 Holographic principle
7 Back-reaction of gravity at large scales
8 Phenomenological models
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1 Symmetry
Witten proposed that in 2+1 dimensions, SUSY
is unbroken but the mass spectrum is not
degenerate (a mass causes a deficit angle so
SUSY is not realized). CC=0
If, in a limit of strong coupling a new large
dimension emerges, we have a 3+1 theory with
CC=0 as in 2+1.
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No concrete model has been proposed except
That Strominger and Beckers wrote a paper on
this.
‘t Hooft-Nobbenhuis proposed that
is a symmetry.
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This leads to
and thus CC=0.
But in dealing with the second quantization,
non-abelian gauge fields prohibit this symmetry
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Kaplan-Sundrum symmetry
For each known field (except for the metric),
introducing a ghost partner
Quantization preserves the above form, so
CC=0.
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If quantum gravity (the metric) is cut-off at
then
Ghost fields induce vacuum instability, but the
decay rate may be sufficiently small.
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2 Anthropic principle
Bousso-Polchinski:
Many different membranes and corresponding
rank 4 F fields, leading to
If there are enough charges, physical CC can
be made sufficiently small.
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To put our universe in a position with a small
CC, the anthropic principle must be invoked.
KKLT proposed an even more realistic scenario
in which all moduli are stablized.
Again, anthropic principle.
But, there is currently no way to experimentally
falsify or verify this landscape scenario.
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3 Self-tuning mechanism
Kachru et al proposed to use a scalar in a 5D
bulk to tune the CC:
energy carried by
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Action
allows for a flat brane solution if the 5D bulk
CC=0, this condition can be provided by a 5D
unbroken SUSY.
But, there are singularities on the both sides of
The brane.
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In order to avoid singularities, Csaki et al
proposed to place a black hole on each side
of the brane.
But, one has to introduce a charge for the BH
in order not to fine tune.
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4 Modifying gravity
Carroll et al proposed an action
This allows an accelerated universe solution,
but the new mass scale is extremely small.
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That can be generalized to more general
Action f(R).
Starobinsky proposed such an action to obtain
inflation long time ago.
This model has many difficulties, such as postNewtonian problem in the solar system,
stability, boundary conditions.
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Other modifying gravity theories:
MOND, relativistic versions of MOND
TeVeS
DGP model (5D Einstein + 4D Einstein) ruled
out by data?
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5 Quantum cosmology
Not much new.
Motl and Carroll, based on a phenomenological
formula
proposed to use the seesaw mechanism to
derive this formula.
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If there are two branches of the universe,
The wave function has two components, so
The CC is a matrix
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If
one of the eigen-values is
Still, there is a fine-tuning problem.
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6 Holographic principle
In 1998, A. Cohen proposed that in order for
QFT to be effective, there must be a bound on
the energy contained in a region of size L.
This leads to a relation between the infrared
cut-off L and the UV cut-off l, if
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Let the dark energy density be one saturating
that bound:
where L is the radius of a certain kind of horizon
S. Hsu pointed out that if one take
there is no acceleration.
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ML pointed out that, instead of the Hubble
horizon, one can use the event horizon
the holographic density indeed behaves as
dark energy, there is
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This model since then has been modified
to:
Interacting holographic dark energy, with
different choice of horizons
IR cut-off dertermined by the Ricci scalar
(Gao, Chen, Shen)
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Agegraphic dark energy (Cai, Wei)
where T is the conformal time
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Instead of viewing the holographic dark
energy as zero-point energy, one can alternatively explain it as that of an exotic gas.
A gas with exotic degeneracy at long wave
lengths (Li, Li, Lin, Wang):
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7 Back-reaction of gravity at large scales
Some people believe that there is no need
for dark energy nor should we modify gravity.
Accelerated expansion is result of the backreaction of large scale fluctuations.
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Start with metric
with
the deceleration parameter is
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It was argued that
is large and helps to
accelerate the expansion.
But this is still a controversial claim.
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8 Phenomenological models
There are numerous such models, the most
popular is the quintessence:
with
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Although it is hard to believe that a REAL
scalar can account for the dark energy, it
remains an excellent phenomenological
description (can mimic other dynamic models)
However, no quintessence model can solve
the fine tuning problem completely.
A simple quintessence model has
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To cross the w=-1 barrier, one introduces
quintom, the simplest model is
quite similar to the Kaplan-Sundrum model.
If the potential has a minimum, this model
predicts a vanishing dark energy in the far
future.
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Another often-studied model is Chaplygin gas,
it has the equation of state:
The simplest solution is
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Chameleon:
A scalar field whose potential depends on
the environment. For example:
This model derives from an effort to evade
violation of the equivalence principle.
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Many other models:
Density inhomogeneous, electroweak symmet.
breaking, relation to neutrinos, Casimir effect
at 1mm, ……
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Thanks!
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