Transcript What could w be?

WHAT COULD w BE?
Bin Wang （王斌）
Fudan University
Outline
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Dark energy: Discords of Concordance Cosmology
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What is w? Could we imagine w<-1?
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Interaction between DE and DM
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Thermodynamics of the universe with DE
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Summary
Concordance Cosmology
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A Golden Age of cosmology: ever better data from CMB, LSS
and SNe yield new insights into our Universe.
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Our Universe is WEIRD: about 70% dark energy, about 30%
dark matter, spatially flat (with 1% precision), with a ‘whiff’ of
baryons, and with a nearly flat spectrum of initial
inhomogeneities.
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Emerging paradigm: ‘CONCORDANCE COSMOLOGY’:
DE+DM. But: this means Universe is controlled by cosmic
coincidences: nearly equal amounts of various ingredients
today evolved very differently in the past.
The Cosmic Triangle

The Friedmann equation
The competition between the
Decelerating effect of the mass density
and the accelerating effect of
the dark energy
density
COSMIC TRIANGLE
Tightest Constraints:
Low z: clusters(mass-to-light method,
Baryon fraction, cluster abundance
evolution)—low-density
Intermediate z: supernova—acceleration
High z: CMB—flat universe
Bahcall, Ostriker, Perlmutter
& Steinhardt, Science 284 (1999) 1481.
Discords in The Garden of Cosmic Delights?
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We have ideas on explaining the coincidences of some relic
abundances, ie photons, baryons, neutrinos and dark matter: Inflation
→ thermal equilibrium in the Early Universe.
However we do not understand the worst problem: DARK ENERGY - a
smooth, non-clumping component contributing almost 70% of the
critical energy density today, with negative equation of state w = p/r < 0.
Usual suspects:
1) Cosmological constant: w = -1, r = (10-3 eV)4
2) Quintessence: ultra-light scalar, r=(f’)2/2 + V(f), w>-1
But: to model dark energy in this way we have to live with HEAVY
FINE-TUNING!
See, e.g. S. Weinberg, ’89.
MORE DISCORDS
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It is important to explore the nature of dark energy: we may gain
insights into new physics from the IR! How does string theory explain
the accelerating universe?
We might learn to “tolerate” dark energy (?): a miracle sorts out the
cosmological constant problem and sets the stage for cosmic
structures (still: fine tunings extremely severe: 10-60-10-120 in the value
of the vacuum energy, and for quintessence, 10-30 in the value of its
mass, as well as sub-gravitational couplings!). But then this stage stays
put…
But how well do we know the nature of dark energy? Is it even there?
Observationally the most interesting property is w. What is it? Could it
even be that w<-1? The data, at least, does not preclude this
possibility…
WHAT COULD w BE?
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At present there is a lot of degeneracy in the data. We need priors to
extract the information. SNe alone however are consistent with w in the
range, roughly
Hannestad et al
-1.5 ≤ weff ≤ -0.7
Melchiorri et al
Carroll et al
w=-1.06{+0.13,-0.08} WMAP 3Y(06)
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One can try to model w<-1 with scalar fields like quintessence. But that
requires GHOSTS: fields with negative kinetic energy, and so with a
Hamiltonian not bounded from below:
3 M42 H2 = - (f’)2/2 + V(f)
`Phantom field’ , Caldwell, 2002
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Ghost INSTABILITIES: no stable ground state, unstable perturbations! The
instabilities are fast, and the Universe is OLD: t ~ 14 billion years. We
should have seen the ‘damage’…
SHOULD WE CARE ABOUT w<-1?
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The case for w<-1 from the data is strong!
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Theoretical prejudice against w<-1 is strong!
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Would we have to live with Phantoms and
their ills: instabilities, negative energies…,
giving up Effective Field Theory?
MAYBE NOT!
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Conspiracies are more convincing if they DO NOT
rely on supernatural elements!
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Ghostless explanations:
1) Change gravity in the IR, eg. scalar-tensor theory (`failed attempt’,
Carroll et al) or DGP braneworlds (Sahni et al; Lue et al; RG et al ) or Dirac
Cosmology (Su RK et al)
In these approaches modifying gravity affect EVERYTHING in the
same way (SNe, CMB, LSS), so the effects are limited to at most w
~ -1.1.
2) Another option: Interaction between DE and DM
Super-acceleration (w<-1) as signature of dark sectors interaction
Exorcising w<-1
Holographic Dark Energy Model

QFT: Short distance cutoff
Long distance cutoff
Cohen etal, PRL(99)
Due to the limit set by formation of a black hole
L – size of the current universe
r D L  LM p r -- quantum zero-point energy density
D
caused by a short distance cutoff
The largest allowed L to saturate this inequality is
2
3
rD  3c M L
2
2 2
p
Li Miao et al
Interaction between DE/DM
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The total energy density
energy density of matter fields
dark energy
conserved
[Pavon PRD(04)]
Interaction between DE/DM
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Ratio of energy densities
It changes with time. (EH better than the HH)

Using Friedmann Eq,
B. Wang, Y.G.Gong and E. Abdalla, hep-th/0506069, Phys.Lett.B624(2005)141
B. Wang, C.Y.Lin and E. Abdalla, Phys.Lett.B637(2006)357.
Evolution of the DE
bigger, DE starts to play the role earlier,
however at late stage, big
DE approaches
a small value
Evolution of the q

Deceleration
Acceleration
Evolution of the equation of state of DE

Crossing -1 behavior

Is the interaction between DE & DM allowed
by observations?
Fitting to Golden SN data
Results of fitting to golden SN data:
If we set c=1, we have
Our model is consistent with SN data
Age constraints

The age of the Universe is a very important
parameter in constraining different
cosmological models
Age of an expanding Universe > age of oldest
objects
 Given
a cosmological model, the age of the Universe
is determined.
 Or alternatively if the age of the Universe is known,
certain constraints can be placed on cosmological
models.

B.Wang et al, astro-ph/0607126
Age constraints
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But different models may give the same age
of an expanding universe  degeneration
Age of objects at high redshift may distinguish
between these degenerated models
 Expanding
age of the Universe at high z > age of the
oldest objects at the z
Age constraints
Simple models
Interacting DE&DM model
NUMERICAL ANALYSIS OF LOW ℓ CMB
SPECTRUM
Since we are lack of the knowledge of the
perturbation theory in including the interaction
between DE and DM, in fitting the WMAP
data by using the CMBFAST we will
first estimate the value of c without
taking into account the coupling between
DE and DM.
Considering the equation of state of DE
is time-dependent, we will adopt two
extensively discussed DE
parametrization models
We have to find the maximum
of the likelihood function
Understanding the interaction between DE & DM

The entropy of the dark energy enveloped by the cosmological
event horizon is related to its energy and the pressure in the
horizon by the Gibb's equation
Considering
and using the equilibrium temperature associated to the event horizon
we get the equilibrium DE entropy described by
Now we take account of small stable fluctuations around equilibrium and assume that
this fluctuation is caused by the interaction between DE and DM. It was shown that due
to the fluctuation, there is a leading logarithmic correction to thermodynamic entropy
around equilibrium in all thermodynamical systems,
C>0 for DE domination. Thus the fluctuation is indeed stable
Understanding the interaction between DE & DM

the entropy correction reads
This entropy correction is supposed arise due to the apparence of the coupling between
DE and DM. Now the total entropy enveloped by the event horizon is
from the Gibb's law we obtain
where
is the EOS of DE when it has coupling to DM
If there is no interaction, the thermodynamical system will go back to equilibrium and the
system will persist equilibrium entropy and
Understanding the interaction between DE & DM
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With interaction:
Understanding the interaction between DE & DM
Understanding the interaction between DE & DM
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Comparing to simple model
Our interacting DE scenario is compatible with the observations.
Thermodynamics of the universe with DE
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Q-space with constant equation of state for the DE
The dynamical evolution of the scale factor and the matter density is
determined by the Einstein equations
Defining
for a constant equation of state we have
accelerating Q-space
The event horizon for the Q-space is
The apparent horizon
The horizons do not differ much, they relate by
Neither the event horizon nor the apparent horizon changes significantly over one
Hubble time
First law of thermodynamics
For the apparent horizon
The amount of energy crossing the apparent horizon during
the time interval dt is
The apparent horizon entropy increases by the amount
Comparing (3) with (4) and using the definition of the temperature, the first law on
the apparent horizon,
For the event horizon
The total energy flow through the event horizon can be similarly got as
The entropy of the event horizon increases by
Using the Hawking temperature for the event horizon we obtain
B.Wang, Y.G.Gong, E. Abdalla PRD74,083520(06),gr-qc/0511051.
Second law of thermodynamics
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The entropy of the universe inside the horizon can be
related to its energy and pressure in the horizon by Gibb’s
equation
For the apparent horizon
we have
Second law of thermodynamics
For the event horizon
GSL breaks down
Summary

Could w be smaller than -1?
Observations & Theoretical understanding
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Is there any interaction between DE & DM?
w crossing -1
SN constraint
Age constraints
Small l CMB fitting
Understanding the interaction between DE and DM ??