Bin Wang （王斌） Fudan University. WHAT COULD w BE?. Outline. Dark energy: Discords of Concordance Cosmology What is w? Could we imagine w<-1? Interaction between DE and DM Thermodynamics of the universe with DE Summary. Concordance Cosmology.
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Bin Wang （王斌）Fudan University
WHAT COULD w BE?
The competition between the
Decelerating effect of the mass density
and the accelerating effect of
the dark energy
density
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.
1) Cosmological constant: w = -1, r = (10-3 eV)4
2) Quintessence: ultra-light scalar, r=(f’)2/2 + V(f), w>-1
See, e.g. S. Weinberg, ’89.
Hannestad et al
-1.5 ≤ weff ≤ -0.7 Melchiorri et al
Carroll et al
w=-1.06{+0.13,-0.08} WMAP 3Y(06)
3 M42 H2 = - (f’)2/2 + V(f)
`Phantom field’ , Caldwell, 2002
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
Long distance cutoff Cohen etal, PRL(99)
Due to the limit set by formation of a black hole
L – size of the current universe
-- quantum zero-point energy density
caused by a short distance cutoff
The largest allowed L to saturate this inequality is
Li Miao et al
energy density of matter fields
dark energy
It changes with time.(EH better than the HH)
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.
bigger, DE starts to play the role earlier, however at late stage, big DE approaches a small value
Results of fitting to golden SN data:
If we set c=1, we have
Our model is consistent with SN data
Simple models
Interacting DE&DM model
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
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
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
Our interacting DE scenario is compatible with the observations.
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
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.
For the apparent horizon
we have
For the event horizon
GSL breaks down
Observations & Theoretical understanding
w crossing -1
SN constraint
Age constraints
Small l CMB fitting
Understanding the interaction between DE and DM ??