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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

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Bin Wang (王斌)Fudan University



  • 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

  • A Golden Age of cosmology: ever better data from CMB, LSS and SNe yield new insights into our Universe.

  • 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.

  • 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



Tightest Constraints:

Low z: clusters(mass-to-light method,

Baryon fraction, cluster abundance


Intermediate z: supernova—acceleration

High z: CMB—flat universe

Bahcall, Ostriker, Perlmutter

& Steinhardt, Science 284 (1999) 1481.

Discords in The Garden of Cosmic Delights?

  • 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.


  • 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…


  • 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)

  • 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

  • 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’…


  • The case for w<-1 from the data is strong!

  • Theoretical prejudice against w<-1 is strong!

  • Would we have to live with Phantoms and their ills: instabilities, negative energies…, giving up Effective Field Theory?


  • Conspiracies are more convincing if they DO NOT rely on supernatural elements!

  • 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

    -- quantum zero-point energy density

    caused by a short distance cutoff

    The largest allowed L to saturate this inequality is

Li Miao et al

Interaction between DE/DM

  • The total energy density

    energy density of matter fields

    dark energy

  • conserved [Pavon PRD(04)]

Interactionbetween DE/DM

  • 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

  • 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


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


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

  • With interaction:

Understanding the interaction between DE & DM

Understanding the interaction between DE & DM

  • Comparing to simple model

Our interacting DE scenario is compatible with the observations.

Thermodynamics of the universe with DE

  • 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


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

  • 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


  • Could w be smaller than -1?

    Observations & Theoretical understanding

  • 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 ??

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