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• 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
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?
• 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 < 0.
• Usual suspects: 1) Cosmological constant: w = -1, = (10-3 eV)4
2) Quintessence: ultra-light scalar, =(’)2/2 + V(), 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• 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?• 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 = - (’)2/2 + V()
`Phantom field’ , Caldwell, 2002 • Ghost INSTABILITIES: no stable ground state, unstable perturbations! The
instabilities are fast, and the Universe is OLD: billion years. We should have seen the ‘damage’…
SHOULD WE CARE ABOUT w<-1?
• 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?
MAYBE NOT!• 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
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
23pD LML
D
2223 LMc pDLi Miao et al
Interaction between DE/DM
The total energy density
energy density of matter fields
dark energy
conserved [Pavon PRD(04)]
Interaction between 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)141Phys.Lett.B624(2005)141
B. Wang, C.Y.Lin and E. Abdalla, Phys.Lett.B637(2006)357.B. Wang, C.Y.Lin and E. Abdalla, Phys.Lett.B637(2006)357.
Evolution of the DEbigger, DE starts to play the role earlier, however at late stage, big DE approaches a small value
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
objectsGiven 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 modelsExpanding age of the Universe at high z > age of the
oldest objects at the z
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 DEparametrization 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
Consideringand 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
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 DEThe 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 thermodynamicsFor the apparent horizon
The amount of energy crossing the apparent horizon during the time interval dt is
The apparent horizon entropy increases by the amountComparing (3) with (4) and using the definition of the temperature, the first law on the apparent horizon,
For the event horizonThe 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