Interacting Dark Energy and Dark Matter : a window to

quintessence.

Elcio Abdalla

Acknowledgements

• Bin Wang (Fudan -- Shanghai)• Ru Keng Su, Jian Yong Shen, Zuo Yi

Huang, Yun Gui Gong, Chi Yong Lin, Jia Dong Zang, Shao Yu Yin (China)

• Diego Pavon (Barcelona)• Raul Abramo, Laerte Sodré, Sandro

Micheletti (USPaulo)

Dark Matter and Dark Energy

• Already in the thirties (1933) Zwicky observed the velocities in the Coma cluster and verified that they are much bigger than what would be expected from the Newton law with a mass M=Mlum as given by the luminous (optically observed) mass:

• V 2= 2GM/R

P.J.E. Peebles

Theory withour Dark Matter

Observation

•

Besides luminous matter there is circa 10 times more matter in an unknown clumping form

Measuring Dark Matter

There are also very strong (indeed undeniable) indications that the Universe is undergoing na accelerated expansion phase:

Observing IA Supernovae

The Spectrum of Cosmic Radiation Background

Dark Energy

3.5 energia escura

SN1997ff

m=1, =0

IA Supernovas

RCF

08.00.10

m

RCF

Supernovae plus CRMB

All observations are consistent with Dark Energy and Dark Matter, where:

1. The total Energy Density equals the critical density

2. Clumping matter (baryons plus DM) represent 1/3 of the total energy content

3. Some strange (very strange) object is responsable for acceleration, representing 2/3 of the energy content of the Universe..

Moreover ...

• 5-year WMAP has extremely tight constraints in that picture, errors are smaller than a few percent ...

The essence of Dark Energy

• What is Dark Energy?• Could it be simple?• A new field?• A Cosmological Constant?• Is it interacting?

)3(3

4p

G

a

a

Friedmann equations lead to

Thus we need a matter which fulfills

3

1

3 wp

How to get acceleration?

How to get acceleration?

The first solution is the cosmological constant. It is a simple solution to the problem with w=-1 . There are however some problems connected with the cosmological constant:

• 1. The energy density required to adjust to observations is of the order of 1 (MeV)4 , 120 of magnitude smaller than what would be obtained from a field theoretic computation.

2. It is a mistery the reason why the cosmological constant is important NOW.

Dark Matter and Dark Energy

• It has become cristal clear that circa 97% of the Universe is formed by two up to now unknown forms of matter.

• Baryonic Matter interacts with eletromagnetism leading to our (very wonderful) world.

• What if Dark Matter (30% of the Universe) interacts with Dark Energy (67% of the Universe)? What are the consequences?

w = -1

1+z = a0/a

radiationmatter:

z~104

today

• The coincidence problem

The Coincidence Problem and DE/DM Interaction

• Why DE and DM are of the same order of magnitude today?

The Coincidence Problem and DE/DM Interaction

• We thus say that a decay of DE into DM aleviates the coincidence problem

• Question: can we test such ideas with observations?

Dark Matter and Dark Energy Interaction: preliminary view.

• We investigated the question of the suppression of the CMB power spectrum for lowest multipoles.

• We used the idea of holographic cosmic duality to understand the problem

• Examining the power spectrum, we have shown a suppression behavior which describes the low l features extremely well.

• The holographic idea (DE density proportional to the square of the scale factor) suits very well non trivial (e.g. no cosmological constant) models.

Holographic Model

• Idea motivated by strings/quantum gravity: the energy/entropy content cannot be larger than that of a Black Hole of the size of the Universe.

• Thus,

23 /

DERc

Interacting Holographic Model

• The simplest interaction Model for DE and DM is obtained from a two-fluid model:

3DM

DM

H Q

3 (1 )DE

DE

H Q

Interacting Holographic Model

• The simplest models for Q is na interaction proportional to the energy density:

23Q Hb

Interacting Holographic Model

• The proportionality constant b is a small number.

• The density appearing in the r.h.s. is either DE, DM or the total (depending on the model).

• They presumably follow one another at large, possibly being equivalent which to use.

Interacting Holographic Model

• Comparison with supernova data and measurements of w show that:

2 0.12

0.000.00b

0.75

0.050.40c

Interacting Holographic Model

• Comparing b and c with data arising also from the allowed values of w and amount of DE and DM today we find

Further on Phenomenology

• Age Constraint: age of Universe

Further on Phenomenology

• Age of Quasar APM 08279+5255.

Further on Phenomenology

• Low l CMB again

Further on Phenomenology

Further on Phenomenology

• Order of magnitude estimate for b2

(with some dependence on the DE equation of state):

• 1: 0.10 < b2 < 0.2• 2: -- 0.10 < b2 < 0.24• Probability of b2 positive: 95%.

Signature in Galaxy Clusters: na apparent correction of the Virial

Theorem• We only observe Baryonic Matter.• Suppose Dark Matter pattern follows

Baryonic Matter pattern• Interaction with Dark Energy works

as na external potential• Thus, Virial Theorem acquires a

correction.

Signature in Galaxy Clusters: na apparent correction of the Virial

Theorem• Usual Virial Theorem: • 2K+U=0.• In General Relativity: Layser Irvine

Equation.

Signature in Galaxy Clusters: an apparent correction of the Virial

Theorem• Results

Signature in Galaxy Clusters: an apparent correction of the Virial

Theorem• Results

Modelling the Interaction

• Suppose there are DE/DM particles in interaction.

• Suppose there is a “Thompson scattering amplitude”.

• Existence of galaxies with MDM of the order of 10 Mbaryons we get b2 3QED

• In agreement with previous computations.

Further on Perturbations

• The interaction dm has strong non perturbative effects.

• Such non perturbative effects arise from classical solutions of the equations of motion of the order of 1/.

• Therefore, perturbative methods fails.

• The interaction de does not show the same behaviour.

• Thus, we need urgently further methods and alternatives.

Hubble “drag”Potencial

V() 03 , VH

)()( 221 V

)()( 221 Vp

1w)()(

)()(w r. s.

221

221

V

Vp

constante)( V

)( Vp

Slow-roll, works as a

cosmological decaying in time

V

Equation of motionsmallScalar Fields

A Field Theoretic Model for DE/DM

• We consider the Lagrangian density

• L= -√(g)V() √(1-mm) -i d -(m-)

• The energy (non)conservation equations have a (nonvanishing) intertwining term proportional to , to the time derivative of and to the density .

Likelihood ---

Do we have any coupling?

• The present field theoretic model is compatible with zero coupling, though overwhelming majority of the integrated likelihood function points to a negative coupling, in conformity with previous results.

• The results are thus because of a severe degeneracy of and .

Thermodynamics and DE/DM

• An interaction between the Dark sectors leads also to similar conclusions.

• However, the thermodynamic functions are not known for the DE sector

• What is the temperature of DE?• What is the temperature of DM?

Thermodynamics and DE/DM

• For the holographic model TDE it is naturally of the order of the Hawking Temperature of the horizon.

• In case this is true the DE temperature is several orders of magnitude smaller than unit.

• In case we use a gas to describe DE , it is natural to assume that TDE is of the order R -3w. For w= -1 this is very, very hot.

• Thus, what is TDE ?

• Do we have a non equilibrium mixture?

Conclusions

• At 1 level there are very good reasons to believe that DE and DM are interacting fields

• What happens to String Theory claims about anthropic principle and all that?

• Are there models in Quantum Field Theory which could properly describe interacting DE/DM (work in progress)?