Dark energy and the accelerating universe Grigoris Panotopoulos - - PowerPoint PPT Presentation

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Dark energy and the accelerating universe Grigoris Panotopoulos - - PowerPoint PPT Presentation

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Dark energy and the accelerating universe Grigoris Panotopoulos University of Valencia & IFIC Astroparticle seminar, 4 November 2010, MPI, Munich Outline Outline Introduction/Motivation Introduction/Motivation Dynamical dark energy

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Dark energy and the accelerating universe

Grigoris Panotopoulos

University of Valencia & IFIC

Astroparticle seminar, 4 November 2010, MPI, Munich

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G Panotopoulos 2 MPI seminar, Munich 2010

Outline Outline

Introduction/Motivation Introduction/Motivation

Dynamical dark energy Dynamical dark energy

Geometrical dark energy Geometrical dark energy

Statefinder diagnostics Statefinder diagnostics

Conclusions Conclusions

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G Panotopoulos 3 MPI seminar, Munich 2010

Evolution of the universe Evolution of the universe

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G Panotopoulos 4 MPI seminar, Munich 2010

1998: The accelerating universe 1998: The accelerating universe breakthrough of the year breakthrough of the year

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G Panotopoulos 5 MPI seminar, Munich 2010

Slow-roll inflation: A paradigm for the early universe Slow-roll inflation: A paradigm for the early universe

V

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G Panotopoulos 6 MPI seminar, Munich 2010

Μagnitude versus red-shift Μagnitude versus red-shift

Several theoretical Several theoretical curves curves

Observational data Observational data

Best fit when dark Best fit when dark energy ~3/4 energy ~3/4

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G Panotopoulos 7 MPI seminar, Munich 2010

Age of the Universe and Hubble constant Age of the Universe and Hubble constant

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G Panotopoulos 8 MPI seminar, Munich 2010

Primordial Nucleosynthesis Primordial Nucleosynthesis

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G Panotopoulos 9 MPI seminar, Munich 2010

Today's picture of the universe Today's picture of the universe

3 independent 3 independent data sets coincide data sets coincide

Concordance cosmological model! Concordance cosmological model!

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G Panotopoulos 10 MPI seminar, Munich 2010

Dark energy dominates in the (flat) universe Dark energy dominates in the (flat) universe

Εnergy in the universe Εnergy in the universe = = Matter 27% Matter 27% (baryons 4% & cold dark matter 23%) (baryons 4% & cold dark matter 23%) + + Dark energy 73% Dark energy 73%

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G Panotopoulos 11 MPI seminar, Munich 2010

Dark energy equation of state w Dark energy equation of state w

Theory : w < - 1/3 Theory : w < - 1/3

Observations : -1.2 < w < -0.8 Observations : -1.2 < w < -0.8

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G Panotopoulos 12 MPI seminar, Munich 2010

What is dark energy? What is dark energy?

Cosmological constant: the simplest case Cosmological constant: the simplest case

 Introduced by Einstein for a

Introduced by Einstein for a static universe static universe

 Allowed by all symmetries

Allowed by all symmetries

 ΛCDM agrees with data

ΛCDM agrees with data

 The cosmological and

The cosmological and coincidence problems coincidence problems

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G Panotopoulos 13 MPI seminar, Munich 2010

Cosmological constant Cosmological constant

Fluid with w=-1 Fluid with w=-1

Very different evolution Very different evolution

Value much lower than expected Value much lower than expected

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G Panotopoulos 14 MPI seminar, Munich 2010

Field equations for gravity Field equations for gravity

Observation: accelerated expansion Observation: accelerated expansion

Theory: with matter or radiation Theory: with matter or radiation → → decelerated expansion decelerated expansion

Disagreement Disagreement between theory and observation between theory and observation

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G Panotopoulos 15 MPI seminar, Munich 2010

Two choices Two choices

 Geometrical

Geometrical dark energy dark energy

 Modify

Modify left left hand side hand side → → new gravitational theory new gravitational theory

 Dynamical

Dynamical dark energy dark energy

 Modify

Modify right right hand side hand side → → new dynamical component new dynamical component

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G Panotopoulos 16 MPI seminar, Munich 2010

A very active field A very active field

  • S. Nojiri, S. D. Odintsov and M. Sami, arXiv:hep-th/0605039; V. Sahni
  • S. Nojiri, S. D. Odintsov and M. Sami, arXiv:hep-th/0605039; V. Sahni

and Y. Shtanov, arXiv:astro-ph/0202346; R. A. Brown, R. Maartens, E. and Y. Shtanov, arXiv:astro-ph/0202346; R. A. Brown, R. Maartens, E. Papantonopoulos and V. Zamarias, arXiv:gr-qc/0508116; P. S. Papantonopoulos and V. Zamarias, arXiv:gr-qc/0508116; P. S. Apostolopoulos and N. Tetradis, arXiv:hep-th/0604014; arXiv:astro- Apostolopoulos and N. Tetradis, arXiv:hep-th/0604014; arXiv:astro- ph/0605450; C. Wetterich, L. P. Chimento, R. Lazkoz, R. Maartens and ph/0605450; C. Wetterich, L. P. Chimento, R. Lazkoz, R. Maartens and

  • I. Quiros, Nucl.\ Phys.\ B 302 (1988) 668; B.Ratra and P.J.E.Peebles,
  • I. Quiros, Nucl.\ Phys.\ B 302 (1988) 668; B.Ratra and P.J.E.Peebles,

Phys.\ Rev.\ D 37 (1988) 3406; Phys.\ Rev.\ D 37 (1988) 3406;

  • R. R. Caldwell, R. Dave and P. J. Steinhardt, arXiv:astro-ph/9708069];
  • R. R. Caldwell, R. Dave and P. J. Steinhardt, arXiv:astro-ph/9708069];
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G Panotopoulos 17 MPI seminar, Munich 2010

Q: Why Ωs of matter and dark energy are so similar in Q: Why Ωs of matter and dark energy are so similar in magnitude ? magnitude ?

First answer First answer

 Special initial conditions

Special initial conditions: current universe : current universe finite point in phase-space finite point in phase-space

Second answer Second answer

 Because of

Because of values of parameters values of parameters: current universe close to a : current universe close to a fixed fixed point point

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G Panotopoulos 18 MPI seminar, Munich 2010

Not so simple to realize ! Not so simple to realize !

Cosmology of type Cosmology of type

 Without

Without energy exchange energy exchange

 With

With energy exchange energy exchange

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G Panotopoulos 19 MPI seminar, Munich 2010

Superstring theory: basic idea Superstring theory: basic idea

Really fundamental objects are one- Really fundamental objects are one- dimensional (strings) dimensional (strings)

In low energies string looks like a In low energies string looks like a point-like particle point-like particle

All known particles are different All known particles are different

  • scillatory modes of the string
  • scillatory modes of the string
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G Panotopoulos 20 MPI seminar, Munich 2010

Εxtended objects: Βranes Εxtended objects: Βranes

String theory does not contain strings only String theory does not contain strings only

Normally, open strings satisfy Neumann Normally, open strings satisfy Neumann boundary conditions boundary conditions

End points move at speed of light End points move at speed of light

Dirichlet boundary conditions also make sense Dirichlet boundary conditions also make sense

 End points are stuck on a hypersurface.

End points are stuck on a hypersurface.

 This hyperurface is interpreted as a heavy solitonic

This hyperurface is interpreted as a heavy solitonic

  • bject, a D-brane.
  • bject, a D-brane.

 Brane-world idea : We are confined on such an object.

Brane-world idea : We are confined on such an object.

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G Panotopoulos 21 MPI seminar, Munich 2010

A simple brane model A simple brane model (Dvali, Gabadadze, Porrati, 2000) (Dvali, Gabadadze, Porrati, 2000)

Action Action

 One extra dimension

One extra dimension

 Gravity in 5D, our world in 4D

Gravity in 5D, our world in 4D

 Reduced to known gravity and cosmology in the early universe

Reduced to known gravity and cosmology in the early universe

 New gravity and cosmology in the recent times

New gravity and cosmology in the recent times

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G Panotopoulos 22 MPI seminar, Munich 2010

Cosmology for DGP Cosmology for DGP (Deffayet, 2001) (Deffayet, 2001)

Friedmann eqn Friedmann eqn

Early times Early times 4D Friedmann 4D Friedmann

Recent times Recent times

Same number of parameters as LCDM Same number of parameters as LCDM

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G Panotopoulos 23 MPI seminar, Munich 2010

A more realistic model A more realistic model (G.Kofinas, G.P., T.N.Tomaras, 2005) (G.Kofinas, G.P., T.N.Tomaras, 2005)

Matter Matter

 in 5 dimensions (undetermined)

in 5 dimensions (undetermined)

 Fluid on the brane

Fluid on the brane

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G Panotopoulos 24 MPI seminar, Munich 2010

Cosmological solution Cosmological solution

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G Panotopoulos 25 MPI seminar, Munich 2010

Cosmological equations Cosmological equations

With new variables With new variables

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G Panotopoulos 26 MPI seminar, Munich 2010

Final form Final form

New quantities for dynamical study New quantities for dynamical study

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G Panotopoulos 27 MPI seminar, Munich 2010

Critical points and their stability Critical points and their stability

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G Panotopoulos 28 MPI seminar, Munich 2010

Numerical results for brane model Numerical results for brane model

Evolution in the Evolution in the ω ωm

m- Z

  • Z plane

plane for for k=0, w=0, A<0 k=0, w=0, A<0

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G Panotopoulos 29 MPI seminar, Munich 2010

Interacting (dynamical) dark energy Interacting (dynamical) dark energy (Quintessence) (Quintessence)

CC problem CC problem OK OK ( (not vaccum energy not vaccum energy any more) any more)

Why now problem Why now problem → → Interaction between DE & DM Interaction between DE & DM

Usually assume source ( Usually assume source (linear linear) )

Model with (0911.3089, Model with (0911.3089, quadratic quadratic) )

Our idea Our idea: : Lagrangian description Lagrangian description & & comparison to data comparison to data

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G Panotopoulos 30 MPI seminar, Munich 2010

Our model (O.Mena, L.L.Honorez, G.P., 2010) Our model (O.Mena, L.L.Honorez, G.P., 2010)

Dark energy Dark energy → Canonical scalar field ( → Canonical scalar field (Quintessence Quintessence) )

Dark matter Dark matter → → Fermion Fermion

Self-interaction potential Self-interaction potential

Interaction Interaction → Lagrangian → Lagrangian mass term for dark matter mass term for dark matter

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G Panotopoulos 31 MPI seminar, Munich 2010

Equations of motion Equations of motion

For dark matter For dark matter

For scalar field For scalar field

The source Q is The source Q is

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G Panotopoulos 32 MPI seminar, Munich 2010

Require Require

For For

→ →

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G Panotopoulos 33 MPI seminar, Munich 2010

Phase-space analysis Phase-space analysis

Define new dimensionless variables Define new dimensionless variables

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G Panotopoulos 34 MPI seminar, Munich 2010

New dynamical equations New dynamical equations

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G Panotopoulos 35 MPI seminar, Munich 2010

Stable fixed point → acceleration Stable fixed point → acceleration

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G Panotopoulos 36 MPI seminar, Munich 2010

Comparison with data Comparison with data

Supernovae Supernovae

CMB CMB

BAO BAO

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G Panotopoulos 37 MPI seminar, Munich 2010

Global analysis Global analysis

Supernovae Supernovae

CMB CMB

BAO BAO

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G Panotopoulos 38 MPI seminar, Munich 2010

Numerical results for 4D model Numerical results for 4D model

SN alone All data SN alone All data

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G Panotopoulos 39 MPI seminar, Munich 2010

Diagnostic for different cosmological models Diagnostic for different cosmological models

Many models with similar expansion history that cannot be excluded by Many models with similar expansion history that cannot be excluded by data data

Quantities that can be measured and computed within model Quantities that can be measured and computed within model

Appropriate quantities (Alam, Saini, Sahni, Starobinsky) Appropriate quantities (Alam, Saini, Sahni, Starobinsky)

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G Panotopoulos 40 MPI seminar, Munich 2010

4D model with interacting dark energy 4D model with interacting dark energy

Use of dimensionless quantities Use of dimensionless quantities

Upon comparison to observational data Upon comparison to observational data

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G Panotopoulos 41 MPI seminar, Munich 2010

Statefinders for the 4D model Statefinders for the 4D model

Special case: cosmological constant Special case: cosmological constant

Critical points Critical points

 Two fixed points

Two fixed points

 At the stable critical point

At the stable critical point

stable unstable

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G Panotopoulos 42 MPI seminar, Munich 2010

(s-r (s-r ) plane for two models ) plane for two models (5D brane model, 4D model in GR) (5D brane model, 4D model in GR)

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G Panotopoulos 43 MPI seminar, Munich 2010

Conclusions Conclusions

Cosmic acceleration → Dark energy Cosmic acceleration → Dark energy

CC & LCDM: Simplest choice CC & LCDM: Simplest choice

Other possibilities: Dynamical dark energy (quintessence) or geometrical Other possibilities: Dynamical dark energy (quintessence) or geometrical dark energy (brane models) dark energy (brane models)

Statefinders: Can descriminate between different dark Statefinders: Can descriminate between different dark energy models with same expansion history energy models with same expansion history