The accelerated expansion of the universe and the cosmological constant problem <ul><ul><li>Spring Summer School on String...
Big issues - observational and theoretical <ul><li>Present accelerated expansion of the universe – observational discovery...
Our concept of the (present) universe <ul><li>Evolution dominated by gravity   </li></ul><ul><ul><li>the interactions gove...
The observed universe <ul><li>Isotropic (CMB, averaged galaxy distribution at scales > 50-100 Mpc) </li></ul><ul><li>Homog...
Expansion of the universe <ul><li>Hubble (1929)  – dynamical universe   </li></ul><ul><li>Cosmological redshift </li></ul>...
FRW model – theoretical description of the expansion <ul><li>Contents: cosmic fluids (general EOS) </li></ul><ul><li>Gener...
FRW model <ul><li>Critical density </li></ul><ul><li>Omega parameters </li></ul><ul><li>Cosmic sum rules </li></ul>
Cosmological observations – mapping the expansion <ul><li>Standard candles (luminosity distance) </li></ul><ul><li>Superno...
Supernovae of the type Ia <ul><li>Standard candles – known luminosity </li></ul><ul><li>Binary stars – physics of SNIa und...
Cosmological observations - SNIa <ul><li>http://imagine.gsfc.nasa.gov/docs/science/know_l2/supernovae.html </li></ul><ul><...
Cosmological observations - CMB <ul><li>http://map.gsfc.nasa.gov/ </li></ul>
Cosmological observations - LSS <ul><li>structure at cosmological scales (LSS) </li></ul><ul><li>http://cas.sdss.org/dr5/e...
Standard cosmological model (up to 1998) <ul><li>Destiny determined by geometry   </li></ul><ul><li>Interplay of spatial c...
Spatial curvature <ul><li>COBE – spatial curvature is small. </li></ul><ul><li>EdS must do the job (models with considerab...
SNIa observations (1998) <ul><li>Observations by two teams </li></ul><ul><ul><li>High z SN Search Team, Riess et al.,  htt...
CMB and BAO <ul><li>Influence to the determination of the acceleration – indirectly </li></ul><ul><li>CMB – mainly through...
Combining observational data <ul><li>Degeneracies of cosmic parameters - different combinations of cosmic parameters may p...
Observational constraints to the DE EOS  <ul><li>E. Komatsu et al., Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) ...
Accelerated expansion <ul><li>In a FRW universe the observed signals strongly favor a presently accelerated expansion of t...
Classification of theoretical approaches  <ul><li>ll </li></ul>R. Bean, S. Caroll, M. Trodden,  Insights into dark energy:...
Distorted signals and unjustified assumptions? <ul><li>Photons from SNIa convert to axions in the intergalactic magnetic f...
Distorted signals and unjustified assumptions? <ul><li>The influence of inhomogeneities (below 50-100 Mpc) </li></ul><ul><...
Distorted signals and unjustified assumptions? <ul><li>Inhomogeneities at scales above the Hubble horizon </li></ul><ul><l...
Mechanism of the acceleration <ul><li>No acceleration in the “old standard cosmological model”  </li></ul><ul><li>Our (pre...
Dark energy <ul><li>Acceleration by adding a new component – a dark energy component </li></ul><ul><li>Key property – suff...
Dark energy <ul><li>DE equation of state  </li></ul><ul><li>Dynamics of  ρ d   in terms of a </li></ul><ul><ul><li>w > -1:...
Dark sector <ul><li>DE interacting with other cosmic components </li></ul><ul><li>Interaction with dark matter </li></ul><...
DE models <ul><li>Cosmic fluid </li></ul><ul><li>Scalar fields (quintessence, phantom) </li></ul><ul><li>... </li></ul><ul...
Λ CDM <ul><li>Benchmark model </li></ul><ul><li>Only known concepts (CC, NR matter, radiation) </li></ul><ul><li>small num...
Quintessence <ul><li>Dynamics of a scalar field in a potential  </li></ul><ul><li>Freezing vs. thawing models </li></ul><u...
Phantom energy <ul><li>Energy density growing with time </li></ul><ul><li>Big rip </li></ul><ul><li>Stability </li></ul><u...
Singularities <ul><li>New types of singularities </li></ul><ul><li>Finite time (finite scale factor) singularities </li></...
Modified gravity <ul><li>Modification of gravity at cosmological scales </li></ul><ul><li>Dark gravity (effective dark ene...
Braneworlds <ul><li>Matter confined to a 4D brane </li></ul><ul><li>Gravity also exists in the bulk </li></ul><ul><li>Dval...
The cosmological constant <ul><li>Formally allowed – a part of geometry  </li></ul><ul><li>Introduced by Einstein in 1917 ...
The expansion with the cosmological constant J. Sol à, hep-ph/0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy <ul><li>Zero point energies – radiative corrections </li></ul><ul><ul><li>Bosonic </li></ul...
Zero point energies <ul><li>QFT estimates </li></ul><ul><ul><li>real scalar field </li></ul></ul><ul><ul><li>spin j </li><...
Condensates <ul><li>Phase transitions leave contributions to the vacuum energy </li></ul><ul><li>Higgs potential </li></ul...
The size of the CC <ul><li>Many disparate contributions </li></ul><ul><li>Virtually all many orders of magnitude larger th...
The “old” cosmological constant problem – the problem of size <ul><li>Discrepancy by many orders of magnitude (first notic...
The “old” cosmological constant problem  <ul><li>Fundamental theoretical problem – the problem of the vacuum energy densit...
DE vs CC <ul><li>Raphael Bousso, “TASI lectures on the cosmological constant” </li></ul><ul><ul><li>“ If a poet sees somet...
Proposed solutions of the “old” CC problem <ul><li>Classification (closely following S. Nobbenhuis, gr-qc/0609011) </li></...
Symmetry <ul><li>Supersymmetry </li></ul><ul><li>Scale invariance </li></ul><ul><li>Conformal symmetry </li></ul><ul><li>I...
Back-reaction mechanisms <ul><li>Scalar </li></ul><ul><li>Gravitons </li></ul><ul><li>Running CC from Renormalization grou...
Violation of the equivalence principle <ul><li>Non-local Gravity, Massive gravitons </li></ul><ul><li>Ghost condensation <...
Statistical approaches <ul><li>Hawking statistics </li></ul><ul><li>Wormholes </li></ul><ul><li>Anthropic Principle </li><...
The cosmic coincidence problem – the problem of timing <ul><li>Why the CC (DE) energy density and the energy density of (N...
Possible solutions of the cosmic coincidence problem <ul><li>Naturally solved in (matter) back-reaction approaches </li></...
Composite dark energy –  Λ XCDM models <ul><li>ordinary matter (radiation and NR matter) separately conserved)  </li></ul>...
Ratio of DE and matter energy density
Parameter constraints <ul><li>primordial nucelosynthesis:  </li></ul><ul><li>Existence of a stopping point   </li></ul><ul...
Parameter constraints – cross sections
The CC relaxation mechansim <ul><li>Two component model (H.Š. Phys.Lett. B 670 (2009) 246) </li></ul><ul><li>The inhomogen...
The model dynamics <ul><li>The dynamics of the Hubble parameter </li></ul><ul><li>Notation  </li></ul><ul><li>Dynamics in ...
α < −1: the relaxation mechanism for the large cosmological constant <ul><li>The α = −3 case </li></ul><ul><li>Closed form...
case <ul><li>Late-time symptotic behavior  </li></ul><ul><li>Ʌ eff  is small because | Ʌ | is large! </li></ul>
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case <ul><li>Asymptotic behavior </li></ul><ul><li>Late-time asymptotic behavior </li></ul><ul><li>Ʌ eff  is small because...
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes <ul><li>For  α > −1 the behavior is different </li></ul><ul><li>The relaxation mechanism is not au...
Fixed points, approach to de Sitter regime <ul><li>general dynamics </li></ul><ul><li>Fixed point  ⇒ </li></ul><ul><li>Exa...
General inhomogeneous EOS <ul><li>dynamics of the scaled Hubble parameter </li></ul><ul><li>condition for the relaxation m...
Variable cosmological term <ul><li>Running CC </li></ul><ul><li>Extended running CC </li></ul><ul><li>Interaction with mat...
Variable cosmological term <ul><li>Late-time asymptotic behavior </li></ul>
f(R) modified gravity <ul><li>general dynamics </li></ul><ul><li>specific example  </li></ul><ul><li>asymptotic de Sitter ...
Important questions  <ul><li>Abruptness of the transition </li></ul><ul><li>The onset of the transition </li></ul><ul><li>...
Summary of the relaxation mechanism properties <ul><li>The solution of the CC problem without fine-tuning for both signs o...
Relaxing a large cosmological constant - adding matter and radiation <ul><li>F. Bauer, J. Sola, H. Š. arXiv:0902.2215  </l...
The formalism <ul><li>The variable cosmological term </li></ul><ul><li>Constructing f from general coordinate  covariant t...
½ Model  <ul><li>f=R </li></ul><ul><li>Radiation domination (controlled by 1-q) </li></ul><ul><li>transition to de Sitter ...
The model <ul><li>Two terms dominated by different values of q and different powers of H </li></ul><ul><li>Sequence of a R...
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions <ul><li>The question of the mechanism of the acceleration of the universe still open </li></ul><ul><li>The cos...
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H. Stefancic: The Accelerated Expansion of the Universe and the Cosmological Constant Problem

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Lecture form Spring School on Strings, Cosmology and Particles (SSSCP2009), March 31-4 2009, Belgrade/Nis, Serbia

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H. Stefancic: The Accelerated Expansion of the Universe and the Cosmological Constant Problem

  1. 1. The accelerated expansion of the universe and the cosmological constant problem <ul><ul><li>Spring Summer School on Strings Cosmology and Particles </li></ul></ul><ul><ul><li>31 March – 4 April 2009, Belgrade-Niš, Serbia </li></ul></ul>Hrvoje Štefančić, Theoretical Physics Division, Ruđer Bošković Institute, Zagreb, Croatia
  2. 2. Big issues - observational and theoretical <ul><li>Present accelerated expansion of the universe – observational discovery </li></ul><ul><li>The cosmological constant (vacuum energy) problem – theoretical challenge </li></ul>
  3. 3. Our concept of the (present) universe <ul><li>Evolution dominated by gravity </li></ul><ul><ul><li>the interactions governing the evolution of the universe have to have long range to be effective at cosmological distances </li></ul></ul><ul><ul><li>matter is neutral at cosmological (and much smaller) scales </li></ul></ul><ul><li>General relativity </li></ul><ul><li>Known forms of matter (radiation, nonrelativistic matter) </li></ul><ul><li>Four dimensional universe </li></ul>
  4. 4. The observed universe <ul><li>Isotropic (CMB, averaged galaxy distribution at scales > 50-100 Mpc) </li></ul><ul><li>Homogeneous – less evidence (indirect) – Copernican principle </li></ul><ul><li>Homogeneous and isotropic – Cosmological principle </li></ul><ul><li>Robertson-Walker metric ! </li></ul>
  5. 5. Expansion of the universe <ul><li>Hubble (1929) – dynamical universe </li></ul><ul><li>Cosmological redshift </li></ul><ul><li>Standard forms of matter lead to decelerated expansion </li></ul><ul><li>Inflation – early epoch of the accelerated expansion </li></ul><ul><li>1998 – universe accelerated (decelerated universe expected) </li></ul>
  6. 6. FRW model – theoretical description of the expansion <ul><li>Contents: cosmic fluids (general EOS) </li></ul><ul><li>General relativity in 4D </li></ul><ul><li>Friedmann equation </li></ul><ul><li>Continuity equation (Bianchi identity - covariant conservation of energy-momentum tensor) </li></ul><ul><li>Acceleration </li></ul>
  7. 7. FRW model <ul><li>Critical density </li></ul><ul><li>Omega parameters </li></ul><ul><li>Cosmic sum rules </li></ul>
  8. 8. Cosmological observations – mapping the expansion <ul><li>Standard candles (luminosity distance) </li></ul><ul><li>Supernovae Ia, GRB </li></ul><ul><li>Standard rulers </li></ul><ul><li>CMB (cosmic microwave background) </li></ul><ul><li>BAO (baryonic acoustic oscillations) </li></ul><ul><li>Others (gravitational lensing...) </li></ul>
  9. 9. Supernovae of the type Ia <ul><li>Standard candles – known luminosity </li></ul><ul><li>Binary stars – physics of SNIa understood </li></ul><ul><li>Light curve fitting </li></ul><ul><li>Luminosity distance – can be determined both observationally and theoretically </li></ul><ul><li>SNIa dimming – signal of the accelerated expansion </li></ul>
  10. 10. Cosmological observations - SNIa <ul><li>http://imagine.gsfc.nasa.gov/docs/science/know_l2/supernovae.html </li></ul><ul><li>http://www.astro.uiuc.edu/~pmricker/research/type1a/ </li></ul>
  11. 11. Cosmological observations - CMB <ul><li>http://map.gsfc.nasa.gov/ </li></ul>
  12. 12. Cosmological observations - LSS <ul><li>structure at cosmological scales (LSS) </li></ul><ul><li>http://cas.sdss.org/dr5/en/tools/places/ </li></ul>
  13. 13. Standard cosmological model (up to 1998) <ul><li>Destiny determined by geometry </li></ul><ul><li>Interplay of spatial curvature and matter content ( Ω m + Ω k =1 ) </li></ul><ul><li>Even EdS model advocated ( Ω m =1) </li></ul>
  14. 14. Spatial curvature <ul><li>COBE – spatial curvature is small. </li></ul><ul><li>EdS must do the job (models with considerable Ω k are ruled out by the observation of CMB temperature anisotropies </li></ul>
  15. 15. SNIa observations (1998) <ul><li>Observations by two teams </li></ul><ul><ul><li>High z SN Search Team, Riess et al., http://cfa-www.harvard.edu/supernova//home.html </li></ul></ul><ul><ul><li>Supernova Cosmology Project, Perlmutter et al., http://supernova.lbl.gov/ </li></ul></ul><ul><li>Λ CDM model – fits the data very well </li></ul><ul><li>Measurement in the redshift range where the expansion of the universe is really accelerated or there is the transition from decelerated to accelerated expansion – “direct measurement” </li></ul>
  16. 16. CMB and BAO <ul><li>Influence to the determination of the acceleration – indirectly </li></ul><ul><li>CMB – mainly through the distance to the surface of last scattering </li></ul><ul><li>BAO – similarly </li></ul>
  17. 17. Combining observational data <ul><li>Degeneracies of cosmic parameters - different combinations of cosmic parameters may produce the same observed phenomena </li></ul><ul><li>Removal of degeneracies – using different observations at different redshifts (redshift intervals) </li></ul><ul><li>SNIa + WMAP + BAO – precision cosmology </li></ul>
  18. 18. Observational constraints to the DE EOS <ul><li>E. Komatsu et al., Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation </li></ul><ul><li>http://arxiv.org/abs/0803.0547 </li></ul>
  19. 19. Accelerated expansion <ul><li>In a FRW universe the observed signals strongly favor a presently accelerated expansion of the universe (and reject EdS model) </li></ul><ul><li>Do we interpret the observational data correctly? </li></ul>
  20. 20. Classification of theoretical approaches <ul><li>ll </li></ul>R. Bean, S. Caroll, M. Trodden, Insights into dark energy: interplay between theory and observation. Rachel Bean ( Cornell U., Astron. Dept. ) , Sean M. Carroll ( Chicago U., EFI & KICP, Chicago ) , Mark Trodden ( Syracuse U. ) . Oct 2005. 5pp. White paper submitted to Dark Energy Task Force. http://arxiv.org/abs/astro-ph/0510059
  21. 21. Distorted signals and unjustified assumptions? <ul><li>Photons from SNIa convert to axions in the intergalactic magnetic field </li></ul><ul><ul><li>light signal dissipated </li></ul></ul><ul><ul><li>Reduction in intensity confused for the effects of acceleration </li></ul></ul><ul><li>C. Csaki, N. Kaloper, J. Terning, Phys. Rev. Lett. 88 (2002) 161302 </li></ul><ul><ul><li>does not work (very interesting attempt – invokes more or less standard (or at least already known physics) </li></ul></ul><ul><ul><li>connection with the phantom “mirage” </li></ul></ul>
  22. 22. Distorted signals and unjustified assumptions? <ul><li>The influence of inhomogeneities (below 50-100 Mpc) </li></ul><ul><li>Nonlinearity of GR in its fundamental form </li></ul><ul><li>Solving Einstein equations in an inhomogeneous universe and averaging the solutions is not equivalent to averaging sources and solving Einsteins equations in a homogeneous universe </li></ul><ul><li>No additional components (just NR matter) </li></ul><ul><li>The acceleration is apparent </li></ul><ul><li>The perceived acceleration begins with the onset of structure formation – very convenient for the cosmic coincidence problem </li></ul><ul><li>The effect is not sufficient to account for acceleration, but is should be taken into considerations in precise determination of cosmic parameters </li></ul>
  23. 23. Distorted signals and unjustified assumptions? <ul><li>Inhomogeneities at scales above the Hubble horizon </li></ul><ul><li>Underdense region </li></ul><ul><li>Relinquishing the Copernican principle? </li></ul><ul><li>Falsifiability? </li></ul><ul><li>No additional components </li></ul><ul><li>The effect of “super large scale structure” </li></ul>
  24. 24. Mechanism of the acceleration <ul><li>No acceleration in the “old standard cosmological model” </li></ul><ul><li>Our (pre)concepts of the universe have to be modified </li></ul><ul><ul><li>Modifying contents – dark energy (+ DM) </li></ul></ul><ul><ul><li>Modyfing gravity – modified (dark) gravity </li></ul></ul><ul><ul><li>Modifying dimensionality – new (large) dimesions – braneworld models </li></ul></ul><ul><ul><li>... </li></ul></ul><ul><ul><li>and combinations </li></ul></ul>
  25. 25. Dark energy <ul><li>Acceleration by adding a new component – a dark energy component </li></ul><ul><li>Key property – sufficiently negative pressure </li></ul><ul><li>Physical realization of a negative pressure? </li></ul><ul><ul><li>Geometric effect (Lambda from the left side of Einstein eq.) </li></ul></ul><ul><ul><li>Dynamics of scalar field - domination of potential energy over kinetic energy </li></ul></ul><ul><ul><li>Corpuscular interpretation – unusual dispersion relation – energy decreasing with the size of momentum </li></ul></ul>
  26. 26. Dark energy <ul><li>DE equation of state </li></ul><ul><li>Dynamics of ρ d in terms of a </li></ul><ul><ul><li>w > -1: quintessence </li></ul></ul><ul><ul><li>w = -1: cosmological term </li></ul></ul><ul><ul><li>w < -1: phantom energy </li></ul></ul><ul><li>Multiple DE components </li></ul><ul><li>Crossing of the cosmological constant barrier </li></ul>
  27. 27. Dark sector <ul><li>DE interacting with other cosmic components </li></ul><ul><li>Interaction with dark matter </li></ul><ul><li>Unification of dark matter and dark energy </li></ul><ul><li>Chaplygin gas </li></ul><ul><ul><li>EOS </li></ul></ul><ul><ul><li>scaling with a </li></ul></ul>
  28. 28. DE models <ul><li>Cosmic fluid </li></ul><ul><li>Scalar fields (quintessence, phantom) </li></ul><ul><li>... </li></ul><ul><li>Effective description of other acceleration mechanisms (at least at the level of global expansion) </li></ul>
  29. 29. Λ CDM <ul><li>Benchmark model </li></ul><ul><li>Only known concepts (CC, NR matter, radiation) </li></ul><ul><li>small number of parameters </li></ul><ul><li>The size of Λ not understood – cosmological constant problem(s) </li></ul><ul><li>Problems with Λ CDM cosmology </li></ul>
  30. 30. Quintessence <ul><li>Dynamics of a scalar field in a potential </li></ul><ul><li>Freezing vs. thawing models </li></ul><ul><li>“ tracker field” models </li></ul><ul><li>k-essence (noncanonical kinetic terms) </li></ul>
  31. 31. Phantom energy <ul><li>Energy density growing with time </li></ul><ul><li>Big rip </li></ul><ul><li>Stability </li></ul><ul><li>Problems with microscopic formulation </li></ul><ul><li>Instability to formation of gradients </li></ul><ul><li>Effective description </li></ul>
  32. 32. Singularities <ul><li>New types of singularities </li></ul><ul><li>Finite time (finite scale factor) singularities </li></ul><ul><li>Sudden singularities </li></ul>
  33. 33. Modified gravity <ul><li>Modification of gravity at cosmological scales </li></ul><ul><li>Dark gravity (effective dark energy) </li></ul><ul><li>F(R) gravity – various formulations (metric, Palatini, metric-affine) </li></ul><ul><li>Conditions for stability </li></ul><ul><li>Stringent precision tests in Solar system and astrophysical systems </li></ul>
  34. 34. Braneworlds <ul><li>Matter confined to a 4D brane </li></ul><ul><li>Gravity also exists in the bulk </li></ul><ul><li>Dvali-Gabadadaze-Poratti (DGP) </li></ul><ul><li>Different DGP models – discussion of the status! </li></ul><ul><li>Phenomenological modifications of the Friedmann equation – Cardassian expansion </li></ul>
  35. 35. The cosmological constant <ul><li>Formally allowed – a part of geometry </li></ul><ul><li>Introduced by Einstein in 1917 – a needed element for a static universe </li></ul><ul><li>Pauli – first diagnosis of a problem with zero point energies </li></ul><ul><li>Identification with vacuum energy – Zeldovich 1967 </li></ul><ul><li>Frequently used “patch” </li></ul>
  36. 36. The expansion with the cosmological constant J. Sol à, hep-ph/0101134v2
  37. 37. The expansion with the cosmological constant
  38. 38. Contributions to vacuum energy <ul><li>Zero point energies – radiative corrections </li></ul><ul><ul><li>Bosonic </li></ul></ul><ul><ul><li>Fermionic </li></ul></ul><ul><li>Condensates – classical contributions </li></ul><ul><ul><li>Higgs condensate </li></ul></ul><ul><ul><li>QCD condensates </li></ul></ul><ul><ul><li>... </li></ul></ul>
  39. 39. Zero point energies <ul><li>QFT estimates </li></ul><ul><ul><li>real scalar field </li></ul></ul><ul><ul><li>spin j </li></ul></ul>
  40. 40. Condensates <ul><li>Phase transitions leave contributions to the vacuum energy </li></ul><ul><li>Higgs potential </li></ul><ul><li>minimum at </li></ul><ul><li>contribution to vacuum energy </li></ul>
  41. 41. The size of the CC <ul><li>Many disparate contributions </li></ul><ul><li>Virtually all many orders of magnitude larger than the observed value </li></ul><ul><li>ZPE - Planck scale “cutoff” ≈ 10 74 GeV 4 </li></ul><ul><li>ZPE - TeV scale “cutoff” ≈ 10 57 GeV 4 </li></ul><ul><li>ZPE - Λ QCD scale “cutoff” ≈ 10 -5 GeV 4 </li></ul><ul><li>Higgs condensate ≈ - 10 8 GeV 4 </li></ul><ul><li>m electron 4 ≈ 10 -14 GeV 4 </li></ul><ul><li>The observed value </li></ul>
  42. 42. The “old” cosmological constant problem – the problem of size <ul><li>Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field) </li></ul><ul><li>Huge fine-tuning implied </li></ul><ul><li>How huge and of which nature </li></ul><ul><ul><li>Numerical example: 10 120 </li></ul></ul><ul><ul><li>1 </li></ul></ul><ul><ul><li>-0.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 </li></ul></ul><ul><ul><li>= 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 </li></ul></ul><ul><ul><li>Financial example </li></ul></ul><ul><ul><li>Instability to variation of a single contribution (parameter) </li></ul></ul>
  43. 43. The “old” cosmological constant problem <ul><li>Fundamental theoretical problem – the problem of the vacuum energy density </li></ul><ul><li>All proposed solutions assume that the “old” CC problem is somehow solved </li></ul><ul><ul><li>Λ CDM model – CC relaxed to the observed value </li></ul></ul><ul><ul><li>DE models and other models – CC is zero or much smaller in absolute value compared to the observed DE energy density </li></ul></ul><ul><li>Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism, the “old” CC problem must be resolved </li></ul>
  44. 44. DE vs CC <ul><li>Raphael Bousso, “TASI lectures on the cosmological constant” </li></ul><ul><ul><li>“ If a poet sees something that walks like a duck and swims like a duck and quacks like a duck, we will forgive him for entertaining more fanciful possibilities. It could be a unicorn in a duck suit – who's to say! But we know that more likely, it's a duck.” </li></ul></ul><ul><li>Conditions for a mechanism solving the CC problem </li></ul>
  45. 45. Proposed solutions of the “old” CC problem <ul><li>Classification (closely following S. Nobbenhuis, gr-qc/0609011) </li></ul><ul><ul><li>Symmetry </li></ul></ul><ul><ul><li>Back-reaction mechanisms </li></ul></ul><ul><ul><li>Violation of the equivalence principle </li></ul></ul><ul><ul><li>Statistical approaches </li></ul></ul>
  46. 46. Symmetry <ul><li>Supersymmetry </li></ul><ul><li>Scale invariance </li></ul><ul><li>Conformal symmetry </li></ul><ul><li>Imaginary space </li></ul><ul><li>Energy -> - Energy </li></ul><ul><li>Antipodal symmetry </li></ul>
  47. 47. Back-reaction mechanisms <ul><li>Scalar </li></ul><ul><li>Gravitons </li></ul><ul><li>Running CC from Renormalization group </li></ul><ul><li>Screening caused by trace anomaly </li></ul>
  48. 48. Violation of the equivalence principle <ul><li>Non-local Gravity, Massive gravitons </li></ul><ul><li>Ghost condensation </li></ul><ul><li>Fat gravitons </li></ul><ul><li>Composite gravitons as Goldstone bosons </li></ul>
  49. 49. Statistical approaches <ul><li>Hawking statistics </li></ul><ul><li>Wormholes </li></ul><ul><li>Anthropic Principle </li></ul>
  50. 50. The cosmic coincidence problem – the problem of timing <ul><li>Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch? </li></ul><ul><li>A problem in a DE (CC) approach to the problem of accelerated expansion: </li></ul><ul><ul><li>DE (CC) energy density scale very differently with the expansion (if presently comparable they were very different in the past and will be very different in the future </li></ul></ul><ul><ul><ul><li>NR: ρ ~ a -3 </li></ul></ul></ul><ul><ul><ul><li>DE: ρ ~ a -3(1+w) , slower than a -2 , CC: ~ 1 </li></ul></ul></ul><ul><li>Also present in many approaches not based on DE </li></ul>
  51. 51. Possible solutions of the cosmic coincidence problem <ul><li>Naturally solved in (matter) back-reaction approaches </li></ul><ul><li>“ tracker field” </li></ul><ul><li>Oscillating DE model </li></ul><ul><li>DE-DM interaction models (although problem still present in e.g. Chaplygin gas model) </li></ul><ul><li>Composite DE model (LambdaXCDM model) </li></ul><ul><ul><li>Two interacting DE components: a (dynamical) cosmological term and an additional DE component (cosmon X) </li></ul></ul><ul><li>… . </li></ul>
  52. 52. Composite dark energy – Λ XCDM models <ul><li>ordinary matter (radiation and NR matter) separately conserved) </li></ul><ul><li>Λ XCDM 1 : CT interacting with cosmon </li></ul><ul><ul><li>J. Grande, J. Sol à , H. Š., JCAP 0608 (2006) 011. </li></ul></ul><ul><li>Λ XCDM 2 : varaible CT i G, X concerved </li></ul><ul><ul><li>J. Grande, J. Sol à , H. Š., Phys. Lett . B645 (2007) 236. </li></ul></ul>
  53. 53. Ratio of DE and matter energy density
  54. 54. Parameter constraints <ul><li>primordial nucelosynthesis: </li></ul><ul><li>Existence of a stopping point </li></ul><ul><li>height of the maximum of r : </li></ul>
  55. 55. Parameter constraints – cross sections
  56. 56. The CC relaxation mechansim <ul><li>Two component model (H.Š. Phys.Lett. B 670 (2009) 246) </li></ul><ul><li>The inhomogeneous equation of state (S. Nojiri, S.D. Odintsov, Phys. Rev. D 72 (2005) 023003) </li></ul><ul><li>The continuity equation </li></ul>
  57. 57. The model dynamics <ul><li>The dynamics of the Hubble parameter </li></ul><ul><li>Notation </li></ul><ul><li>Dynamics in terms of dimensionless parameters </li></ul><ul><li>with the initial condition </li></ul><ul><li>H X and a X in principle arbitrary </li></ul>
  58. 58. α < −1: the relaxation mechanism for the large cosmological constant <ul><li>The α = −3 case </li></ul><ul><li>Closed form solution </li></ul>
  59. 59. case <ul><li>Late-time symptotic behavior </li></ul><ul><li>Ʌ eff is small because | Ʌ | is large! </li></ul>
  60. 60. Dependence on model parameters
  61. 61. Dependence on model parameters
  62. 62. Dependence on model parameters
  63. 63. Dependence on model parameters
  64. 64. case <ul><li>Asymptotic behavior </li></ul><ul><li>Late-time asymptotic behavior </li></ul><ul><li>Ʌ eff is small because Ʌ is large! </li></ul>
  65. 65. Dependence on model parameters
  66. 66. Dependence on model parameters
  67. 67. Dependence on model parameters
  68. 68. Dependence on model parameters
  69. 69. Other parameter regimes <ul><li>For α > −1 the behavior is different </li></ul><ul><li>The relaxation mechanism is not automatic </li></ul>
  70. 70. Fixed points, approach to de Sitter regime <ul><li>general dynamics </li></ul><ul><li>Fixed point ⇒ </li></ul><ul><li>Example: ⇒ </li></ul>
  71. 71. General inhomogeneous EOS <ul><li>dynamics of the scaled Hubble parameter </li></ul><ul><li>condition for the relaxation mechanism </li></ul><ul><li>for a small h at late-time </li></ul>
  72. 72. Variable cosmological term <ul><li>Running CC </li></ul><ul><li>Extended running CC </li></ul><ul><li>Interaction with matter + put β n -> 0 </li></ul><ul><li>Dynamics of the Hubble parameter </li></ul>
  73. 73. Variable cosmological term <ul><li>Late-time asymptotic behavior </li></ul>
  74. 74. f(R) modified gravity <ul><li>general dynamics </li></ul><ul><li>specific example </li></ul><ul><li>asymptotic de Sitter regime </li></ul><ul><li>n=1 </li></ul>
  75. 75. Important questions <ul><li>Abruptness of the transition </li></ul><ul><li>The onset of the transition </li></ul><ul><li>The connection to other eras of (accelerated) expansion </li></ul><ul><li>Addition of other components and other cosmological (RD,MD) eras </li></ul><ul><li>Cosmological coincidence problem </li></ul><ul><li>Stability of the mechanism to perturbations </li></ul><ul><li>Precision tests and the comparisons with the observational data </li></ul><ul><ul><li>astrophysical scales (e.g. solar system tests) </li></ul></ul><ul><ul><li>cosmological scales (growth of inhomogeneities) </li></ul></ul>
  76. 76. Summary of the relaxation mechanism properties <ul><li>The solution of the CC problem without fine-tuning for both signs of the CC </li></ul><ul><li>The universe with a large CC has a small positive positive effective CC </li></ul><ul><li>Ʌ eff is small because | Ʌ| is large </li></ul><ul><li>Ʌ eff ~ 1/ | Ʌ| </li></ul><ul><li>candidate physical mechanisms: modified gravity, (nonlinear) viscosity, quantum effects </li></ul><ul><li>Exchanging “unnatural” parameters for some new (not too complicated) dynamics </li></ul>
  77. 77. Relaxing a large cosmological constant - adding matter and radiation <ul><li>F. Bauer, J. Sola, H. Š. arXiv:0902.2215 </li></ul><ul><li>Components: </li></ul><ul><ul><li>variable cosmological term (containing a large constant term) </li></ul></ul><ul><ul><li>dark matter </li></ul></ul><ul><ul><li>baryons </li></ul></ul><ul><ul><li>radiation </li></ul></ul><ul><li>Variable cosmological term and DM interact </li></ul>
  78. 78. The formalism <ul><li>The variable cosmological term </li></ul><ul><li>Constructing f from general coordinate covariant terms </li></ul><ul><li>Interaction with the DM component </li></ul>
  79. 79. ½ Model <ul><li>f=R </li></ul><ul><li>Radiation domination (controlled by 1-q) </li></ul><ul><li>transition to de Sitter regime (controlled by small H 2 ) </li></ul><ul><li>abrupt transition removed </li></ul><ul><li>RD phase introduced </li></ul>
  80. 80. The model <ul><li>Two terms dominated by different values of q and different powers of H </li></ul><ul><li>Sequence of a RD, MD and de Sitter phases </li></ul><ul><li>Realistic cosmological model with a relaxed CC </li></ul>
  81. 81. The deceleration parameter
  82. 82. Normalized energy densities
  83. 83. Absolute energy densities
  84. 84. Effective DE EOS
  85. 85. Conclusions <ul><li>The question of the mechanism of the acceleration of the universe still open </li></ul><ul><li>The cosmological constant problem(s) – many proposed approaches – decisive arguments still to come </li></ul><ul><li>The nexus of physics at many very different distance/energy scales </li></ul><ul><li>Testing ground of the future theoretical, observational and experimental efforts </li></ul>

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