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

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

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

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