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L. Perivolaropoulos http://leandros.physics.uoi.gr Department of Physics University of Ioannina

Open page. Accelerating Universe:. Recent Observations and Implications for Extended Gravity Theories. L. Perivolaropoulos http://leandros.physics.uoi.gr Department of Physics University of Ioannina. Main Points.

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L. Perivolaropoulos http://leandros.physics.uoi.gr Department of Physics University of Ioannina

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  1. Open page Accelerating Universe: Recent Observations and Implications for Extended Gravity Theories L. Perivolaropouloshttp://leandros.physics.uoi.gr Department of Physics University of Ioannina

  2. Main Points SNLS astro-ph/0510447Gold06-HST astro-ph/0611572Essence astro-ph/0701041WMAP50803.0547SDSS (BAO) 0705.3323v2 New High Quality Cosmological Datahave confirmed and mapped in detail the accelerating expansion The Cosmological Constant (ρ=const) remainsconsistent with all current data as a driving force of the acceleration and can be generated by quantum fluctuations of the vacuum with a proper cutoff. Asignature in the Casimir effect would be expected in that case. An Evolving Dark Energy Density (ρ=ρ(t)) is also allowed by the dataand a subset of the allowed evolving forms is inconsistent with most G. R. based models Scalar Tensor extensions of General Relativity are consistent withthe full range of allowed expansion histories. Demanding consistency of Scalar-Tensor theorieswith solar system tests and full range of allowed expansionhistories implies constraints on Newton’s constant evolution G(t)

  3. The Dark Energy Puzzle Friedmann Equation Flat General Relativity DirectlyObservable Dark Energy(Inferred) DirectlyObservable Not Consistent Q: Is GR the correct theory on the Largest Scales? What is the Correct Theory? No Yes What are the properties of the dark energy? What microphysical theory can reproduce these properties?

  4. Observed Hubble Diagram Dark Energy Equation of State History of Fundamentally New Phenomena Measure Planet Motions Collect Data Tycho-Brahe 1588 Parametrize Data: Ellipses Johan Kepler 1621 Parametrize Data ??? Isaac Newton 1687 Physical Law Modified Gravity? or Dark Energy?

  5. Negative Pressure Acceleration from Friedman eqn I: Dark Energy Evolution: Friedman eqn II: Best Fit ? (from CMB and large scale structure observations)

  6. Candidate Model Classes Cosmological Constant Expansion History Gmn- L gmn = k Tmn Dark Energy Gmn = k (Tmmn+ T’μν) Allowed Sector Eq. of state evolution Forbidden(ghosts) Modified Gravity G’mn = k Tmmn Allowed Sector

  7. SnIa Obs GRB Direct Probes of the Cosmic Metric: Geometric Observational Probes Direct Probes of H(z): Luminosity Distance (standard candles: SnIa,GRB): flat Significantly less accurate probesS. Basilakos, LP, arXiv:0805.0875 Angular Diameter Distance (standard rulers: CMB sound horizon, clusters):

  8. Geometric Constraints Parametrize H(z): Minimize: WMAP3+SDSS(2007) data ESSENCE+SNLS+HST data Standard Candles (SnIa) Lazkoz, Nesseris, LParxiv: 0712.1232 2σ tension between standard candles and standard rulers Standard Rulers (CMB+BAO)

  9. Dynamical Constraints Measure growth function of cosmological perturbations: Evolution of δ : Parametrization: Fit to LSS data: ΛCDM ΛCDM provides an excellent fit to the linear perturbations growth data best fit S. Nesseris, LP, Phys.Rev.D77:023504,2008

  10. Quantum Vacuum: Simplest Origin of Cosmological Constant Quantum Vacuum is not empty! Sea of virtual particles Whose existence has been detected (eg shift of atomic levels in H) W. Lamb, Nobel Prize 1955 Quantum Vacuum is elastic (p=-ρ) ΔV 1st law F same as Λ Quantum Vacuum is Repulsive (ρ+3p=-2ρ) Quantum Vacuum is divergent! Vacuum Energy of a Scalar Field: cutoff

  11. Zero Point Energy of Vacuum and Lab Experiments Q: Can we probe a diverging zero point energy of the vacuum in the lab? A: No! Non-gravitational experiments are only sensitive to changes of the zero point energy. But: This is not so in the presence of a physical finite cutoff ! Majajan, Sarkar, Padmanbhan, Phys.Lett.B641:6-10,2006 Casimir Force Experiments can pick up the presence of a physical cutoff !! Vacuum Energy gets modified in the presence of the plates (boundary conditions) Attractive Force Density of Modes (relative to continuum) decreases

  12. The Experimental Effects of a Cutoff Cutoff: EM vacuum energy with cutoff (allow for compact extra dimension): Density of Modes is Constant.Energy of Each Mode Increases.Force becomes repulsive! Required Cutoff: With Cutoff Compact Extra dim, No cutoff LP, Phys. Rev. D 77, 107301 (2008) No extra dim. Poppenhaeger et. al.hep-th/0309066 Phys.Lett.B582:1-5,2004 with compact extra dim The cutoff predicts a Casimir force which becomes repulsive for d<0.6mm

  13. The Coincidence Problem What is so special about today?

  14. Beyond the Cosmological Constant: Candidate Class II: Dark Energy Q1: What theories are consistent with range of observed H(z)? • Minimally Couled Scalars (Quintessence) • Barotropic fluids (eg Chaplygin Gas) • k-Essence • Topological Defect Network • … Q2: What forms of H(z) are inconsistent with each theory? (forbidden sectors) Q3: What is the overlap of the observationally allowed range of H(z)with the forbidden sector of each theory? Address Q2-Q3 for Quintessence

  15. Minimally Coupled Scalar: No w=-1 crossing Homogeneous Minimally Coupled Scalar: Quintessence Equation of State: To cross the w=-1 line the kinetic energy term must change sign (impossible for a quintessence field) Generalization for k-essence:

  16. Quintessence Forbidden Parameter Sector ESSENCE+SNLS+HST data

  17. Candidate Class III: Modified Gravity Q1: What theories are consistent with range of observed H(z)? • Extended (Scalar–Tensor) Quintessence • f(R) Modified Gravity • Braneworld models (eg DGP) • … Q2: What forms of H(z) are inconsistent with each theory? (forbidden sectors) Q3: What is the overlap of the observationally allowed range of H(z)with the forbidden sector of each theory? Address Q2-Q3 for Extended Quintessence

  18. Scalar-Tensor Theories: Extended Quintessence Vary ST action in flat FRW background assuming perfect fluid: +

  19. Redshift Space Convert t to z, solve for U and Φ': where S. Nesseris, LP , Phys.Rev.D75:023517,2007 Consistency Requirements: solar system Q.: What constraints do the consistency requirements imply for H(z), F(z) at low z and are these constraints respected by observations?

  20. H(z) Forbidden Parameter Sectors Freezing Thawing

  21. w(z) Forbidden Parameter Sectors G(t) close to maximum G(t) close to minimum Solar System Constraints on g2: Lower bound on g2: J. Mueller 2006 E. Pitjeva 2007

  22. SUMMARY w(z) is close to -1 w(z) crossing the w=-1 Observational Probes of the Accelerating Expansion The cosmological constant may be generated by quantum fluctuations of the vacuum with a cutoff. A change of sign of the Casimir force is predicted in that case. w(z) =-1 Inconsistent with Minimally Coupled Quintessenceand also with Scalar Tensor Quintessenceif G(t) is increasing with time. w(z) crossing the w=-1 Consistency of Scalar-Tensor Quintessencewithlocal gravity andcrossing of w=-1

  23. Why Not Scalar-Tensor Theories Sringent Observational Constraints: Solar System: Cosmology:

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