L. Perivolaropoulos Department of Physics University of Ioannina Open page

New High Quality Cosmological Data have confirmed and mapped in detail the accelerating expansion SNLS astro-ph/ Gold06-HST astro-ph/ Essence astro-ph/ WMAP SDSS (BAO) v2 The Cosmological Constant (ρ=const) remains consistent 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. A signature in the Casimir effect would be expected in that case. An Evolving Dark Energy Density (ρ=ρ(t)) is also allowed by the data and a subset of the allowed evolving forms is inconsistent with most G. R. based models Scalar Tensor extensions of General Relativity are consistent with the full range of allowed expansion histories. Demanding consistency of Scalar-Tensor theories with solar system tests and full range of allowed expansion histories implies constraints on Newton’s constant evolution G(t)

Directly Observable Dark Energy (Inferred) No Yes Flat Friedmann Equation Not Consistent

(from CMB and large scale structure observations) Friedman eqn I: Friedman eqn II:

Dark Energy Allowed Sector Cosmological Constant Modified Gravity Allowed Sector Forbidden (ghosts) Expansion History Eq. of state evolution G  -  g  =  T  G  =  T m   T’ μν ) G’  =  T m 

Luminosity Distance (standard candles: SnIa,GRB): Angular Diameter Distance (standard rulers: CMB sound horizon, clusters): SnIa Obs GRB flat Direct Probes of H(z): Significantly less accurate probes S. Basilakos, LP, arXiv:

Parametrize H(z): Minimize: Standard Candles (SnIa) Standard Rulers (CMB+BAO) Lazkoz, Nesseris, LP arxiv: σ tension between standard candles and standard rulers ESSENCE+SNLS+HST data WMAP3+SDSS(2007) data

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

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 Repulsive (ρ+3p=-2ρ) 1 st law same as Λ F ΔVΔV Quantum Vacuum is elastic (p=-ρ) Vacuum Energy of a Scalar Field: cutoff Quantum Vacuum is divergent!

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 ! Casimir Force Experiments can pick up the presence of a physical cutoff !! Majajan, Sarkar, Padmanbhan, Phys.Lett.B641:6-10,2006 Vacuum Energy gets modified in the presence of the plates (boundary conditions) Attractive Force Density of Modes (relative to continuum) decreases

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

What is so special about today?

Minimally Couled Scalars (Quintessence) Barotropic fluids (eg Chaplygin Gas) k-Essence Topological Defect Network … Q1: What theories are consistent with range of observed H(z)? 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

Quintessence To cross the w=-1 line the kinetic energy term must change sign (impossible for a quintessence field) Generalization for k-essence:

ESSENCE+SNLS+HST data

Extended (Scalar–Tensor) Quintessence f(R) Modified Gravity Braneworld models (eg DGP) … Q1: What theories are consistent with range of observed H(z)? 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

Consistency Requirements: S. Nesseris, LP, Phys.Rev.D75:023517,2007 Q.: What constraints do the consistency requirements imply for H(z), F(z) at low z and are these constraints respected by observations? solar system

Freezing Thawing

Solar System Constraints on g 2 : J. Mueller 2006 E. Pitjeva 2007 Lower bound on g 2 : G(t) close to maximum G(t) close to minimum

Observational Probes of the Accelerating Expansion w(z) is close to -1 w(z) crossing the w=-1 w(z) crossing the w=-1 Inconsistent with Minimally Coupled Quintessence and also with Scalar Tensor Quintessence if G(t) is increasing with time. Consistency of Scalar-Tensor Quintessence with local gravity and crossing of w=-1 w(z) =-1 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.