1 L. Perivolaropoulos Department of Physics University of Ioannina Open page

2 Introduction - Key Questions - Latest Data Geometric Constraints: Standard Rulers vs Standard Candles Gamma Ray Bursts as Standard Candles Current Dynamical Constraints: Growth Rate from Redshift Distortion Weak Lensing Potential Constraints from Laboratory Experiments: Signatures of a cutoff in the Casimir Effect Conclusions

3 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 

4 Is General Relativity the correct theory on cosmological scales? What is the most probable form of w(z) and what forms of w(z) can be excluded? Is ΛCDM (GR + Λ) consistent with all cosmological observations? What is the recent progress?

5 Latest data (307 SnIa) Kowalski et. al. arXiv: years ago Riess et. al. astro-ph/ Astrophys.J.607: ,2004 Recent data Wood Vasey et. al. astro-ph/ Chevallier-Polarski, Linder

6 Latest data (307 SnIa) Kowalski et. al. arXiv: years ago Riess et. al. astro-ph/ Astrophys.J.607: ,2004

7 Is ΛCDM (GR + Λ) consistent with all cosmological observations? Yes! Flat, ΛCDM remains at 1σ distance from the best fit since The 1σ parameter contour areas remain about the same since 2004 despite of the double size of the SnIa sample and ΛCDM remains at the lower right part of the (w 0,w a ) contour! Q: Which Dark Energy Probe has the weakest consistency with ΛCDM?

8 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:

9 Parametrize H(z): Minimize: Standard Candles (SnIa) Standard Rulers (CMB+BAO) Lazkoz, Nesseris, LP JCAP 0807:012,2008. arxiv: σ tension between standard candles and standard rulers ESSENCE+SNLS+HST data WMAP3+SDSS(2007) data

10 Gamma-ray bursts (GRBs): The most luminus electromagnetic events (10 52 ergs~mass of Sun) occurring in the universe since the Big Bang Collimated emissions ( seconds long) caused either by the collapse of the core of a rapidly rotating, high-mass star into a black holes or from merging binary systems (short bursts). GRBs are extragalactic events, observable to the limits of the visible universe; a typical GRB has a z > 1.0 while the most distant known (GRB080913) has z=6.7 Swift Satellite (2004) Shells of energy and matter ejected by the newly-formed hole collide and merge ("internal shocks"). The shell sweeps up more and more material it slows down and releases energy (afterglow).

11 GRBs are not standard candles but may be calibrated using empirical correlation relations between energy output and lightcurve measurable observables. Example of Correlation: L obtained from Steps for cosmological fitting (Schaefer astro-ph/ , Hong Li et. al. Phys.Lett.B658:95-100, 2008) : 1. Assume or and fit for a, b using a specific cosmological model to find L i 2. Use the fitted a, b to find the ‘correct’ L i from the observed E peak i 3. Use the new L i, along with l i, z i to fit cosmological parameters Circularirty problem: A cosmological model has been used to calibrate a, b !! Schaefer astro-ph/

12 Fit a, b along with the cosmological parameters (eg Ω m ): Minimize χ 2 wrt a, b, Ω m : S. Basilakos, LP, arXiv: , accepted in MNRAS (to appear)

13 Current GRB data are not competitive with other geometric probes. The calibration has too much scatter and there are additional parameters to be fit.

14 The power spectrum at a given redshift is affected by systematic differences between redshift space and real space measurements due to the peculiar velocities of galaxies. Galaxy power spectrum in redshift space Galaxy power spectrum in real space space μ=cosθ and θ is the angle between and the line of sight. Measure β Find f

15 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 :

16 L. Fu et al.: Very weak lensing in the CFHTLS Wide, arxiv Use weak lensing to observe the projected dark matter power spectrum (cosmic shear spectrum) and compare with ΛCDM predictions using maximum likelihood.

17 Flat models 1, 2, 3 have identical shift parameter R and Ω m but different H(z). The growth function D(a) in the context of G.R. is mainly determined by the shift parameter R and Ω m. This may be used as a test of G.R. S. Nesseris, LP, JCAP 0701:018,2007 S. Basilakos, S. Nesseris, LP, Mon.Not.Roy.Astron.Soc.387: ,2008.

18 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!

19 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

20 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

21 The most probable probe that may lead to disfavor of ΛCDM in the next few years appears to be observations of Baryon Acoustic Oscillations Laboratory Experiments related to Casimir effect have the potential to reveal useful signatures of a physical cutoff associated with vacuum energy. After the ‘Golden Age’ of new dark energy observational constraints, the improvement of these constraints has slowed down. No. of papers with words ‘dark energy’ and ‘CMB’ in title per year (from spires database ‘dark energy’ ‘cmb’