1

L. Perivolaropouloshttp://leandros.physics.uoi.gr

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

w z

z

1w

Dark Energy

Allowed Sector

w z

z

1w

Cosmological Constant

w z

z

1w

Modified Gravity

Allowed Sector

2

300

2 ln1 1( ) 3

( )1 1

X

Xm

d Hzp z dzw z

z Hz

H

Forbidden(ghosts)

1

'3 (1 ( '))

'~

ada

w aa

e

32

2 002

8( )

3 m

aa GH z a

a a

1

1a

z

Expansion History

Eq. of state evolution

G - g = T

G = TmT’μν)

G’ = Tm

2

300

2 ln1 1

3

1 1m

d Hz

dzw zH

zH

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:0804.4142

4 years ago Riess et. al. astro-ph/0402512

Astrophys.J.607:665-687,2004

0.27 0.03m

Recent data Wood Vasey et. al.

astro-ph/0701041

0 1a

zw z w w

z

0 'w z w w z

Chevallier-Polarski, Linder

6

Latest data (307 SnIa) Kowalski et. al. arXiv:0804.4142

4 years ago Riess et. al. astro-ph/0402512

Astrophys.J.607:665-687,2004

1.2

0.7

1.2

0.7

7

Is ΛCDM (GR + Λ) consistent with all cosmological observations?

Yes! Flat, ΛCDM remains at 1σ distance from the best fit since 2004.

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 (w0,wa) contour!

Q: Which Dark Energy Probe has the weakest consistency with ΛCDM?

8

Luminosity Distance (standard candles: SnIa,GRB):

24 L

Ll

d 0

( ) 1z

L th

dzd z c z

H z

: (0,1.7]

: [0.1,6]

SnIa z

GRB z

Angular Diameter Distance (standard rulers: CMB sound horizon, clusters):

sA

rd z

sr Ad z

0

( )1

z

A th

c dzd z

z H z

: 0.35, 0.2

: 1089

BAO z z

CMB Spectrum z

Ld z

SnIa Obs

GRB

flat

Direct Probes of H(z):

Significantly less accurate probes

S. Basilakos, LP, arXiv:0805.0875

9

2

10 , , 0 120 1 2

1

5log ( ) 5log ( ; , ), , min

L A i obs L A i th

mi

N

i

d z d z w ww w

Parametrize H(z): 0 1, 1,0CDM w w

Minimize:

Standard Candles (SnIa)

Standard Rulers (CMB+BAO)

Lazkoz, Nesseris, LP

JCAP 0807:012,2008. arxiv: 0712.1232

0 1 1

zw z w w

z

0 0.24m

2σ 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 (1052 ergs~mass of Sun)

occurring in the universe since the Big Bang

Collimated emissions (0.1-100 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.

: Peak Energy of spectrumpeakE, : Parameters to fitpeak peaka B

Example of Correlation:

L obtained from

Steps for cosmological fitting (Schaefer astro-ph/0612285, 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 Li

2. Use the fitted a, b to find the ‘correct’ Li from the observed Epeak i

3. Use the new Li , along with li, zi to fit cosmological parameters

Circularirty problem: A cosmological model has been used to calibrate a, b !!

log log logi peakL B a E Schaefer astro-ph/0612285

12

Fit a, b along with the cosmological parameters (eg Ωm):

,log logi peak iL b a E

2,log log 4 ,i L i m bolo iL d z P

ix ,log peak iE

ix ,

loglog i

peak i

L bE

a

Minimize χ2 wrt a, b, Ωm:

S. Basilakos, LP, arXiv:0805.0875,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.

0.28 0.05m

14

:sP k

:gP k

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.k

Measure β Find f

f

b

15

Parametrization: 6

11

Fit to LSS data:

: deCDM const

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:

mf a

best fit

ΛCDM

0 0.3m

Evolution of δ :

16

L. Fu et al.: Very weak lensing in the CFHTLS Wide, arxiv. 0712.0884

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 Ωm but different H(z).

The growth function D(a) in the context of G.R. is mainly

determined by the shift parameter R and Ωm . 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.387:1126-1130,2008.

18

Quantum Vacuum is not empty!

ee

ee

ee

eeee

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)

dE pdV 1st law

vac vac vac vacdV p dV p

same as Λ

FΔV

vacp vac ee

eeee

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

d

2d

Vacuum Energy gets modified in the presence of the plates (boundary conditions)

Attractive Force

2

4

2

3

240

720

Cas

Cas

hcF

d

hcE

d

1k

2k

3k

1k

2k

3k

d

Density of Modes (relative to continuum) decreases

d

20

EM vacuum energy with cutoff (allow for compact extra dimension):

No extra dim.

with compact extra dim

Poppenhaeger et. al.hep-th/0309066 Phys.Lett.B582:1-5,2004

LP, Phys. Rev. D 77, 107301 (2008)

The cutoff predicts a Casimir force which becomes repulsive for d<0.6mm

3 30 310 0.1 10c c VeV l mm g cm Required Cutoff:

Compact Extra dim, No cutoff

1k

2k

d d

Cutoff:

2k

1k

Density of Modes is Constant.Energy of Each Mode Increases.

Force becomes repulsive!

With Cutoff

cd l

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’ 1998-2005 of new dark energy observational constraints, the improvement of these constraints has slowed down.

2000 2002 2004 2006 2008

0

50

100

150

200

250

300

No. of papers with words ‘dark energy’ and ‘CMB’ in title per year (from spires database

http://www-spires.dur.ac.uk/spires/hep/

‘dark energy’

‘cmb’