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

Department of Physics

University of Ioannina

Open page

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Model Classes - Key Questions

Geometric Constraints: Standard Rulers - Standard Candles

Comparison of Recent Standard Candle SnIa Data:-Figure of Merit-Consistency with ΛCDM-Consistency with Standard Rulers

Potential Conflicts of ΛCDM with Data:- Large Scale Velocity Flows- Cluster Halo Profiles- Emptiness of Voids - Brightness of High z SnIa

Conclusion

Dynamical Constraints: Linear Growth of Perturbations

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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

00

mm

cr

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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?

What is the consistency level of ΛCDM (GR + Λ) with cosmological observations?

What is the recent progress?

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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 probesS. Basilakos, LP, MBRAS ,391, 411, 2008

arXiv:0805.0875

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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

ESSENCE (+SNLS+HST) data WMAP3+SDSS(2007) data

Chevallier, Pollarski, Linder

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Q2: What is the consistency of each dataset with ΛCDM?

Q3: What is the consistency of each dataset with Standard Rulers?

J. C. Bueno Sanchez, S. Nesseris, LP, 0908.2636

Q1: What is the Figure of Merit of each dataset?

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The Figure of Merit: Inverse area of the 2σ parameter contour. A measure of the effectiveness of the dataset in constraining the

given parameters.

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2 .0 1 .5 1 .0 0 .5 0 .0

6

4

2

0

2

4

6

w 0

w1

2 .0 1 .5 1 .0 0 .5 0 .0

6

4

2

0

2

4

6

w 0

w1

2 .0 1 .5 1 .0 0 .5 0 .0

6

4

2

0

2

4

6

w 0

w1

2 .0 1 .5 1 .0 0 .5 0 .0

6

4

2

0

2

4

6

w 0

w1

2 .0 1 .5 1 .0 0 .5 0 .0

6

4

2

0

2

4

6

w 0

w1

2 .0 1 .5 1 .0 0 .5 0 .0

6

4

2

0

2

4

6

w 0

w1

2 .0 1 .5 1 .0 0 .5 0 .0

6

4

2

0

2

4

6

w 0

w1

SNLS ESSENCE GOLD06 UNION

CONSTITUTION WMAP5+SDSS5 WMAP5+SDSS7

0 0 28m .

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ESSENCE+SNLS+HST data

SNLS 1yr data

Trajectories of Best Fit Parameter Point

The trajectories of SNLS and Constitution clearly closer to ΛCDM for most values of Ω0m

Gold06 is the furthest from ΛCDM for most values of Ω0m

Q: What about the σ-distance (dσ) from ΛCDM?

Ω0m=0.24

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ESSENCE+SNLS+HST data

Trajectories of Best Fit Parameter Point

Consistency with ΛCDM Ranking:

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Consistency with Standard Rulers Ranking:

ESSENCE+SNLS+HST

Trajectories of Best Fit Parameter Point

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Consistency with ΛCDM Ranking

Consistency with Standard Rulers Ranking:

Identical Ranking Sequence!(Independent Criteria)

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Trajectories of Best Fit Parameter Point

0 1 1 4 2w ,w . ,

0 1 1 4 2w ,w . ,

Consistency with Dynamical Dark Energy Ranking:

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Consistency with ΛCDM Ranking: Consistency with Standard Rulers Ranking:

Consistency with Dynamical Dark Energy Ranking

Identical Ranking Sequence

Reversed Ranking Sequence

Tests Quality of SnIa Data

J. C. Bueno Sanchez, S. Nesseris, LP, 09082636

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Flat, ΛCDM remains at 1σ (or less) distance from the best fit with trend to further improve consistency with geometric probes

The 2σ parameter contour areas have improved by a factor of about 4 since 2005 while the number of filtered SnIa has increased by about the same factor. The consistency with standard rulers remains good

(except for Gold06 dataset)

Q: Which Dark Energy Probes have weak consistency with ΛCDM?

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Large Scale Velocity Flows

- Predicted: On scale larger than 50 h-1Mpc Dipole Flows of 110km/sec or less. - Observed: Dipole Flows of more than 400km/sec on scales 50 h-1Mpc or larger.- Probability of Consistency: 1%

Cluster and Galaxy Halo Profiles:

- Predicted: Shallow, low-concentration mass profiles- Observed: Highly concentrated, dense halos- Probability of Consistency: 3-5%

4 5virc ~

10 15virc ~

Bright High z SnIa:

- Predicted: Distance Modulus of High z SnIa close to best fit ΛCDM - Observed: Dist. Modulus of High z SnIa lower (brighter) than best fit ΛCDM - Probability of Consistency for Union and Gold06: 3-6%

The Emptiness of Voids:

- Predicted: Many small dark matter halos should reside in voids.- Observed: Smaller voids (10Mpc) look very empty (too few dwarf galaxies)- Probability of Consistency: 3-5%

From LP, 0811.4684

R. Watkins et. al. , 0809.4041

Broadhurst et. al. ,ApJ 685, L5, 2008, 0805.2617, S. Basilakos, J.C. Bueno Sanchez, LP., 0908.1333, PRD, 80, 043530, 2009.

LP and A. Shafielloo , PRD 79, 123502, 2009, 0811.2802

P.J.E. Peebles , astro-ph/0101127, Klypin et. al. APJ, 522, 82, 1999, astro-ph/9901240

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The dipole moment of large scale velocity flows (bulk flow) extends on scales up to 100h-1 Mpc with amplitude larger than 400km/sec.

ΛCDM predicted amplitude on scale larger than 50h-1 Mpc :

110km/sec

From R. Watkins, H. Feldman and M. J. Hudson, 0809.4041

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NFW profile:

4 2 0 2 4

0 .0

0 .2

0 .4

0 .6

0 .8

1 .0

1 .2

vir

s

rc

r

1c

2c

1 2c cΛCDM prediction:

The predicted concentration parameter cvir is significantly smaller than the observed.

From S. Basilakos, J.C. Bueno-Sanchez and LP,

PRD, 80, 043530, 2009, 0908.1333.

Data from:

Navarro, Frenk, White, Ap.J., 463,

563, 1996

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Parametrization:

6

11 : deCDM const

Measure growth function of cosmological perturbations:

mf a

Evolution of δ(sub-Hubble scales) :

James, Dutta, LP., 0903.5296

Horizon scales

Horizon scales

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Fit to LSS data:

ΛCDM provides an excellent fit to the linear perturbations

growth data

S. Nesseris, LP, Phys.Rev.D77:023504,2008

best fit

ΛCDM

0 0.3m

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The consistency of ΛCDM with geometric probes of accelerating expansion is very good and it appears to be further improving with

time.

There are a few puzzling potential conflicts of ΛCDM specific cosmological data mainly related with dynamical large scale structure

probes.

Data from dynamical probes on the linear growth of perturbations are currently not as constraining as geometric probes but they also have

good consistency with ΛCDM.