Dark energy I :Observational constraints

Shinji Tsujikawa(Tokyo University of Science)

Dark energy From the observations of SN Ia, CMB, and BAO etc, about 70 % of the energy density of the Universe is dark energy responsible for cosmic acceleration.

Observational constraints on dark energy

The properties of dark energy can be constrained by a number of observations:

1. Supernovae type Ia (SN Ia)2. Cosmic Microwave Background (CMB) 3. Baryon Acoustic Oscillations (BAO)

4. Large-scale structure (LSS)5. Weak lensing

The cosmic expansion history is constrained.

The evolution of matter perturbations is constrained.This is especially important for modified gravity models.

Supernovae Ia observations

The luminosity distance L s : Absolute lumonisity

F : Observed flux

is related with the Hubble parameter H, as

for the flat Universe (K=0)

The absolute magnitude M of SN Ia is related with the observedapparent magnitude m, via

Luminosity distance in the flat Universe

Luminosity distance with/without dark energy

Flat Universe withoutdark energy

Open Universe without dark energy

Flat Universe withdark energy

Perlmutter et al, Riess et al (1998)

(Perlmutter et al, 1998)

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mB −M = 5log10(dL /10pc)

Perlmutter et al showed thatthe cosmological constant ( ) is present at the 99 % confidence level, withthe matter density parameter

The rest is dark energy.

High-z data

A. RiessB. Schmidt(Head of Perlmutter et al group)

Observational constraints on the dark energy equation of state for constant w (Kowalski et al, 2008)

SN Ia data only

DE

Time-varying dark energy equation of state

where

Parametrization of the dark energy equation of state

Best-fit case

Observational constraints using the parametrization

Komatsu et al (2010)Zhao et al (2007)

(SNIa, WMAP, SDSS)

Observational constraints from CMBThe observations of CMB temperature anisotropies can also place constraints on dark energy.

2012 PLANCK data will be released.

　　 CMB temperature anisotropiesDark energy affects the CMB anisotropies in two ways.

1. Shift of the peak position2. Integrated Sachs Wolfe (ISW) effect

ISW effect

Larger

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ΩDE(0)

Smaller scales

(Important for large scales)

Shift for

Angular diameter distance

The angular diameter distance is

(flat Universe)

(duality relation)

Causal mechanism for the generation of perturbations

Second Hubble radius crossing

After the perturbations leave theHubble radius during inflation, the curvature perturbations remainconstant by the second Hubble radius crossing.

Scale-invariant CMB spectra on large scales

After the perturbationsenter the Hubble radius, they start to oscillate asa sound wave.

Physical wavelength

Hubble radius

CMB acoustic peaks

where

Hu Sugiyama

(CMB shift parameter)where

and

The WMAP 7-yr bound:

(Komatsu et al, WMAP 7-yr)

Observational constraints on the dark energy equation of state

Flat Universe

Joint data analysis of SN Ia + CMB (for constant w )

The constraints from SN Ia and CMB are almost orthogonal.

DE

(Kowalski et al, 2008)

DE

(0)

　　 ISW effect on CMB anisotropies

　　 Evolution of matter density perturbations

( )

The growing mode solution is

The growing mode solution is

Responsible forlarge-scale structure

Perturbationsdo not grow.

　　　 Poisson equation

The Poisson equation is given by

(i) During the matter era

(ii) During the dark energy era

(no ISW effect)

Usually the constraint coming from the ISW effect is notso tight compared to that from the CMB shift parameter.(apart from some modified gravity models)

ISW effect

　　　 CMB lensing The Atacama Cosmology telescope found the observational evidence of w = -1 dark energy from the CMB data alone by using the new CMB lensing data (2011).

The lensing deflection spectrum is

　　　 Baryon Acoustic Oscillations (BAO)

Baryons are tightly coupled to photons before the decoupling.

The oscillations of sound waves should be imprinted in the baryon perturbations as well as the CMB anisotropies.

In 2005 Eisenstein et al founda peak of acoustic oscillations in the large scale correlation function at

　　　 BAO distance measure

The sound horizon at which baryons were released from the Compton drag of photons determines the location of BAO:

We introduce

(orthogonal to the line of sight)

(the oscillations along the line of sight)

The spherically averaged spectrum is

We introduce the relative BAO distance

where

The observational constraint by Eisenstein et al is

The case (i) is favored.

Observational constraints on the dark energy equation of state from the joint data analysis of SN Ia + CMB + BAO

Kowalski et al