dark energy i : observational constraints shinji tsujikawa (tokyo university of science)
TRANSCRIPT
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