lecture 2: observational constraints on dark energy
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Lecture 2: Observational constraints on dark energy. Shinji Tsujikawa (Tokyo University of Science). Observational constraints on dark energy. The properties of dark energy can be constrained by a number of observations:. Supernovae type Ia (SN Ia) - PowerPoint PPT PresentationTRANSCRIPT
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Lecture 2:Observational constraints on dark energy
Shinji Tsujikawa(Tokyo University of Science)
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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.Especially important for modified gravity models.
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Supernovae Ia constraints
The cosmic expansion history is known by measuring the luminosity distance
(for the flat Universe)
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Parametrization to constrain dark energy
Consider Einstein gravity in the presence of non-relativistic matterand dark energy with the continuity equations
In the flat Universe the Friedmann equation gives
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where
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Joint data analysis of SN Ia, WMAP, and SDSS with the parametrization (Zhao et al, 2007)
Best fit case
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Cost for standard two-parameter compressions
The two-parameter compression may not accommodate thecase of rapidly changing equation of state.
Bassett et al (2004) proposed the ‘Kink’ parametrization allowing rapid evolution of w :
DE
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Maximizied limits of kink parametrizations
Parmetrization (i)
Parmetrization (iii)
Parmetrization (ii)
Kink
The best-fit kink solutionpasses well outside the limits of all the other parametrizations.
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Observational constraints from CMBThe observations of CMB temperature anisotropies can also place constraints on dark energy.
2013? PLANCK
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CMB temperature anisotropiesDark energy affects CMB anisotropies in two ways.
1. Shift of the peak position2. Integrated Sachs Wolfe (ISW) effect
ISW effect
Larger
€
ΩDE(0)
Smaller scales
(Important for large scales)
Shift for
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Angular diameter distance
The angular diameter distance is
(flat Universe)
This is related with the luminosity distance via
(duality relation)
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Causal mechanism for the generation of perturbations
Second horizon crossing
After the perturbations leavethe horizon during inflation, the curvature perturbations remain constant by the second horizon crossing.
Scale-invariant CMB spectra on large scales
After the perturbationsenter the horizon, they start to oscillate as a sound wave.
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CMB acoustic peaks
where
Hu Sugiyama
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(CMB shift parameter)where
and
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The WMAP 5yr bound:
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(Komatsu et al, WMAP 5-yr data)
Observational constraints on the dark energy equation of state
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Joint data analysis of SN Ia + CMB (for constant w)
The constraints from SN Ia and CMB are almost orthogonal.
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ISW effect on CMB anisotropies
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Evolution of matter density perturbations
( )
The growing mode solution is
The growing mode solution is
Responsible for LSS
Perturbationsdo not grow.
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Poisson equation
The Poisson equation is given by
(i) During the matter era
(ii) During the dark energy era
(no ISW effect)
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Usually the constraint coming from the ISW effect is notstrong compared to that from the CMB shift parameter.(apart from some modified gravity models)
ISW effect
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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
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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 light)
(the oscillations along the line of sight)
The spherically averaged spectrum is
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We introduce the relative BAO distance
where
The observational constraint by Eisenstein et al is
The case (i) is favored.
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Joint data analysis of SN Ia + CMB + BAO (for constant w)