Dark Energy and baryon oscillations

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Dark Energy and baryon oscillations
Domenico Sapone Université de Genève,
Département de Physique théorique In
collaboration with Luca Amendola (INAF,
Osservatorio astronomico di Roma)
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First theoretical and observational informations

• Inflation
• Nucleosynthesis
• SNIa
• CMB
• LSS

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(No Transcript)
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Cosmic Microwave background

• Before decoupling
  oscillating fluid
• ANISOTROPIES
• Gravitational redshift
• Redshift Doppler
• Overdensity

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After decoupling
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Acoustic oscillations
The equations in the Newtonian limit for a
self-gravitational gas are
Considering the perturbed quantities, it can be
obtained the equation for perturbations in the
Fourier space
This is only an approximation, we need to
consider all the components in the universe at
that epoch
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Acoustic oscillations
The components that filled the primordial
universe are CDM, b, and can be
excluded because are decoupled very early at CDM
has been coupled to gravity b and can be
considered like a single component
Gravitational field Perturbation associated to
the spatial curvature
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Acoustic oscillations
The solution for the above equation is

• The characteristics of the peaks give information
  on fundamental cosmological parameters
• decreasing it, the spectrum is shifted to the
  right part ( bigger)
• increasing it, the eight of the peaks
  increases
• increasing it, the position of the peaks is
  shifted
• increasing it, the amplitude of the power
  spectrum of increases
• changing the value would have been
  suppressed by a factor
• changing the value, there is a shift in the
  position of the peaks
• tensorial modes, this is related to the
  spectral index

Hu, Sugiyama Silk 1995
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Peaks position
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Sloan Digital Sky SurveyOur first detailed local
universe map
LSS depends on the Dark Energy
Needs to know
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Dark Energy equation

• Dependence on redshift
• Parametrization of
• Hubble parameter and angular diameter distance

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Matter power spectrum
Just looking at the galaxies
The first 4 acoustic peaks
Transfer function What do we need to consider?
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Observed galaxy power spectrum
Growth factor
bias
Redshift distortion
Kaiser (1987)
Reference cosmology
Shot noise Poissonian
z distance error
H. J. Seo D. J. Eisenstein 2003
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Fisher Matrix
Given a distribution function
of the variable depending on and given
an ensemble of N
independent variables, it is defined the
Likelihood function, as
The value of that maximize the likelihood
is the best value of
H. J. Seo D. J. Eisenstein 2003 M. Tegmark
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Fisher Matrix
If the dimension of the sample is sufficiently
big, the distribution function can be considered
Gaussian, with mean value and variance
It can be defined the Fisher Matrix, as
The can be considered as the
best covariance matrix of the parameters
H. J. Seo D. J. Eisenstein 2003 M. Tegmark 1997
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Fisher Matrix
The Fisher matrix is
with the effective volume
We need to have in mind that we have to divide
the survey in different bins
H. J. Seo D. J. Eisenstein 2003
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Parameters
Parameters
1) Fraction matter density
2) Fraction baryon density
3) Optical thickness
4) Spectral index
5) Matter density
For each bin
6) Shot noise
7) Angular diameter distance
8) Hubble parameter
9) Growth factor
10) Bias
Depend on Cosmology
Depend on redshift
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Fisher matrix for CMB
Where spectrum of the multipole
of the component
Depend on Cosmology
Depend on CMB
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Total Fisher matrix
Submatrix
The rootsquare of the diagonal elements of the
submatrix are the cosmological parameters errors,
i.e. H, D and G
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Dark energy matrix
The new set of parameters is
The old set of parameters is
The dark energy matrix is
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dimension of the DE matrix
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Results
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Marginalizing over G
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Comparing with SNIa
L. Amendola, C. Quercellini E. Giallongo
astro-ph/0404599
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comparing with SNIa

• SN constraints 400 SNIa in z0-1.5
• Magnitude errors
• for the shaded areas at
• The dotted contour assumes 10
  Gaussian error on

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Conclusions

• Future deep and wide redshift surveys explore
  z1-3
• Epoch at which the Universe begins its expansion
• Comparing recent and early Universe
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  up to z1.5
• SNIa as standard candles have 2 limits
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  to big errors
• Other probes (as GRBs, lensing) at large
  distances might be promising but the physics are
  unknown
• well-known
  physics
• Baryon oscillation best constraints
• z0-3.5 with
  high precision

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References

• L. Amendola, C. Quercellini E. Giallongo,
  arXivastro-ph/0404599
• C.A. Blake K. Glazerbrook, arXivastro-ph/030163
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• D. Eisenstein W. Hu, arXivastro-ph/9709112
• D. Eisenstein at al., arXivastro-ph/9807130
• H. J. Seo D. Eisenstein, arXivastro-ph/0307460
• M. Tegmark et al., arXivastro-ph/0310723