1. Dark Energy and baryon oscillations Domenico Sapone Université de Genève, Département de Physique théorique In collaboration with: Luca Amendola (INAF, Osservatorio astronomico di Roma)

2. First theoretical and observational informations Inflation Nucleosynthesis SNIa CMB LSS

4. Cosmic Microwave background Before decoupling oscillating fluid ANISOTROPIES: 1) 1) Gravitational redshift 2) 2) Redshift Doppler 3) 3) Overdensity

5. After decoupling…

6. 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…

7. 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

8. Acoustic oscillations The solution for the above equation is: Hu, Sugiyama & Silk 1995 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

9. Peaks position

10. Sloan Digital Sky Survey Our first detailed local universe map LSS depends on the Dark Energy Needs to know:

11. Dark Energy equation Dependence on redshift: Parametrization of: Hubble parameter and angular diameter distance

12. Matter power spectrum The first 4 acoustic peaks Transfer function What do we need to consider? Just looking at the galaxies

13. Observed galaxy power spectrum Growth factor bias Redshift distortion Shot noise Poissonian Reference cosmology z distance error Kaiser (1987) H. J. Seo & D. J. Eisenstein 2003

14. 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

15. 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

16. 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

17. 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

18. Fisher matrix for CMB Where: spectrum of the multipole of the component ; Depend on Cosmology Depend on CMB

19. Total Fisher matrix Submatrix: The rootsquare of the diagonal elements of the submatrix are the cosmological parameters errors, i.e. H, D and G…

20. Dark energy matrix The new set of parameters is: The old set of parameters is: The dark energy matrix is:

21. …dimension of the DE matrix

22. Results

23. Marginalizing over G…

24. Comparing with SNIa L. Amendola, C. Quercellini & E. Giallongo astro-ph/0404599

25. …comparing with SNIa SN constraints 400 SNIa in z=0-1.5 Magnitude errors for the shaded areas at The dotted contour assumes 10% Gaussian error on

26. Conclusions Future deep and wide redshift surveys explore z=1-3 Epoch at which the Universe begins its expansion Comparing recent and early Universe up to z=1.5 SNIa as standard candles have 2 limits: to big errors Other probes (as GRB’s, lensing) at large distances might be promising but the physics are unknown well-known physics Baryon oscillation best constraints z=0-3.5 with high precision

27. References L. Amendola, C. Quercellini & E. Giallongo, arXiv:astro-ph/0404599 C.A. Blake & K. Glazerbrook, arXiv:astro-ph/0301632 D. Eisenstein &W. Hu, arXiv:astro-ph/9709112 D. Eisenstein at al., arXiv:astro-ph/9807130 H. J. Seo & D. Eisenstein, arXiv:astro-ph/0307460 M. Tegmark et al., arXiv:astro-ph/0310723