METHODS OF COSMOLOGICAL MODELS SELECTION

1. METHODS OF COSMOLOGICAL MODELS SELECTION Włodzimierz Godłowski Marek Biesiada Zong-Hong Zhu Institute of Physics UO Institute of Physics UŚ Department of Astronomy BeijingNormal University Chongqing 2013

2. Present Status of the Universe Problem: Many cosmological models gives fits with similar quality. For more complicated model with more free parameters usually we obtain better fits How discriminate between the models?

3. BayesTheorem Where maximum likelihoodL : Information criteria AIC is useful in obtaining upper limit to thenumber of parameters which should be incorporated to the model, the BIC ismore conclusive. Of course only the relative value between BIC of differentmodels has statistical significance More advanced is evidence E and Bayes factor Bij (which is odds of evidencesfor two models) - often approximationbut usually wrong. Could be obtained with Nested Sampling Algorithm (Skilling 2004, Mukherjee 2008 see also many papers of Bolejko) or directly from computing full likelihood function (present work, take long computer time) For deeper analysis of statistical results it would be useful to considerthe information entropy of the distribution

4. Sahni – Shtanow brane models

5. Popular models

6. State of art – popular models with Gold SNIa data

7. State of art – popular models with UnionSNIa data

8. Comparisons of results for Gold and Union SNIa data For Gold SNIA data the model with high Wm,0 were preferred Union SNIa preferred LCDM and Deffayet-Dvali-Gabadadze models but Both model have different prediction for Wm,0 - possible to discriminated between the models

9. Randall – Sundrum Model

11. Different observational data • Supernovae Ia, Gamma Ray Bursts (luminosity distances) • Angular diameter of radio-sources , Sunayaev –Zeldovich effect , (angular distances ) • FRII radiogalaxies , Barion oscillation peaks, CMBR „shift parameter” (coordinate distance) • X-ray gas mass fraction • Age of astronomical objects • Primordial nucleosynthesis • Position of peaks in CMBR • Strong lensing

15. Age of the Universe –be careful – Universe can not be older than astronomical objects

17. Combined analysis

19. Kombinowana analiza na

23. Observational constraints on a modified Friedmann equation obtained from the generalized Lagrangian L~Rn minimally coupled with matter via the Palatini first-orderformalism (Borowiec et al. 2006, 2007) • The nonlinear gravity models withn<2can beexcluded by combined analysis of both SNIa dataand the baryon oscillation peak detected in theSDSS Luminous Red Galaxy Survey of Eisensteinet al.[2005] at the2sconfidence level • Use the Akaike and Bayesian information criteria for comparison and discrimination between theanalyzed models. We find that these criteria stillfavor theLCDMmodel over the nonlinear gravitymodel, because (with similar quality of the fit forboth models) theLCDMmodel contains one lessparameter. • Although amount of "dark energy" (of non-substantial origin) is consistent with SNIa data and flat curves of spiral galaxies are reproduces in the framework of modified Einstein's equation we still need substantial dark matter.

24. Conclusions • High Precision cosmology allowed us to test not only value of particular cosmological parameters but also prediction of particular models. • Different cosmological models give fits of „formally” similar quality but fortunately usually gives different predictions for cosmological parameters (for example Wm,0) • Presently „the best model” is LCDM

28. Modele Kosmologiczne a gęstość materii pyłowej