CHASING LAMBDA Aleksandra Kurek *, Marek Szyd � owski * ° * Astronomical Observatory, Jagiellonian University, Poland °Complex System Research Centre, Jagiellonian University, Poland
MODELS WITH DARK ENERGY (Weinberg 1989) (Caldwell 2002) (Chevallier & Polarski 2001) (Peebles & Ratra 1988) � (Rahvar & Movahed 2007) mean of the coefficient of the EQS in the log scale factor
MODELS WITH MODIFIED THEORY OF GRAVITY (Dvali et al. 2000) (Singh & Vandersloot 2005) (Szydlowski et al. 2006) ; (Freese & Lewis 2002) (Shtanov 2000)
BAYESIAN FRAMEWORK OF MODEL SELECTION
BAYESIAN FRAMEWORK OF MODEL SELECTION vector of model likelihood of the model prior probability for model parameters parameters approximation to -2 ln E number maximum number of of data points likelihood model assumptions parameters 1. iid 2. 1.prior for model parameters � 0 in the neighborhood of the maximum likelihood 2. prior is bound in the whole parameter space 3. prior for model parameters � 0 in the 3.sample size large with respect to the number maximum likelihood of model parameters 4.sample size large with respect to the number of model parameters Cavanough & Neath 1999 Schwarz 1978
BAYESIAN FRAMEWORK OF MODEL SELECTION POSTERIOR ODDS BAYES FACTOR - B 12 evidence in favor model 1 2 ln B 12 not worth than a bare mention <0,2) <2,6) positive <6,10) strong >10 very strong (Kass & Raftery 1995)
APPLICATION TO COSMOLOGICAL MODELS COMPARISON (Riess et al. 2007; Wood-Vasey et al. 2007; Davis et al. 2007) SN R (Spergel et al. 2006; Wang & Mukherjee 2006)
APPLICATION TO COSMOLOGICAL MODELS COMPARISON A (Eisenstein et al. 2005) (differential ages of the passively evolving galaxies) H (Simon et al. 2005) L L sn L R L A L H N=192+1+1+9
POSTERIOR PROBABILITIES FOR MODELS WITH DARK ENERGY 0.84 0.02 0.06 0.04 0.04
POSTERIOR PROBABILITIES FOR MODELS WITH MODIFIED GRAVITY 0.07 0.03 0.13 0.74 0.03
POSTERIOR PROBABILITIES FOR ALL MODELS 0.74 0.02 0.05 0.04 0.03 0.01 0.005 0.01 0.09 0.005
CONCLUSIONS In the light of data used in analysis: • � CDM model is the best one from the set of models with dark energy as well as the best one from the set of all models considered • Cardassian model is the best one from the set of models with modified gravity
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