Bright High z SnIa: A Challenge for LCDM?

📝 Abstract

It has recently been pointed out by Kowalski et. al. (arxiv:0804.4142) that there is `an unexpected brightness of the SnIa data at z>1’. We quantify this statement by constructing a new statistic which is applicable directly on the Type Ia Supernova (SnIa) distance moduli. This statistic is designed to pick up systematic brightness trends of SnIa datapoints with respect to a best fit cosmological model at high redshifts. It is based on binning the normalized differences between the SnIa distance moduli and the corresponding best fit values in the context of a specific cosmological model (eg LCDM). We then focus on the highest redshift bin and extend its size towards lower redshifts until the Binned Normalized Difference (BND) changes sign (crosses 0) at a redshift z_c (bin size N_c). The bin size N_c of this crossing (the statistical variable) is then compared with the corresponding crossing bin size N_{mc} for Monte Carlo data realizations based on the best fit model. We find that the crossing bin size N_c obtained from the Union08 and Gold06 data with respect to the best fit LCDM model is anomalously large compared to N_{mc} of the corresponding Monte Carlo datasets obtained from the best fit LCDM in each case. In particular, only 2.2% of the Monte Carlo LCDM datasets are consistent with the Gold06 value of N_c while the corresponding probability for the Union08 value of N_c is 5.3%. Thus, according to this statistic, the probability that the high redshift brightness bias of the Union08 and Gold06 datasets is realized in the context of a (w_0,w_1)=(-1,0) model (LCDM cosmology) is less than 6%. The corresponding realization probability in the context of a (w_0,w_1)=(-1.4,2) model is more than 30% for both the Union08 and the Gold06 datasets.

💡 Analysis

It has recently been pointed out by Kowalski et. al. (arxiv:0804.4142) that there is `an unexpected brightness of the SnIa data at z>1’. We quantify this statement by constructing a new statistic which is applicable directly on the Type Ia Supernova (SnIa) distance moduli. This statistic is designed to pick up systematic brightness trends of SnIa datapoints with respect to a best fit cosmological model at high redshifts. It is based on binning the normalized differences between the SnIa distance moduli and the corresponding best fit values in the context of a specific cosmological model (eg LCDM). We then focus on the highest redshift bin and extend its size towards lower redshifts until the Binned Normalized Difference (BND) changes sign (crosses 0) at a redshift z_c (bin size N_c). The bin size N_c of this crossing (the statistical variable) is then compared with the corresponding crossing bin size N_{mc} for Monte Carlo data realizations based on the best fit model. We find that the crossing bin size N_c obtained from the Union08 and Gold06 data with respect to the best fit LCDM model is anomalously large compared to N_{mc} of the corresponding Monte Carlo datasets obtained from the best fit LCDM in each case. In particular, only 2.2% of the Monte Carlo LCDM datasets are consistent with the Gold06 value of N_c while the corresponding probability for the Union08 value of N_c is 5.3%. Thus, according to this statistic, the probability that the high redshift brightness bias of the Union08 and Gold06 datasets is realized in the context of a (w_0,w_1)=(-1,0) model (LCDM cosmology) is less than 6%. The corresponding realization probability in the context of a (w_0,w_1)=(-1.4,2) model is more than 30% for both the Union08 and the Gold06 datasets.

📄 Content

arXiv:0811.2802v2 [astro-ph] 1 Jun 2009 Bright High z SnIa: A Challenge for LCDM? L. Perivolaropoulosa and A. Shafieloob,c aDepartment of Physics, University of Ioannina, Greece bDepartment of Physics, University of Oxford, 1 Keble Road, Oxford, OX1 3NP, UK cBIPAC, University of Oxford, Denys Wilkinson Building, 1 Keble Road, Oxford OX1 3RH, UK (Dated: November 3, 2018) It has recently been pointed out by Kowalski et. al. (arXiv:0804.4142) that there is ‘an unexpected brightness of the SnIa data at z > 1’. We quantify this statement by constructing a new statistic which is applicable directly on the Type Ia Supernova (SnIa) distance moduli. This statistic is designed to pick up systematic brightness trends of SnIa datapoints with respect to a best fit cosmological model at high redshifts. It is based on binning the normalized differences between the SnIa distance moduli and the corresponding best fit values in the context of a specific cosmological model (eg ΛCDM). These differences are normalized by the standard errors of the observed distance moduli. We then focus on the highest redshift bin and extend its size towards lower redshifts until the Binned Normalized Difference (BND) changes sign (crosses 0) at a redshift zc (bin size Nc). The bin size Nc of this crossing (the statistical variable) is then compared with the corresponding crossing bin size Nmc for Monte Carlo data realizations based on the best fit model. We find that the crossing bin size Nc obtained from the Union08 and Gold06 data with respect to the best fit ΛCDM model is anomalously large compared to Nmc of the corresponding Monte Carlo datasets obtained from the best fit ΛCDM in each case. In particular, only 2.2% of the Monte Carlo ΛCDM datasets are consistent with the Gold06 value of Nc while the corresponding probability for the Union08 value of Nc is 5.3%. Thus, according to this statistic, the probability that the high redshift brightness bias of the Union08 and Gold06 datasets is realized in the context of a (w0, w1) = (−1, 0) model (ΛCDM cosmology) is less than 6%. The corresponding realization probability in the context of a (w0, w1) = (−1.4, 2) model is more than 30% for both the Union08 and the Gold06 datasets indicating a much better consistency for this model with respect to the BND statistic. PACS numbers: 98.80.Es,98.65.Dx,98.62.Sb 1. INTRODUCTION The discovery of the accelerating expansion of the uni- verse about a decade ago [1] has led to an intensive pur- sue of the physical origin of this acceleration. This pursue has been taking place in both the observational and the theoretical aspects of the problem. On the theoretical aspect, there has been significant progress made by pointing out several models that may produce the observed accelerating expansion and clarify- ing the limits of their predictions with respect to the ob- served expansion rate as a function of redshift. For exam- ple it has been pointed out that theoretical models based on modifications of general relativity [2], interacting dark energy [3] or higher dimensional brane world models [4] can easily predict an effective dark energy equation of state w(z) that crosses the Phantom Divide Line (PDL) w = −1. On the other hand, models based on general relativity that are free from instabilities[5] and conserve energy and momentum of dark energy have a w(z) con- fined in the range w(z) ≥−1. On the observational aspect there has been significant improvement of the constraints on the recent Hubble ex- pansion history H(z) coming from a diverse set of cos- mological observations. Such observations include direct geometrical probes (standard candles like SnIa [1, 6], gamma ray bursts [7] and standard rulers like the CMB sound horizon[8, 9]) and dynamical probes (growth rate of cosmological perturbations [10] probed by the redshift distortion factor or by weak lensing [11]). All these observational probes are converging towards confirming the accelerating expansion of the universe as- suming the homogeneity of the universe. They have ruled out at several σ a flat matter dominated universe (assum- ing a power-law form of the primordial spectrum) and they have produced excellent fits for the simplest cosmo- logical model predicting accelerating cosmic expansion. This model is based on the presence of the cosmological constant Λ and Cold Dark Matter (ΛCDM )[12]. In view of the significant present and forecasted im- provement of relevant cosmological observations there are specific theoretical questions that are becoming particu- larly interesting. For example the question ‘Is general relativity the correct theory on cosmological scales?’ is particularly interesting but perhaps premature for the current status of observational data which still allow a considerable range of w(z) forms around the simplest al- lowed value w = −1 corresponding to ΛCDM . A more realistic but equally important question for the current status of observational data is the following: ‘Is ΛCDM the correct model of

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