We use type Ia supernovae (SN Ia) data in combination with recent baryonic acoustic oscillations (BAO) and cosmic microwave background (CMB) observations to constrain a kink-like parametrization of the deceleration parameter (q). This q-parametrization can be written in terms of the initial (q i ) and present (q 0 ) values of the deceleration parameter, the redshift of the cosmic transition from deceleration to acceleration (z t ) and the redshift width of such transition (τ ). By assuming a flat space geometry, q i = 1/2 and adopting a likelihood approach to deal with the SN Ia data we obtain, at the 68% confidence level (C.L.), that: z t = 0.56 +0.13 −0.10 , τ = 0.47 +0.16 −0.20 and q 0 = −0.31 +0.11 −0.11 when we combine BAO/CMB observations with SN Ia data processed with the MLCS2k2 light-curve fitter. When in this combination we use the SALT2 fitter we get instead, at the same C.L.: z t = 0.64 +0.13 −0.07 , τ = 0.36 +0.11 −0.17 and q 0 = −0.53 +0.17 −0.13 . Our results indicate, with a quite general and model independent approach, that MLCS2k2 favors Dvali-Gabadadze-Porrati-like cosmological models, while SALT2 favors ΛCDM-like ones. Progress in determining the transition redshift and/or the present value of the deceleration parameter depends crucially on solving the issue of the difference obtained when using these two light-curve fitters.

We compare the traditional χ 2 and complete-likelihood approaches for determining parameter constraints from type Ia supernovae (SNe Ia) when the magnitude dispersion is to be estimated as well. The dataset we used was sample combination "e" from Kessler (2009, ApJS, 185, 32), comprising the first-year SDSS-II Supernova Survey together with ESSENCE, SNLS, HST, and a compilation of nearby SNe Ia. We considered cosmological constant + cold dark matter (ΛCDM) and spatially flat, constant w dark energy + cold dark matter (FwCDM) cosmological models and show that, for current data, there is a small difference in the best-fit values and a difference of about 30% in confidence contour areas if the MLCS2k2 light-curve fitter is adopted. For the SALT2 light-curve fitter the differences in area are less significant ( < ∼ 13%). In both cases the likelihood approach gives more restrictive constraints. We argue for using the complete likelihood instead of the χ 2 approach when dealing with parameters in the expression for the variance.

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We performed computing calculations of SNe Ia (type Ia supernova) in observational cosmology using CPU (Central Processing Unit) and GPU/CUDA (Graphics Processing Unit/Compute Unified Device Architecture) in 7 different programming methods : CUDA called from C/C++, Python with CUDA (Py-CUDA), Wolfram Mathematica with CUDA, C/C++, pure Python, Python with NumPy and Wolfram Mathematica calculated in CPU. With CUDA, we obtained speedup of approximately 3 to 7 hundred times with respect to CPU when performing calculations of the SNe Ia distance modulus (µ 0 ). So we confirmed that CUDA (Compute Unified Device Architecture) is an excellent choice for GPU High Performance Computing (HPC) architecture applied to observational cosmology calculations.

The type Ia supernovae observational data is one of the most important in observational cosmology nowadays. Here we present the first public version of BETOCS (BayEsian Tools for Observational Cosmology using SNe Ia), which is a powerful and high productivity tool aimed to help the theoretical physicist community investigate cosmological models using type Ia supernovae (SNe Ia) observational data. BETOCS is applied to the generalized Chaplygin gas model (GCGM), traditional Chaplygin gas model (CGM) and ΛCDM, ranging from 5 to 3 free parameters, respectively. The "gold sample" of 157 supernovae data is used. It is shown that the Chaplygin gas scenario is viable (in most cases the ΛCDM is disfavoured) and the quartessence scenario (that unifies the description for dark matter and dark energy) is favoured. The Hubble parameter (H 0) is important and should not be fixed and it can be estimated or marginalized with or without the Hubble Space Telescope prior.