Abstract
We review the distance modulus in twelve different cosmologies: the ΛCDM model, the wCDM model, the Cardassian model, the flat case, the ?CDM cosmology, the Einstein—De Sitter model, the modified Einstein—De Sitter model, the simple GR model, the flat expanding model, the Milne model, the plasma model and the modified tired light model. The above distance moduli are processed for three different compilations of supernovae and a supernovae + GRBs compilation: Union 2.1, JLA, the Pantheon and Union 2.1 + 59 GRBs. For each of the 48 analysed cases we report the relative cosmological parameters, the chi-square, the reduced chi-square, the AIC and the Q parameter. The angular distance as function of the redshift for five cosmologies is reported in the framework of the minimax approximation.
Highlights
At the moment of writing, the determination of the Hubble constant is oscillating between a low value as derived by the Planck collaboration [1], H0= (67.4 ± 0.5) km ⋅ s−1 ⋅ Mpc−1, and an high value, H=0 (74.03 ±1.42) km ⋅ s−1 ⋅ Mpc−1, as measured on 70 long-period Cepheids in the Large Magellanic Cloud (LMC) [2]
We review the distance modulus in twelve different cosmologies: the ΛCDM model, the wCDM model, the Cardassian model, the flat case, the φCDM cosmology, the Einstein—De Sitter model, the modified Einstein—De Sitter model, the simple GR model, the flat expanding model, the Milne model, the plasma model and the modified tired light model
−(m σi where N is the number of SNs, (m − M )i is the observed distance modulus evaluated at a redshift of zi, σi is the error in the observed distance modulus evaluated at zi, and
Summary
At the moment of writing, the determination of the Hubble constant is oscillating between a low value as derived by the Planck collaboration [1], H0= (67.4 ± 0.5) km ⋅ s−1 ⋅ Mpc−1 , and an high value, H=0 (74.03 ±1.42) km ⋅ s−1 ⋅ Mpc−1 , as measured on 70 long-period Cepheids in the Large Magellanic Cloud (LMC) [2]. The above difference is referred to as the Hubble constant tension [3] and takes the value of 4.4σ. It fixes an acceptable interval for the evaluation of H0. The availability of SN compilations allows testing old and new cosmological models.
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