Sparse formulae for the distance modulus in cosmology

Abstract

We review the distance modulus in twelve different cosmologies: the $\Lambda$CDM model, the wCDM model, the Cardassian model, the flat case, the $\varphi$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.

arXiv comment24 pages and 11 figures. arXiv admin note: text overlap with arXiv:1602.06418

References in corpus (38)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• The Complete Light-curve Sample of Spectroscopically Confirmed Type Ia Supernovae from Pan-STARRS1 and Cosmological Constraints from The Combined Pantheon Sample
• CODATA Recommended Values of the Fundamental Physical Constants: 2010
• Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond LambdaCDM
• Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS supernova samples
• The Hubble Space Telescope Cluster Supernova Survey: V. Improving the Dark Energy Constraints Above z>1 and Building an Early-Type-Hosted Supernova Sample
• CDM Models with a Smooth Component
• How many cosmological parameters?
• Cardassian Expansion: a Model in which the Universe is Flat, Matter Dominated, and Accelerating
• Interferometric detection of gravitational waves: the definitive test for General Relativity
• Detection of lensing substructure using ALMA observations of the dusty galaxy SDP.81
• Cosmological constraints on f(R) gravity theories within the Palatini approach
• Measuring Dark Energy Properties with Photometrically Classified Pan-STARRS Supernovae. II. Cosmological Parameters
• Observational Constraints on Cosmological Models with the Updated Long Gamma-Ray Bursts
• ALMA Long Baseline Observations of the Strongly Lensed Submillimeter Galaxy HATLAS J090311.6+003906 at z=3.042
• The Megamaser Cosmology Project. V. An Angular Diameter Distance to NGC 6264 at 140 Mpc
• The Megamaser Cosmology Project. II. The Angular-Diameter Distance to UGC 3789
• Dark energy equation of state parameter and its variation at low redshifts
• Constraints on reconstructed dark energy model from SN Ia and BAO/CMB observations
• ALMA imaging of SDP.81 - II. A pixelated reconstruction of the CO emission lines
• Generalized Cardassian Expansion: Models in Which the Universe is Flat, Matter Dominated, and Accelerating
• High-resolution ALMA Observations of SDP.81. II. Molecular Clump Properties of a Lensed Submillimeter Galaxy at z=3.042
• The Innermost Mass Distribution of the Gravitational Lens SDP.81 from ALMA Observations
• Testing logarithmic corrections on $R^2$-exponential gravity by observational data
• Pantheon update on a model-independent analysis of cosmological supernova data
• Non-parametric reconstruction of dark energy and cosmic expansion from the Pantheon compilation of type Ia supernovae
• Cosmology under Milne's shadow
• Distance-redshift relation in plane symmetric universes
• The Maximum Angular-Diameter Distance in Cosmology
• Analytical expressions and numerical evaluation of the luminosity distance in a flat cosmology
• On the number of galaxies at high redshift
• SNe Ia Redshift in a Non-Adiabatic Universe
• The observational constraints on the flat $\varphi$CDM models
• Utilizing the Updated Gamma-Ray Bursts and Type Ia Supernovae to Constrain the Cardassian Expansion Model and Dark Energy
• A new analytical solution for the distance modulus in flat cosmology
• The distance modulus in dark energy and Cardassian cosmologies via the hypergeometric function
• Cosmic Time Transformations in Cosmological Relativity
• The Ring Produced by an Extra-Galactic Superbubble in Flat Cosmology

Cited by in corpus (1)

• Cosmic-time quantum mechanics and the passage-of-time problem