Original image by NASA, ESA, H. Teplitz and M. Rafelski (IPAC/Caltech), A. Koekemoer (STScI), R. Windhorst (Arizona State University), and Z. Levay (STScI); cropped by L. Marmet.

## Cosmology CalculatorDirect measurements of the Hubble constant disagree with predictions made by the Standard Model of Cosmology (ΛCDM) based on measurements of the cosmic microwave background radiation. The Hubble tension is forcing cosmologists to question every aspect of the ΛCDM model. This webpage provides two Cosmology Calculators: one for the ΛCDM model, the other for a Static Tired-Light (STL) model with the Spectral Transfer Redshift (STz). Enter values and the results will appear immediately. |
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## ΛCDM Cosmology Based on the calculator written by Ned
Wright (2006, PASP, 118, 1711): The size evolution of star-forming galaxies follows the power law: _{e} = r_{0} (1 + z)^{nS} kpc.
The Tolman test for expansion predicts a surface brightness <SB> that decreases as (1 + z) ^{4-nL} mag,
where n _{evol} = 2.5 log (1 +z)^{nL} mag.
These two functions are included below so that the calculated distances correspond to raw observational data. The calculation includes three massless neutrino species and a correction for annihilations of particles not present now (e.g. e km/s/Mpc Open: uses Ω _{Λ} = 0 giving an open Universe [if you
entered Ω_{M} < 1].Flat: uses Ω _{Λ} = 1 - Ω_{M}
giving a flat Universe.General: uses the Ω _{Λ} that you entered.used for sample selection introduces a bias, c.f. 'Fundamental Plane' scaling relations. ## ΛCDM Cosmology*** JavaScript not enabled or script file missing *** Source for default parameters H _{0}, Ω_{M} and Ω_{Λ}Source for default parameter n _{S}Source for default parameter n _{L} |
## STL Cosmology An equivalent to the Mattig formula is obtained in a Static Universe Cosmology from the differential equation -d(hν) = H(hν) dD/c expressing _{A} = (c/H_{0}) ln (1 + z).
Since the universe is flat and static, the radial distance is equal to the angular distance D _{L} = (1 + z)^{(1+y)/2} D_{A}.
For the transient signal of a Type Ia supernova, STz Tired-Light modulates the observed spectrum with the rest-frame light-curve of duration ∝ λ An extended object at temperature T is seen as a blackbody at the Wien temperature T _{0}(λ_{0}, T_{W}) = (1 + z)^{3} 2hc^{2} / [λ_{0}^{5} (e^{hc/(λ0 k TW)} - 1)].
/Gpc Flat Universe ## STL Cosmology*** JavaScript not enabled or script file missing *** Source for default parameter H _{z} ≡ H_{0}/cSource for default parameter y all parameters to default values. the value of H _{0} that gives raw d_{A}(ΛCDM) = d_{A}(STL). |
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## DiscussionIt is difficult to compare the two models to a high accuracy. Astrophysical data are currently analyzed with the assumptions of ΛCDM cosmology and corrected for various effects in powers of 1 + z (e.g. luminous flux, time dilation, galactic evolution, Hubble residuals, deceleration parameter, etc.) Both calculators give observed quantities which, for ΛCDM, are corrected to include the large effects of galactic evolution. However other effects are difficult to disentangle from an analysis based on the ΛCDM model. Interpreting observations with the ΛCDM model one concludes: " Updated 2021-10-20 © 2020--2021 Louis Marmet |