Cosmology Calculators

Milky Way

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 Calculators Recent observations by the Webb Telescope (JWST) have shown a large number of galaxies at high redshifts. Contrary to expectations based on galaxy-formation models and the Standard Model of Cosmology (ΛCDM), these galaxies appear small and very bright. The Hubble constant derived from the expansion rate of the local universe is in tension with the value derived from the Cosmic Microwave Background Radiation (CMBR) released by the hot Big Bang. This "Hubble tension" is forcing cosmologists to question every aspect of the ΛCDM model. This webpage hosts two Cosmology Calculators: one for the ΛCDM model, the other for a Static Cosmology with Stimulated-Transfer redshift (SSTz). Enter values and the results will appear immediately.
	ΛCDM Cosmology Based on the calculator written by Ned Wright (2006, PASP, 118, 1711): http://www.astro.ucla.edu/~wright/CosmoCalc.html. The calculation includes three massless neutrino species and a correction for annihilations of particles not present now (e.g. e⁺/e^– ). The Hubble parameter is H²(z) = H₀² (Ω_M(1 + z)³ + Ω_k(1 + z)² + Ω_Λ). The size evolution of star-forming galaxies follows the power law r_e = r₀ (1 + z)^n_S . The Tolman test for expansion predicts a surface brightness <SB> that decreases as (1 + z)⁴. Luminosity evolution produces the Tolman signal Δ<SB>_evol = 2.5 log (1 + z)^4-n_L mag, where n_L describes the luminosity evolution of galaxies ΔM_evol = 2.5 log (1 + z)^n_L mag. These relations are used for the calculations of reported observations, without model-dependent evolution corrections.	SSTz Cosmology The distance-redshift relation in a Static Cosmology is obtained from the photon energy loss per unit distance d(hν)/dr = -H_z(n_e) hν, where H_z(n_e) is proportional to the number density of free electrons. Ponderomotive forces produce a Stimulated-Transfer redshift that is independent of wavelength, with the distance-redshift relation d_A = (1/H_z) ln(1 + z). In a flat and static cosmology, the radial distance r is equal to the angular distance d_A. The photon energy being proportional to (1 + z)^-1 implies a bolometric luminosity distance d_L = (1 + z)^1/2 d_A, with an additional (1 + z)^1/2 factor for the redshift of a transient event that conserves the number of photons (e.g. supernovae light-curves). A distant object at temperature T is seen by an observer as a blackbody at the Wien temperature T_w(z) = T/(1 + z), but with a spectral radiance enhanced by a factor of (1 + z)³, B_ν(ν, T_w, z) = (1 + z)³ (2hν³/c²) [e^hν/(kT_w) - 1]^-1.
	Parameters
	H₀ = km/s/Mpc Ω_M = Ω_Λ = 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. Galactic luminosity evolution exponent n_L = Galactic size evolution exponent n_S = used for sample selection introduces a bias, c.f. 'Fundamental Plane' scaling relations.	Hubble redshift H_z = /Gpc Euclidean (Light-matter interactions provide the pressure that counterbalances gravitation.)
	Redshift of the object: z =
	ΛCDM Cosmology * JavaScript not enabled or script file not updated * Source for default parameters H₀, Ω_M and Ω_Λ Source for default parameter n_S Source for default parameter n_L Source for default parameter n_B	SSTz Cosmology * JavaScript not enabled or script file not updated * Source for default parameter H_z all parameters to default values. which H₀ gives reported d_A(ΛCDM) = d_A(SSTz).
	Discussion It is difficult to compare the two models to a high accuracy. Astrophysical data are 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, dust reddening, etc.) Both calculators give observed quantities as interpreted in the framework of the models. Other effects are difficult to disentangle from an analysis based on the ΛCDM model. Interpreting observations with the ΛCDM model one concludes that: "compared to typical galaxies at later times, [young galaxies in the first billion years of cosmic time] show more extreme emission-line properties, higher star formation rates, lower masses, and smaller sizes." [Ref. (2017)] This is confirmed by new observations from the Webb Telescope. In a static cosmology, galaxies are farther away and their stars appear to have a blackbody spectrum with an excess brightness. Louis Marmet @redshiftdrift@astrodon.social on Last update: 2023-4-24 https://www.websiteout.net/counter.php © 2020--2023 Louis Marmet