The CMB Luminosity Distance and Cosmological Redshifts

We will outline the relationship between luminosity distance and cosmological redshifts, demonstrating that it is consistent with a new cosmological model recently proposed by Haug and Tatum [1] , which appears to resolve the Hubble tension within the Rh=ctcosmology.

Legendre-Jacobi’s Elliptic Integrals Shed Light on the Luminosity Distance in Cosmology

This article concerns the integral related to the transverse comoving distance and, in turn, to the luminosity distance both in the standard non-flat and flat cosmology. The purpose is to determine a straightforward mathematical formulation for the luminosity distance as function of the transverse comoving distance for all cosmology cases with a non-zero cosmological constant by adopting a different mindset. The applied method deals with incomplete elliptical integrals of the first kind associated with the polynomial roots admitted in the comoving distance integral according to the scientific literature. The outcome shows that the luminosity distance can be obtained by the combination of an analytical solution followed by a numerical integration in order to account for the redshift. This solution is solely compared to the current Gaussian quadrature method used as basic recognized algorithm in standard cosmology.

The Theory of Gravitons in the Expansion of the Universe

The theory that gravitons lose energy thru gravitational redshift while traveling in a gravitational field is applied to the universe. It is proposed that a co-moving volume element is required for the luminosity distance relation because the gravitational field acts simultaneously in three dimensions rather than just along a geodesic curve. With only a relatively small baryonic mass density the curve fit of the novel luminosity distance relation to Type Ia supernovae distance data is of the same quality as for the standard Lambda Cold Dark Matter model.

The Origin of Cosmic Structures Part 5— Resolution of the Hubble Tension Problem

The two principal contributors to the Hubble tension problem are the predictions of the baryonic acoustic oscillation model and the H0 parameter fit of the “Tip of the Red Giant Branch” collaboration. In this paper, we show that the former is neither necessary nor possible and that the latter yields a value in agreement with the supernovae results when adjustments are made for errors in the peculiar velocity model used to isolate the recession velocities of galaxies. We also make comparisons between the predictions of our new model of cosmology and the curve fits of the standard model. For values of redshift ≤ 1 we find that, with a Hubble constant of H0 = 73, the two agree almost exactly. We resolve the Hubble constant problem and validate the new model predictions for small redshifts.

Hubble Expansion as an Einstein Curvature

Extending the spacetime manifold of general relativity (GR) to incorporate the Hubble expansion of space as a specific curvature, generates a modified solution with three additional non-zero Christoffel symbols and a reformulated Ricci tensor and curvature. The observational consequences of this reformulation are compared with the ΛCDM model for luminosity distance using the extensive type 1a supernovae (SNe 1a) data with redshift corrected to the CMB, and for angular diameter distance using the recent baryonic acoustic oscillation (BAO) data. For the SNe 1a data, the modified GR and ΛCDM models differ by mag. over zcmb = 0.01 - 1.3, with overall weighted RMS errors of ±0.136μB mag for modified GR and ±0.151μB mag for ΛCDM respectively. The BAO measures span a range z = 0.106 - 2.36, with weighted RMS errors of ±0.034 Mpc with H0 = 67.6 ± 0.25 for the modified GR model, and ±0.085 Mpc with H0 = 70.0 ± 0.25 for the ΛCDM model. The derived GR metric for this new solution describes both the SNe 1a and the BAO observations with comparable accuracy to the w’ΛCDM model. By incorporating the Hubble expansion of space within general relativity as a specific curvature term, these observations may be described without requiring additional parameters for either dark matter or accelerating dark energy.

Determining H0 using a model-independent method

By using type Ia supernovae （SNIa） to provide the luminosity distance （LD） directly, which depends on the value of the Hubble constant H0 = 100h km·s^-1· Mpc^-1, and the angular diameter distance from galaxy clusters or baryon acoustic oscillations （BAOs） to give the derived LD according to the distance duality relation, we propose a model-independent method to determine h from the fact that different observations should give the same LD at a given redshift. Combining the Sloan Digital Sky Survey II （SDSS-II） SNIa from the MLCS2k2 light curve fit and galaxy cluster data, we find that at the 1σ confidence level （CL）, h = 0.5867±0.0303 for the sample of the elliptical β model for galaxy clusters, and h = 0.6199± 0.0293 for that of the spherical β model. The former is smaller than the values from other observations, whereas the latter is consistent with the Planck result at the 2σ CL and agrees very well with the value reconstructed directly from the H（z） data. With the SDSS-II SNIa and BAO measurements, a tighter constraint, h = 0.6683 ± 0.0221, is obtained. For comparison, we also consider the Union 2.1 SNIa from the SALT2 light curve fitting. The results from the Union 2.1 SNIa are slightly larger than those from the SDSS-II SNIa, and the Union 2.1 SNIa ＋ BAOs give the tightest value. We find that the values from SNIa ＋ BAOs are quite consistent with those from the Planck and the BAOs, as well as the local measurement from Cepheids and very-low-redshift SNIa.