[Paper Review] Two fundamental cosmological laws of the Local Universe

Yu. V. Baryshev|arXiv (Cornell University)|Oct 19, 2016

Cosmology and Gravitation Theories32 references3 citations

TL;DR

This paper identifies two empirical cosmological laws in the Local Universe: the linear Hubble-Humason-Sandage redshift-distance law (z ∝ R) and the density-radius power-law (Γ(r) ∝ r⁻ᵞ), both observed independently of theoretical models. The key contribution is the challenge these laws pose to the standard cosmological model, which assumes homogeneity as the basis for Hubble's law, yet the laws hold in strongly inhomogeneous, fractal-like structures at scales of 1–100 Mpc.

ABSTRACT

The Local Universe is the most detail studied part of the observable region of space with the radius R about 100 Mpc. There are two empirical fundamental cosmological laws directly established from observations in the Local Universe independently from cosmological theory: first, the Hubble-Humason-Sandage linear redshift-distance law and second, Carpenter- Karachentsev-deVaucouleurs density-radius power-law. Review of modern state of these empirical laws and their cosmological significance is given. Possible theoretical interpretations of the surprising coexistence of both laws at the spatial scales from 1 Mpc to 100 Mpc are discussed. Comparison of the standard space-expansion explanation of the cosmological redshift with possible global gravitational redshift model is given

Motivation & Objective

• To establish and review two fundamental empirical cosmological laws observed in the Local Universe without relying on theoretical models.
• To investigate the cosmological significance of the coexistence of the linear redshift-distance law and the density-radius power-law in a region of 1–100 Mpc.
• To challenge the standard cosmological model's assumption that Hubble's law arises from large-scale homogeneity, by showing it holds in inhomogeneous, fractal-like structures.
• To explore theoretical interpretations of these laws, including space expansion versus global gravitational redshift models.
• To propose and evaluate direct observational tests for distinguishing between cosmological expansion and global gravitational redshift.

Proposed method

• Analysis of observational data from 869 galaxy distances in the Local Volume (1–100 Mpc) to verify the linear redshift-distance relation.
• Application of the complete correlation function Γ(r) to quantify galaxy clustering and derive the power-law density-radius relation Γ(r) ∝ r⁻ᵞ.
• Use of the Hubble-Humason-Sandage law (z = H_loc × R / c) to express cosmological redshift as an apparent radial velocity.
• Comparison of the space-expansion model with a global gravitational redshift model, both of which reproduce the same redshift-distance relation.
• Evaluation of proposed direct tests: Sandage’s z(t) test (dz/dt ∼ 1 cm s⁻¹/yr) and Kopeikin’s Δν/ν test (Δν/ν ≈ 4×10⁻¹⁵ for H₀ = 70 km s⁻¹/Mpc).
• Use of high-precision solar system tracking data and future missions like PHARAO to detect cosmological frequency drift from global expansion.

Experimental results

Research questions

• RQ1 Why does the linear redshift-distance law hold in the Local Universe despite the presence of strong inhomogeneities and fractal-like galaxy distributions?
• RQ2 What is the physical origin of the density-radius power-law Γ(r) ∝ r⁻ᵞ in the context of large-scale structure formation?
• RQ3 Can the cosmological redshift be explained by global gravitational redshift instead of space expansion, and how can this be distinguished observationally?
• RQ4 What direct observational tests can confirm or rule out the physical reality of space expansion at cosmological scales?
• RQ5 How do the empirical laws of the Local Universe challenge the foundational assumption of homogeneity in the standard cosmological model?

Key findings

• The Hubble-Humason-Sandage linear redshift-distance law (z = H_loc × R / c) is robustly confirmed for 156 Local Volume galaxies with H_loc = 72 ± 3 km s⁻¹/Mpc.
• The density-radius power-law Γ(r) ∝ r⁻ᵞ is observed in the Local Universe, with γ ≈ 1 for the VL2N sample from the 2MRS survey.
• The linear Hubble law holds at scales as small as 1–10 Mpc, where galaxy distribution is strongly inhomogeneous and fractal-like, contradicting the standard model’s reliance on homogeneity.
• The space-expansion and global gravitational redshift models produce identical redshift-distance relations, making them observationally degenerate without direct distance-time measurements.
• A crucial test of space expansion is proposed: measuring the time derivative of redshift (dz/dt ∼ 1 cm s⁻¹/yr) using future Extremely Large Telescope (ELT) observations.
• The frequency drift Δν/ν ≈ 4×10⁻¹⁵ over 10³ seconds in the solar system could detect cosmological expansion via atomic clock experiments like PHARAO, with zero drift expected in a non-expanding universe.