[Paper Review] Relative Standard of Measurement and Supernova Data

D. Blaschke, Danilo Behnke+2 more|arXiv (Cornell University)|Jan 31, 2003

Cosmology and Gravitation Theories4 references3 citations

TL;DR

This paper proposes a conformal cosmology where the universe is nonexpanding, and the observed cosmic redshift arises from time-varying particle masses rather than metric expansion. Using a relative standard of measurement based on the scale factor $ a(t) $, it shows that supernova luminosity-distance data and primordial nucleosynthesis are equally well described by a homogeneous, massless scalar field (scalar quintessence) with a rigid equation of state, eliminating the need for dark energy or a cosmological constant.

ABSTRACT

We show that in the units of the relative Paris meter both the latest data on the Supernova luminosity-distance -- redshift relation and primordial nucleosynthesis are described by the dynamics of a homogeneous, massless scalar field (Scalar Quintessence) in a nonexpanding universe.

Motivation & Objective

• To challenge the standard cosmological model's assumption of metric expansion by proposing a conformal cosmology with a nonexpanding universe.
• To resolve the cosmological constant problem by replacing dark energy with a dynamic scalar field.
• To show that supernova data and primordial nucleosynthesis are consistent with a universe where all masses scale with time via $ a(t) $.
• To explain the observed time-dilation in Type Ia supernova light curves as a consequence of mass-dependent decay rates.

Proposed method

• Adopt a relative Paris meter defined as $ 1\,\text{m} \times a(t) $, making all measurable lengths and masses scale with the cosmic scale factor.
• Use conformal time $ \eta $ with $ d\eta = dt/a(t) $, leading to a Minkowski-like line element $ ds^2/a^2 = d\eta^2 - dx^i dx^i $, which is nonexpanding.
• Introduce a homogeneous, massless scalar field with action $ S_{\rm SQ} = \int d^4x \sqrt{-g} \, \varphi_0^2 \partial_\mu Q \partial^\mu Q $, termed scalar quintessence.
• Derive a rigid equation of state $ (z+1)^{-1}(\eta) = \sqrt{1 + 2H_0(\eta - \eta_0)} $ that fits the luminosity-redshift relation of Type Ia supernovae.
• Reinterpret redshift as a consequence of time-varying particle masses, including the Planck mass and W-boson mass, rather than Doppler or metric expansion.
• Show that Boltzmann factors in CMB and nucleosynthesis are invariant under the mass-scale transformation, preserving observed abundances and temperature evolution.

Experimental results

Research questions

• RQ1 Can the luminosity-distance relation of high-redshift Type Ia supernovae be explained without assuming metric expansion or a cosmological constant?
• RQ2 Does a nonexpanding universe with time-varying particle masses reproduce the observed redshift dependence of the cosmic microwave background temperature?
• RQ3 Can the time-dilation of supernova light curves be explained by the redshift dependence of decay rates due to mass scaling?
• RQ4 Is primordial nucleosynthesis consistent with a conformal cosmology where particle masses evolve with $ a(t) $?

Key findings

• The luminosity-redshift data from 42 high-redshift supernovae and SN1997ff are well described by a conformal cosmology with a rigid equation of state $ (z+1)^{-1}(\eta) = \sqrt{1 + 2H_0(\eta - \eta_0)} $.
• The same data are fitted equally well by scalar quintessence, a homogeneous, massless scalar field with purely kinetic energy, in a nonexpanding universe.
• The observed redshift independence of the CMB temperature is reproduced not as a constant temperature, but as a result of invariant Boltzmann factors under mass scaling.
• The time-dilation of supernova light curves arises naturally from the redshift dependence of decay times, which scale inversely with the W-boson mass, itself proportional to $ a(t) $.
• Primordial nucleosynthesis abundances are preserved because the ratio $ m(z)/T(0) $ is invariant under the conformal transformation, matching observed values.