Matter scale field: cosmological redshift from evolving material standards

Abstract

Abstract We formulate Matter Scale Field (MSF) as a relativistic framework in which a homogeneous scalar field controls the evolution of the physical metric and material standards through one common scale. Cosmological redshift is interpreted as a comparison between propagated light and material standards whose scale has evolved between emission and detection. The action is written on a single physical metric $g_{\mu\nu}$: gravity, electromagnetism, the Standard Model, clocks and rulers, emission and detection are all defined on this metric. Consequently, the local Standard-Model description, local Lorentz invariance, universal matter coupling and the operational meaning of dimensionless constants are preserved. For a homogeneous solution, we write $g_{\mu\nu}(t)=b(\phi(t))^2g^0_{\mu\nu}$, where $b(\phi)>0$ is the scalar-controlled metric scale and $g^0_{\mu\nu}\equiv g_{\mu\nu}(t_0)$ is the physical metric at the present epoch, with $b(\phi(t_0))=1$. When the same action is expressed relative to the present value, source-free Maxwell propagation contains no explicit factor $b(\phi)$, whereas the coefficients setting the Higgs vacuum scale, generated particle masses and atomic transition frequencies acquire the corresponding powers of $b(\phi)$. Particle masses and atomic frequencies therefore scale with $b(\phi)$, while material lengths scale as $b(\phi)^{-1}$. A photon emitted at $t_{\rm em}$ has a present-calibrated frequency proportional to $b_{\rm em}$, which is conserved during source-free propagation. At observation, it is compared with the present material standard proportional to $b_0$, giving $1+z=b_0/b_{\rm em}$. Light-curve time dilation and the FLRW distance relations follow from the physical metric. We derive the homogeneous kinematics, physical-metric action and Standard-Model scale organization behind this mechanism. For a canonical scalar, a log-linear field-to-scale map yields a model-specific expansion and distance--redshift relation directly testable against $\Lambda$CDM and other background cosmologies. Cosmological perturbations, structure growth, gravitational lensing and CMB anisotropies are decisive tests of the framework.