Hubble law, Accelerating Universe and Pioneer Anomaly as effects of the space-time conformal geometry

TL;DR

This paper proposes that the Hubble law, accelerating universe, and Pioneer Anomaly can be explained through space-time conformal geometry, linking cosmological expansion with local effects via conformal transformations.

Contribution

It introduces a conformal geometry framework that unifies cosmological expansion and local anomalies, providing explicit formulas connecting acceleration, redshift, and observed frequency drifts.

Findings

Reproduces the Hubble law with a connection between acceleration and Hubble constant.

Explains the Pioneer Anomaly as a consequence of conformal time deformation.

Predicts a universal blue-shifted frequency drift consistent with observations.

Abstract

The description of the cosmological expansion and its possible local manifestations via treating the proper conformal transformations as a coordinate transformation from a comoving Lorentz reference frame to an uniformly accelerated one is given. The explicit form of the conformal time inhomogeneity is established. The expression defining the location cosmological distance in the form of simple function on the red shift is obtained. By coupling it with the relativistic formula for the longitudinal Doppler effect, the explicit expression for the Hubble law is obtained, which gives rise to the connection between acceleration and the Hubble constant. The expression generalizing the conventional Hubble law reproduces kinematically the experimentally observed phenomenon treated conventionally as a Dark Energy manifestation. The conformal time deformation in the small time limit leads to the quadratic time nonlinearity. Being applied to describe the location-type experiments, this predicts the existence of the universal uniformly changing blue-shifted frequency drift. The obtained formulae reproduce the Pioneer Anomaly experimental data.