Accelerating Universe and Pioneer anomaly as manifestation of conformal time inhomogeneity

TL;DR

This paper proposes a conformal time inhomogeneity framework to explain cosmological expansion and local anomalies like the Pioneer anomaly, deriving new formulas that match experimental data and suggest a unified interpretation of cosmic acceleration and local frequency shifts.

Contribution

It introduces a conformal transformation approach to cosmological and local phenomena, deriving explicit formulas linking time deformation, the Hubble law, and anomalies like Pioneer.

Findings

Reproduces Pioneer anomaly experimental data.

Derives a generalized Hubble law consistent with observed cosmic acceleration.

Predicts a uniform blue-shifted frequency drift in location experiments.

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 (RF) to an uniformly accelerated RF is given. The explicit form of the conformal deformation of time 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 well known relativistic formula defining the relative velocity of the mutually moving apart source and receiver of the signal, the explicit analytic expression for the Hubble law is obtained. The connection between acceleration and the Hubble constant follows therefrom immediately. The expression for 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 uniformly changing blue-shifted frequency drift. Phenomenon of the Pioneer Anomaly (PA) is treated as the first of such a kind of effects discovered experimentally. The obtained formulae reproduce the PA experimental data. The expression generalizing the conventional Hubble law reproduces the experimentally observed phenomenon which in the frame of the conventional cosmological paradigm is treated as the transition from the decelerated expansion of the Universe to the accelerated one.