Gravitational orbits in the expanding Universe revisited

Abstract

Modified Newtonian equations for gravitational orbits in the expanding Universe indicate that local gravitationally bounded systems like galaxies and planetary systems are unaffected by the expansion of the Universe. This result is derived for the space expansion described by the standard FLRW metric. In this paper, the modified Newtonian equations are derived for the space expansion described by the conformal cosmology (CC) metric. In this metric, the comoving and proper times are different similarly as the comoving and proper distances. As shown by Vavryčuk (Front. Phys. 2022), this metric is advantageous, because it properly predicts the cosmic time dilation, and fits the Type Ia supernova luminosity observations with no need to introduce dark energy. Surprisingly, the solution of the equations for gravitational orbits based on the CC metric behaves quite differently than that based on the FLRW metric. In contrast to the common opinion that local systems resist the space expansion, they expand according to the Hubble flow in the CC metric. The evolution of the local systems with cosmic time is exemplified on numerical modelling of spiral galaxies. The size of the spiral galaxies grows consistently with observations and a typical spiral pattern is well reproduced. The theory predicts flat rotation curves without an assumption of dark matter surrounding the galaxy. The theory resolves challenges to the ΛCDM model such as the problem of faint satellite galaxies, baryonic Tully-Fisher relation or the radial acceleration relation. Furthermore, puzzles in the solar system are successfully explained such as the Faint young Sun paradox or the Moon’s and Titan’s orbit anomalies.