Conformal Cosmology

An interesting GR based response to dark matter and dark energy that makes one subtle adjustment to the standard analysis. I'll have to give it a more careful read before saying more about it.

This paper is published in a peer reviewed journal (although not a high profile one) and the author has seven prior peer reviewed journal publications since 2016, one with Pavel Kroupa, a leading astronomer in the MOND literature, as a co-author. So, this is not the work of a crackpot non-astronomer.

The cosmic time dilation observed in Type Ia supernova light curves suggests that the passage of cosmic time varies throughout the evolution of the Universe. This observation implies that the rate of proper time is not constant, as assumed in the standard FLRW metric, but instead is time-dependent. Consequently, the commonly used FLRW metric should be replaced by a more general framework, known as the Conformal Cosmology (CC) metric, to properly account for cosmic time dilation. 

The CC metric incorporates both spatial expansion and time dilation during cosmic evolution. As a result, it is necessary to distinguish between comoving and proper (physical) time, similar to the distinction made between comoving and proper distances. In addition to successfully explaining cosmic time dilation, the CC metric offers several further advantages: (1) it preserves Lorentz invariance, (2) it maintains the form of Maxwell's equations as in Minkowski space-time, (3) it eliminates the need for dark matter and dark energy in the Friedmann equations, and (4) it successfully predicts the expansion and morphology of spiral galaxies in agreement with observations.

Vaclav Vavrycuk, "Time dilation observed in Type Ia supernova light curves and its cosmological consequences" arXiv:2506.19099 (June 23, 2025) (published in 13 Galaxies 55 (2025)).

Kroupa has also published a new cosmology paper (although I'm not optimistic about this MOND plus sterile neutrinos in clusters approach).

The νHDM is the only cosmological model based on Milgromian Dynamics (MOND) with available structure formation simulations. While MOND accounts for galaxies, with a priori predictions for spirals and ellipticals, a light sterile neutrino of 11 eV can assist in recovering scaling relations on the galaxy-cluster scales. In order to perform MONDian cosmological simulations in this theoretical approach, initial conditions derived from a fit to the angular power spectrum of Cosmic Microwave Background (CMB) fluctuations are required. 

In this work, we employ CosmoSIS to perform a Bayesian study of the νHDM model. Using the best-fit values of the posterior, the CMB power spectrum is reevaluated. The excess of power in the transfer function implies a distinct evolution scenario, which can be used further as an input for a set of hydro-dynamical calculations. The resulting values H0 ≈ 56 km/s/Mpc and Ωm0≈0.5 are far from agreement with respect to the best fit ones in the canonical Cold Dark Matter model, but may be significant in MONDian cosmology. The assumed Planck CMB initial conditions are only valid for the ΛCDM cosmology. This work constitutes a first step in an iterative procedure needed to disentangle the model dependence of the derived initial density and velocity fields.

Nick Samaras, Sebastian Grandis, Pavel Kroupa, "On the initial conditions of the νHDM cosmological model" arXiv:2506.19196 (June 23, 2025) (accepted for publication in MNRAS).