Understanding the Universe Without Dark Matter and Without the Need to Modify Gravity: Is the Universe an Anamorphic Structure?

We envision a minimalist way to explain a number of astronomical facts associated with the unsolved missing mass problem by considering a new phenomenological paradigm. In this model, no new exotic particles need to be added, and the gravity is not modified; it is the perception that we have of a purely Newtonian (or purely Einsteinian) Universe, dubbed the Newton basis or Einstein basis (actually “viewed through a pinhole” which is “optically” distorted in some manner by a so-called magnifying effect). The $\kappa$ model is not a theory but rather an exploratory technique that assumes that the sizes of the astronomical objects (galaxies and galaxy clusters or fluctuations in the CMB) are not commensurable with respect to our usual standard measurement. To address this problem, we propose a rescaling of the lengths when these are larger than some critical values, say >100 pc - 1 kpc for the galaxies and ∼1 Mpc for the galaxy clusters. At the scale of the solar system or of a binary star system, the $\kappa$ effect is not suspected, and the undistorted Newtonian metric fully prevails. A key point of an ontological nature rising from the $\kappa$ model is the distinction which is made between the distances depending on how they are obtained: (1) distances deduced from luminosity measurements (i.e. the real distances as potentially measured in the Newton basis, which are currently used in the standard cosmological model) and (2) even though it is not technically possible to deduce them, the distances which would be deduced by trigonometry. Those “trigonometric” distances are, in our model, altered by the kappa effect, except in the solar environment where they are obviously accurate. In outer galaxies, the determination of distances (by parallax measurement) cannot be carried out, and it is difficult to validate or falsify the kappa model with this method. On the other hand, it is not the same within the Milky Way, for which we have valuable trigonometric data (from the Gaia satellite). Interestingly, it turns out that for this particular object, there is strong tension between the results of different works regarding the rotation curve of the galaxy. At the present time, when the dark matter concept seems to be more and more illusive, it is important to explore new ideas, even the seemingly incredibly odd ones, with an open mind. The approach taken here is, however, different from that adopted in previous papers. The analysis is first carried out in a space called the Newton basis with pure Newtonian gravity (the gravity is not modified) and in the absence of dark matter-type exotic particles. Then, the results (velocity fields) are transported into the leaves of a bundle (observer space) using a universal transformation associated with the average mass density expressed in the Newton basis. This approach will make it much easier to deal with situations where matter is not distributed centrosymmetrically around a center of maximum density. As examples, we can cite the interaction of two galaxies or the case of the collision between two galaxy clusters in the bullet cluster. These few examples are difficult to treat directly in the bundle, especially since we would include time-based monitoring (with an evolving $\kappa$ effect in the bundle). We will return to these questions later, as well as the concept of average mass density at a point. The relationship between this density and the coefficient $\kappa$ must also be precisely defined.