Can corrections to gravity at galactic distances be decisive to the problem of dark matter and dark energy?

TL;DR

This paper proposes that modifications to gravity involving higher derivatives, specifically using Ostrogradsky formalism, can explain galactic phenomena without dark matter or dark energy, potentially leading to a Steady State Universe model.

Contribution

It introduces a novel approach applying Ostrogradsky formalism to gravity, eliminating the need for dark matter and dark energy in explaining galactic dynamics.

Findings

Higher derivatives can account for galactic rotation curves.

Dark matter and dark energy may be unnecessary under this formalism.

Potential support for a Steady State Universe model.

Abstract

Are Dark Matter the result of uncalculated addition derivatives? The need to introduce dark matter dark becomes unnecessary if we consider that, the phenomenon of dark matter is a result of not computing the additional derivatives of the equation of motion. For this purpose, we use higher derivatives in the form of non-local variables, known as the Ostrogradsky formalism. As a mathematician, Ostrogradsky considered the dependence of the Lagrange function on acceleration and its higher derivatives with respect to time. This is the case that fully correspond with the real frame of reference, and that can be both inertial and non-inertial frames. The problem of dark matter and dark energy presented starting from basic observations to explain the different results in theory and experiment. The study of galactic motion, especially the rotation curves, showed that a large amount of dark matter can be found mainly in galactic halos. The search for dark matter and dark energy has not confirmed with the experimental discovery of it, so we use Ostrogradsky formalities to explain the effects described above, so that the need to introduce dark matter and dark energy disappears. We hope that this description can lead to a Steady State Model (SSM) of the Universe.