Perturbations of Dark Matter Gravity

TL;DR

This paper applies Nash's perturbative geometry to analyze dark matter's gravitational effects, explaining early universe perturbations and structure formation within a higher-dimensional framework consistent with cosmological observations.

Contribution

It introduces a novel geometric approach using Nash's theory to study dark matter gravity independently, linking extrinsic curvature to observed cosmological phenomena.

Findings

Dark matter perturbations relate to extrinsic curvature in higher dimensions.

The model aligns with WMAP power spectrum and universe acceleration data.

Local structure formation may be explained by similar geometric mechanisms.

Abstract

Until recently the study of the gravitational field of dark matter was primarily concerned with its local effects on the motion of stars in galaxies and galaxy clusters. On the other hand, the WMAP experiment has shown that the gravitational field produced by dark matter amplifies the higher acoustic modes of the CMBR power spectrum, more intensely than the gravitational field of baryons. Such a wide range of experimental evidences from cosmology to local gravity suggests the necessity of a comprehensive analysis of the dark matter gravitational field per se, regardless of any other attributes that dark matter may eventually possess. In this paper we introduce and apply Nash's theory of perturbative geometry to the study of the dark matter gravitational field alone, in a higher-dimensional framework. It is shown that the dark matter gravitational perturbations in the early universe can be explained by the extrinsic curvature of the standard cosmology. Together with the estimated presence of massive neutrinos, such geometric perturbation is compatible not only with the observed power spectrum in the WMAP experiment but also with the most recent data on the accelerated expansion of the universe. It is possible that the same structure formation exists locally, such as in the cases of young galaxies or in cluster collisions. In most other cases it seems to have ceased when the extrinsic curvature becomes negligible, leading to Einstein's equations in four dimensions. The slow motion of stars in galaxies and the motion of plasma substructures in nearly colliding clusters are calculated with the geodesic equation for a slowly moving object in a gravitational field of arbitrary strength.