The concept of smooth deformations of a Riemannian manifolds, recently evidenced by the solution of the Poincaré conjecture, is applied to Einstein's gravitational theory and in particular to the standard FLRW cosmology. We present a brief review of the deformation of Riemannian geometry, showing how such deformations can be derived from the Einstein-Hilbert dynamical principle. We show that such deformations of space-times of general relativity produce observable effects that can be measured by four-dimensional observers. In the case of the FLRW cosmology, one such observable effect is shown to be consistent with the accelerated expansion of the universe.
We study the possibility that the universe is subjected to a deformation, besides its expansion described by Friedmann's equations. The concept of smooth deformation of a riemannian manifolds associated with the extrinsic curvature is applied the standard FLRW cosmology. Starting from the resulting modified Friedman's equation we study two possible solutions with six models for each one in low redshift. In other to constrain the models, we calculate deceleration, jerk and Hubble parameters and compare with different data as the latest BAO/CMB + SNIa constraints, SNLS SNIa, x-ray galaxy clusters and the gold sample (SNIa). As a result, we obtain a set of proper models compatible with the current observational data.
In the present paper we apply the Nash's theory of perturbative geometry to the study of dark matter gravity in a higher-dimensional space-time. It is shown that the dark matter gravitational perturbations at local scale can be explained by the extrinsic curvature of the standard cosmology. In order to test our model, we use a spherically symmetric metric embedded in a five-dimensional bulk. As a result, considering a sample of 10 low surface brightness and 6 high surface brightness galaxies, we find a very good agreement with the observed rotation curves of smooth hybrid alpha-HI measurements.
In this paper we examine the evolution of cosmic density parameters in a four-dimensional space-time embedded in a five-dimensional bulk space. We show that the extrinsic curvature is an independent spin-2 field governed by the Gupta equations. Without evoking a dark energy fluid, the corresponding cosmological model is compared with the phenomenological XCDM model and shows a good concordance with recent cosmological datasets from Planck Collaboration and the latest Baryons Acoustic Oscillations/Cosmic Microwave Background (BAO/CMBR) + SNIa studying the evolution of density parameters. In addition, a discussion on the coincidence problem is also proposed.
Until recently the study of the gravitational field of dark matter was primarily concerned with its local effects on the motion of stars on galaxies and galaxy clusters. On the other hand, the WMAP experiment has shown that the gravitational field produced by dark matter amplify the higher acoustic modes of the CMBR power spectrum, more intensely than the gravitational field of baryons. Such 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 the present note 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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.