Dark Gravitational Field on Riemannian and Sasaki Spacetime

Abstract

The aim of this paper is to provide the geometrical structure of a gravitational field that includes the addition of dark matter in the framework of a Riemannian and a Riemann--Sasaki spacetime. By means of the classical Riemannian geometric methods we arrive at modified geodesic equations, tidal forces, and Einstein and Raychaudhuri equations to account for extra dark gravity. We further examine an application of this approach in cosmology. Moreover, a possible extension of this model on the tangent bundle is studied in order to examine the behavior of dark matter in a unified geometric model of gravity with more degrees of freedom. Particular emphasis shall be laid on the problem of the geodesic motion under the influence of dark matter.

arXiv comment20 pages

References in corpus (38)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• f(R) Theories Of Gravity
• Type Ia Supernova Discoveries at z>1 From the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution
• f(R) theories
• Dark Energy and the Accelerating Universe
• Non-minimal dark sector physics and cosmological tensions
• Fluid Dark Matter
• Generalized curvature-matter couplings in modified gravity
• Dark energy and dark matter as curvature effects
• First Cosmology Results using Type Ia Supernovae from the Dark Energy Survey: Constraints on Cosmological Parameters
• Milky Way Satellite Census. II. Galaxy--Halo Connection Constraints Including the Impact of the Large Magellanic Cloud
• The Raychaudhuri equations: a brief review
• Constraining Dark Energy Dynamics in Extended Parameter Space
• SHARP -- VII. New constraints on the dark matter free-streaming properties and substructure abundance from gravitationally lensed quasars
• Measuring the Hubble constant with Type Ia supernovae as near-infrared standard candles
• A Unifying Theory of Dark Energy and Dark Matter: Negative Masses and Matter Creation within a Modified $\Lambda$CDM Framework
• A precise extragalactic test of General Relativity
• Marginal evidence for cosmic acceleration from Type Ia supernovae
• Resolving Cosmological Singularities
• Dark energy, inflation and dark matter from modified F(R) gravity
• Dark Fluid: a complex scalar field to unify dark energy and dark matter
• Dark matter and dark energy as a effects of Modified Gravity
• Early-type Host Galaxies of Type Ia Supernovae. II. Evidence for Luminosity Evolution in Supernova Cosmology
• Geodesic deviation, Raychaudhuri equation, and tidal forces in modified gravity with an arbitrary curvature-matter coupling
• Direct Detection Signals from Absorption of Fermionic Dark Matter
• Soundness of Dark Energy properties
• Constraining Dark Matter Models with a Light Mediator from PandaX-II Experiment
• CMB tensions with low-redshift $H_0$ and $S_8$ measurements: impact of a redshift-dependent type-Ia supernovae intrinsic luminosity
• From Dark Energy and Dark Matter to Dark Metric
• Cosmological searches for a non-cold dark matter component
• The KBC Void: Consistency with Supernovae Type Ia and the Kinematic SZ Effect in a $\Lambda$LTB Model
• Dark Energy, A Cosmological Constant, and Type Ia Supernovae
• {\it Gauging} the cosmic acceleration with recent type Ia supernovae data sets
• Is dark matter an extra-dimensional effect?
• Classical and quantum cosmology with two perfect fluids: stiff matter and radiation
• Gravity with extra dimensions and dark matter interpretation: A straightforward approach
• Two-component perfect fluid in FRW universe

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