On the de Sitter Space-Time - the Geometric Foundation of Inflationary Cosmology

We discuss the physics of interacting fields and particles living in a de Sitter Lorentzian manifold (dSLM), a submanifold of a 5-dimensional pseudo-Euclidean (5dPE) equipped with a metric tensor inherited from the metric of the 5dPE space. The dSLM is naturally oriented and time oriented and is the arena used to study the energy-momentum conservation law and equations of motion for physical systems living there. Two distinct de Sitter space-time structuresMdSLandMdSTPare introduced given dSLM, the first equipped with the Levi-Civita connection of its metric field and the second with a metric compatible parallel connection. Both connections are used only as mathematical devices. Thus, for example,MdSLis not supposed to be the model of any gravitational field in the General Relativity Theory (GRT). Misconceptions appearing in the literature concerning the motion of free particles in dSLM are clarified. Komar currents are introduced within Clifford bundle formalism permitting the presentation of Einstein equation as a Maxwell like equation and proving that in GRT there are infinitely many conserved currents. We prove that in GRT even when the appropriate Killing vector fields exist it is not possible to define a conserved energy-momentum covector as in special relativistic theories.

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“…In order to analyze this expression we put (without loss of generality, see the reason in [42]) y = z = 0. In this case…”

Section: On the Geodesics Of The M Dslmentioning

confidence: 99%

Notes on Conservation Laws, Equations of Motion of Matter, and Particle Fields in Lorentzian and Teleparallel de Sitter Space-Time Structures

Rodrigues

Wainer

2016

Advances in Mathematical Physics

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“…Therefore, the spacetime has constant curvature. As de-Sitter space is a Lorentzian manifold of constant curvature with implied negative pressure driving cosmic inflation (see [21]) we can state the following:…”

Section: Geometrical Structure Of Perfect Fluid Spacetime With Torse-forming Vector Fieldmentioning

confidence: 99%

On Ricci–Yamabe soliton and geometrical structure in a perfect fluid spacetime

Singh

Khatri

2021

Afr. Mat.

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In this paper, we studied the geometrical aspects of a perfect fluid spacetime with torseforming vector field ξ under certain curvature restrictions, and Ricci-Yamabe soliton and η-Ricci-Yamabe soliton in a perfect fluid spacetime. Conditions for the Ricci-Yamabe soliton to be steady, expanding or shrinking are also given. Moreover, when the potential vector field ξ of η-Ricci-Yamabe soliton is of gradient type, we derive a Poisson equation and also looked at its particular cases. Lastly, a non-trivial example of perfect fluid spacetime admitting η-Ricci-Yamabe soliton is constructed.

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“…This work is an attempt to bring together all the known coordinate frames that have been utilised or mentioned in the literature for de Sitter spacetime. There have been a number of rather thorough reviews in this sense, the most important of which is the one made by Eriksen and Grøn [14], but also in part by Schmidt [13], Bičák and Krtouš [15] or Spradlin, Strominger and Volovich [20].…”

Section: Introductionmentioning

confidence: 99%

“…There is also when the coordinates are "rotated" in the sense of the coodinate used being pure imaginary: r rot = ir. This has been done even by de Sitter himself, as Schmidt [13] carefully points out. Then, cos(ωr) = cosh(ωr rot ), cosh(ωr) = cos(ωr rot ) and sin(ωr) = −i sinh(ωr rot ), sinh(ωr) = −i sin(ωr rot ).…”

Section: Introductionmentioning

confidence: 99%

Atlas of Coordinate Charts on de Sitter Spacetime

Pascu¹

2012

Preprint

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The de Sitter manifold admits a wide variety of interesting coordinatizations. The 'atlas' is a compilation of the coordinate charts referenced throughout the literature, and is presented in the form of tables, the starting point being the embedding in a higher-dimensional Minkowski spacetime. The metric tensor and the references where the coordinate frame is discussed or used in applications are noted. Additional information is given for the entries with significant use: a convenient tetrad and the form taken by the Killing vectors in the respective coordinate frame.

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On the de Sitter Space-Time - the Geometric Foundation of Inflationary Cosmology

Cited by 17 publications

References 24 publications

Notes on Conservation Laws, Equations of Motion of Matter, and Particle Fields in Lorentzian and Teleparallel de Sitter Space-Time Structures

Notes on Conservation Laws, Equations of Motion of Matter, and Particle Fields in Lorentzian and Teleparallel de Sitter Space-Time Structures

On Ricci–Yamabe soliton and geometrical structure in a perfect fluid spacetime

Atlas of Coordinate Charts on de Sitter Spacetime

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