Cosmological solutions of the Einstein-KÄhler field equations in Robertson-Walker backgrounds

1994 ◽  
Vol 26 (7) ◽  
pp. 663-679 ◽  
Author(s):  
Wathek Talebaoui
Keyword(s):  
Field Equations ◽  
Cosmological Solutions

scholarly journals The (2+1) dimensional metric f (R) gravity non-minimally coupled with fermion field

2021 ◽  
Vol 2090 (1) ◽  
pp. 012065
Author(s):  
Nurgissa Myrzakulov ◽  
Gulnur Tursumbayeva ◽  
Shamshyrak Myrzakulova
Keyword(s):  
Gravitational Theory ◽  
Noether Symmetry ◽  
Fermion Field ◽  
Field Equations ◽  
Friedmann Equations ◽  
Fermion Fields ◽  
Cosmological Solutions

Abstract In this article, we examine a gravitational theory including a fermion field that is non-minimally coupled to metric f (R) gravity in (2+1) dimensions. We give the field equations for fermion fields and Friedmann equations. In this context, we study cosmological solutions of the field equations using these forms obtained by the existent of Noether symmetry.

scholarly journals New cosmological solutions in hybrid metric-Palatini gravity from dynamical symmetries

2021 ◽  
pp. 2150100
Author(s):  
Andronikos Paliathanasis
Keyword(s):  
Conservation Laws ◽  
Integrable Systems ◽  
Functional Form ◽  
Analytic Solutions ◽  
Momentum Conservation ◽  
Field Equations ◽  
Dynamical Symmetries ◽  
Cosmological Solutions ◽  
Liouville Integrable

We investigate the existence of Liouville integrable cosmological models in hybrid metric-Palatini theory. Specifically, we use the symmetry conditions for the existence of quadratic in the momentum conservation laws for the field equations as constraint conditions for the determination of the unknown functional form of the theory. The exact and analytic solutions of the integrable systems found in this study are presented in terms of quadratics and Laurent expansions.

COSMOLOGICAL SOLUTIONS AND THEIR EFFECTIVE PROPERTIES OF MATTER IN KALUZA-KLEIN THEORY

1994 ◽  
Vol 03 (03) ◽  
pp. 627-637 ◽  
Author(s):  
HONGYA LIU ◽  
PAUL S. WESSON
Keyword(s):  
Globular Clusters ◽  
Effective Properties ◽  
Plane Waves ◽  
Big Bang ◽  
Field Equations ◽  
Fifth Dimension ◽  
Cosmological Solutions ◽  
Klein Theory ◽  
The Universe ◽  
Kaluza Klein

We derive a “wave-like” class of exact cosmological solutions of the apparently empty 5D Kaluza-Klein field equations. Here by “wave-like” we mean that the solutions look like plane waves propagating in the fifth dimension. In the interpretation that the fifth dimension in Kaluza-Klein theory may induce matter in four dimensions, we then calculate the effective energy density ρ and pressure p, and study in detail the case for which the equation of state is p=γρ (where γ is an arbitrary constant). We show that for both the matter-dominated (γ=0) and radiation-dominated (γ=1/3) eras of the universe, the 4D spacetime defined by hypersurfaces of the 5D metrics are just the same as those of the standard Friedmann-Robertson-Walker models of general relativity. However, in our models the big bang is like a shock wave propagating along the fifth dimension, and different observers can measure different ages for the universe. This property may be tested using the spread in ages of astrophysical objects such as globular clusters.

scholarly journals Noether Gauge Symmetry of Dirac Field in (2 + 1)-Dimensional Gravity

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Ganim Gecim ◽  
Yusuf Kucukakca ◽  
Yusuf Sucu
Keyword(s):  
Gauge Symmetry ◽  
Early Time ◽  
Gravitational Theory ◽  
Dirac Field ◽  
Late Time ◽  
Field Equations ◽  
Dynamical Equations ◽  
Symmetry Approach ◽  
Cosmological Solutions ◽  
Dimensional Gravity

We consider a gravitational theory including a Dirac field that is nonminimally coupled to gravity in 2 + 1 dimensions. Noether gauge symmetry approach can be used to fix the form of coupling functionF(Ψ)and the potentialV(Ψ)of the Dirac field and to obtain a constant of motion for the dynamical equations. In the context of (2 + 1)-dimensional gravity, we investigate cosmological solutions of the field equations using these forms obtained by the existence of Noether gauge symmetry. In this picture, it is shown that, for the nonminimal coupling case, the cosmological solutions indicate both an early-time inflation and late-time acceleration for the universe.

scholarly journals FREE CURVILINEAR SPACE WITH TORSION

Globus ◽  
2021 ◽  
Vol 7 (6(63)) ◽  
pp. 27-33
Author(s):  
Y.A. Sharin
Keyword(s):  
Field Theory ◽  
Mass Density ◽  
Classical Field Theory ◽  
Classical Field ◽  
Field Equations ◽  
Curved Space ◽  
Astronomical Observations ◽  
Average Mass ◽  
Cosmological Solutions ◽  
The Universe

Under the classical field theory, a variant unification of gravity and electromagnetism on the basis of four-dimensional curved space with torsion is proposed. The connection between electromagnetic field and torsion of space is discovered, a physical interpretation of the space scalar curvature as the density of matter mass is proposed. The solution for the eigenstate of a curved space with torsion, corresponding to the electron is obtained. The identification of the field equations as the Schrodinger equation for the hydrogen atom is shown. Cosmological solutions for the expanding Universe are found, the average mass density in the Universe is estimated, and the results corresponding to the data of astronomical observations are obtained.

scholarly journals Self-similar cosmological solutions in f(R,T) gravity theory

2021 ◽  
pp. 2150206
Author(s):  
José Antonio Belinchón ◽  
Carlos González ◽  
Sami Dib
Keyword(s):  
Exact Solutions ◽  
The Self ◽  
Exact Form ◽  
Field Equations ◽  
Self Similarity ◽  
Similarity Hypothesis ◽  
Geometrical Quantity ◽  
Cosmological Solutions ◽  
Self Similar ◽  
Matter Collineation

We study the [Formula: see text] cosmological models under the self-similarity hypothesis. We determine the exact form that each physical and geometrical quantity may take in order that the field equations (FE) admit exact self-similar (SS) solutions through the matter collineation approach. We study two models: the case[Formula: see text] and the case [Formula: see text]. In each case, we state general theorems which determine completely the form of the unknown functions [Formula: see text] such that the FE admit SS solutions. We also state some corollaries as limiting cases. These results are quite general and valid for any homogeneous SS metric[Formula: see text] In this way, we are able to generate new cosmological scenarios. As examples, we study two cases by finding exact solutions to these particular models.

scholarly journals Non-local curvature and Gauss–Bonnet cosmologies by Noether symmetries

2020 ◽  
Vol 135 (12) ◽  
Author(s):  
Francesco Bajardi ◽  
Salvatore Capozziello ◽  
Daniele Vernieri
Keyword(s):  
Noether Symmetries ◽  
Field Equations ◽  
Local Curvature ◽  
Symmetry Approach ◽  
Local Gravity ◽  
Cosmological Solutions ◽  
Related Point ◽  
Functional Forms ◽  
Non Local ◽  
Scalar Invariants

AbstractNon-local gravity cosmologies are considered under the standard of Noether symmetry approach. In particular, we focus on non-local theories whose gravitational actions depend on curvature and Gauss–Bonnet scalar invariants. Specific functional forms of the related point-like Lagrangians are selected by Noether symmetries, and we solve the corresponding field equations finding out exact cosmological solutions.

scholarly journals Anisotropic cosmological solutions to the Y(R)F2 gravity

2019 ◽  
Vol 34 (35) ◽  
pp. 1950286 ◽  
Author(s):  
Özcan Sert ◽  
Muzaffer Adak
Keyword(s):  
Variational Principle ◽  
Magnetic Fields ◽  
Electromagnetic Fields ◽  
Electric Fields ◽  
Isotropic Case ◽  
Field Equations ◽  
Cosmological Solutions

We investigate anisotropic cosmological solutions of the theory with non-minimal couplings between electromagnetic fields and gravity in [Formula: see text] form. After we derive the field equations by the variational principle, we look for spatially flat cosmological solutions with magnetic fields or electric fields. Then, we give exact anisotropic solutions by assuming the hyperbolic expansion functions. We observe that the solutions approach the isotropic case in late-times.

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