scholarly journals Integrability and cosmological solutions in Einstein-æther-Weyl theory

2021 ◽  
Vol 81 (3) ◽  
Author(s):  
Andronikos Paliathanasis ◽  
Genly Leon
Keyword(s):  
Scalar Field ◽  
Cosmological Model ◽  
Conservation Law ◽  
Analytic Solutions ◽  
Special Interests ◽  
Field Equations ◽  
Background Space ◽  
Weyl Theory ◽  
Cosmological Solutions

AbstractWe consider a Lorentz violating scalar field cosmological model given by the modified Einstein-æther theory defined in Weyl integrable geometry. The existence of exact and analytic solutions is investigated for the case of a spatially flat Friedmann–Lemaître–Robertson–Walker background space. We show that the theory admits cosmological solutions of special interests. In addition, we prove that the cosmological field equations admit the Lewis invariant as a second conservation law, which indicates the integrability of the field equations.

scholarly journals Cosmological solutions in Hořava-Lifshitz scalar field theory

2020 ◽  
Vol 75 (6) ◽  
pp. 523-532 ◽  
Author(s):  
Andronikos Paliathanasis ◽  
Genly Leon
Keyword(s):  
Scalar Field ◽  
Singularity Analysis ◽  
Exponential Potential ◽  
Field Equations ◽  
Explicit Integration ◽  
Gravitational Field Equations ◽  
Background Space ◽  
Painlevé Property ◽  
Cosmological Solutions ◽  
Scalar Field Cosmology

AbstractWe perform a detailed study of the integrability of the Hořava-Lifshitz scalar field cosmology in a Friedmann-Lemaître-Robertson-Walker background space-time. The approach we follow to determine the integrability is that of singularity analysis. More specifically, we test whether the gravitational field equations possess the Painlevé property. For the exponential potential of the scalar field, we are able to perform an analytic explicit integration of the field equations and write the solution in terms of a Laurent expansion and more specifically write the solution in terms of right Painlevé series.

scholarly journals Exact Kantowski–Sachs spacetimes in Einstein–Aether scalar field theory

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
Genly Leon ◽  
Andronikos Paliathanasis ◽  
N. Dimakis
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Functional Form ◽  
Analytic Solution ◽  
Analytic Solutions ◽  
Field Equations ◽  
Scalar Field Theory ◽  
Gravitational Field Equations ◽  
Background Space ◽  
Gravitational Model

AbstractExact and analytic solutions in Einstein–Aether scalar field theory with Kantowski–Sachs background space are determined. The theory of point symmetries is applied to determine the functional form of the unknown functions which defines the gravitational model. Conservation laws are applied to reduce the order of the field equations and write the analytic solution. Moreover, in order to understand the physical behaviour of the cosmological model a detailed analysis of the asymptotic behaviour for solutions of the gravitational field equations is performed.

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.

scholarly journals Non-linear composition and infinite conformal symmetry of topologically non-trivial solutions in $$(3+1)$$-dimensional Yang–Mills theory

2021 ◽  
Vol 81 (11) ◽  
Author(s):  
Fabrizio Canfora
Keyword(s):  
Scalar Field ◽  
Charge Density ◽  
Topological Charge ◽  
Conformal Symmetry ◽  
Analytic Solutions ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Field Equations ◽  
Yang Mills ◽  
Non Linear

AbstractAn infinite-dimensional family of analytic solutions in pure SU(2) Yang–Mills theory at finite density in $$(3+1)$$ ( 3 + 1 ) dimensions is constructed. It is labelled by two integeres (p and q) as well as by a two-dimensional free massless scalar field. The gauge field depends on all the 4 coordinates (to keep alive the topological charge) but in such a way to reduce the (3+1)-dimensional Yang–Mills field equations to the field equation of a 2D free massless scalar field. For each p and q, both the on-shell action and the energy-density reduce to the action and Hamiltonian of the corresponding 2D CFT. The topological charge density associated to the non-Abelian Chern–Simons current is non-zero. It is possible to define a non-linear composition within this family as if these configurations were “Lego blocks”. The non-linear effects of Yang–Mills theory manifest themselves since the topological charge density of the composition of two solutions is not the sum of the charge densities of the components. This leads to an upper bound on the amplitudes in order for the topological charge density to be well-defined. This suggests that if the temperature and/or the energy is/are high enough, the topological density of these configurations is not well-defined anymore. Semiclassically, one can show that (depending on whether the topological charge is even or odd) some of the operators appearing in the 2D CFT should be quantized as Fermions (despite the Bosonic nature of the classical field).

scholarly journals EXACT SOLUTIONS FOR COSMOLOGICAL MODELS WITH A SCALAR FIELD

2002 ◽  
Vol 17 (03) ◽  
pp. 375-381 ◽  
Author(s):  
H. MOTAVALI ◽  
M. GOLSHANI
Keyword(s):  
Scalar Field ◽  
Exact Solutions ◽  
Cosmological Models ◽  
Coupling Function ◽  
Noether Symmetry ◽  
Scalar Tensor Theory ◽  
Frw Cosmology ◽  
Field Equations ◽  
Tensor Theory ◽  
Cosmological Solutions

We consider the existence of a Noether symmetry in the scalar–tensor theory of gravity in flat Friedman–Robertson–Walker (FRW) cosmology. The forms of coupling function ω(ϕ) and generic potential V(ϕ) are obtained by requiring the existence of a Noether symmetry for such theory. We derive exact cosmological solutions of the field equations from a point-like Lagrangian.

ROTATING STRING COSMOLOGIES WITH SCALAR FIELD AND HEAT FLUX

2001 ◽  
Vol 10 (06) ◽  
pp. 935-942 ◽  
Author(s):  
HÜSNÜ BAYSAL ◽  
İHSAN YILMAZ ◽  
İSMAIL TARHAN
Keyword(s):  
Heat Flux ◽  
Temperature Distribution ◽  
Scalar Field ◽  
Heat Flow ◽  
Cosmological Model ◽  
Exact Solutions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Rotating String

We obtain some cosmological model that are exact solutions of Einstein field equations. The metric utilized is the nonstatic Gödel-type cosmological model and the curvature source is a string cloud with scalar field and heat flow. The solutions have nonzero expansion, shear, and rotating. The properties of the solutions are studied and the temperature distribution is also given explicitly.

scholarly journals TENSOR–SCALAR TORSION

2001 ◽  
Vol 16 (03) ◽  
pp. 113-119 ◽  
Author(s):  
CHARRO GRUVER ◽  
RICHARD HAMMOND ◽  
P. F. KELLY
Keyword(s):  
Angular Momentum ◽  
Scalar Field ◽  
Conservation Law ◽  
Torsion Tensor ◽  
Equations Of Motion ◽  
Exterior Derivative ◽  
Field Equations ◽  
Theory Of Gravity ◽  
Rotational Angular Momentum

A theory of gravity with torsion is examined in which the torsion tensor is constructed from the exterior derivative of an antisymmetric rank-two potential plus the dual of the gradient of a scalar field. Field equations for the theory are derived by demanding that the action be stationary under variations with respect to the metric, the antisymmetric potential, and the scalar field. A material action is introduced and the equations of motion are derived. The correct conservation law for rotational angular momentum plus spin is observed to hold in this theory.

scholarly journals f(T) cosmology with nonzero curvature

2021 ◽  
Vol 36 (38) ◽  
Author(s):  
Andronikos Paliathanasis
Keyword(s):  
Cosmological Constant ◽  
Cosmological Solution ◽  
Constant Term ◽  
Analytic Solutions ◽  
De Sitter ◽  
Spatial Curvature ◽  
Field Equations ◽  
Background Space ◽  
Nonzero Curvature ◽  
Text Model

We investigate exact and analytic solutions in [Formula: see text] gravity within the context of a Friedmann–Lemaître–Robertson–Walker background space with nonzero spatial curvature. For the power-law theory [Formula: see text] we find that the field equations admit an exact solution with a linear scalar factor for negative and positive spatial curvature. That Milne-like solution is asymptotic behavior for the scale factor near the initial singularity for the model [Formula: see text]. The analytic solution for that specific theory is presented in terms of Painlevé series for [Formula: see text]. Moreover, from the value of the resonances of the Painlevé series we conclude that the Milne-like solution is always unstable while for large values of the independent parameter, the field equations provide an expanding universe with a de Sitter expansion of a positive cosmological constant. Finally, the presence of the cosmological term [Formula: see text] in the studied [Formula: see text] model plays no role in the general behavior of the cosmological solution and the universe immerge in a de Sitter expansion either when the cosmological constant term [Formula: see text] in the [Formula: see text] model vanishes.

scholarly journals New Anisotropic Exact Solution in Multifield Cosmology

Universe ◽  
2021 ◽  
Vol 7 (9) ◽  
pp. 323 ◽  
Author(s):  
Andronikos Paliathanasis
Keyword(s):  
Exact Solution ◽  
Scalar Field ◽  
Chiral Model ◽  
Stability Conditions ◽  
Field Equations ◽  
Background Space ◽  
Scalar Field Cosmology ◽  
The Stability

In the case of two-scalar field cosmology, and specifically for the Chiral model, we determine an exact solution for the field equations with an anisotropic background space. The exact solution can describe anisotropic inflation with a Kantowski–Sachs geometry and can be seen as the anisotropic analogue of the hyperbolic inflation. Finally, we investigate the stability conditions for the exact solution.

Brans–Dicke scalar field cosmological model in Lyra’s geometry with time-dependent deceleration parameter

2018 ◽  
Vol 15 (11) ◽  
pp. 1850186
Author(s):  
Rashid Zia ◽  
Dinesh Chandra Maurya
Keyword(s):  
Scalar Field ◽  
Cosmological Model ◽  
Deceleration Parameter ◽  
Momentum Tensor ◽  
Energy Conditions ◽  
Physical Parameters ◽  
Type I ◽  
Field Equations ◽  
Modified Gravity Theory ◽  
Lyra’S Geometry

From the recent observations, it is well known that the expansion rate of our universe varies with time (early decelerating and accelerating in the present epoch) which is an unsolved problem. This motivated to us to consider this paper and so we have developed a new cosmological model in Einstein’s modified gravity theory using two types of modifications: (i) Geometrical modification, in which we have used Lyra’s geometry in the curvature part of the Einstein field equations (EFE) and (ii) Modification in gravity (energy momentum tensor) on right hand side of EFE, as per the Brans–Dicke model. With these two modifications, we have obtained the exact solutions of Einstein Brans–Dicke field equations in Lyra’s geometry for a spatially homogeneous Bianchi type-I space-time with time variable deceleration parameter (DP). We have calculated various physical parameters for the model and found them consistent with recent observations. We have also examined the energy conditions for the model and found them satisfactory. We have found that the scalar field of Brans–Dicke theory behaves like a best fit dark energy candidate in the reference of Lyra’s geometry.

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