scholarly journals On f(R) gravity in scalar–tensor theories

2017 ◽  
Vol 14 (07) ◽  
pp. 1750107 ◽  
Author(s):  
Joseph Ntahompagaze ◽  
Amare Abebe ◽  
Manasse Mbonye
Keyword(s):  
Scalar Field ◽  
Gordon Equation ◽  
Gravity Models ◽  
Index Formula ◽  
Coupling Constant ◽  
The Third ◽  
Slow Roll ◽  
Klein Gordon ◽  
Early Universe Cosmology ◽  
Klein Gordon Equation

We study [Formula: see text] gravity models in the language of scalar–tensor (ST) theories. The correspondence between [Formula: see text] gravity and ST theories is revisited since [Formula: see text] gravity is a subclass of Brans–Dicke models, with a vanishing coupling constant ([Formula: see text]). In this treatment, four [Formula: see text] toy models are used to analyze the early-universe cosmology, when the scalar field [Formula: see text] dominates over standard matter. We have obtained solutions to the Klein–Gordon equation for those models. It is found that for the first model [Formula: see text], as time increases the scalar field decreases and decays asymptotically. For the second model [Formula: see text], it was found that the function [Formula: see text] crosses the [Formula: see text]-axis at different values for different values of [Formula: see text]. For the third model [Formula: see text], when the value of [Formula: see text] is small, the potential [Formula: see text] behaves like the standard inflationary potential. For the fourth model [Formula: see text], we show that there is a transition between [Formula: see text]. The behavior of the potentials with [Formula: see text] is totally different from those with [Formula: see text]. The slow-roll approximation is applied to each of the four [Formula: see text] models and we obtain the respective expressions for the spectral index [Formula: see text] and the tensor-to-scalar ratio [Formula: see text].

BEHAVIOR OF NON-CLASSICAL INFLATON IN THE FRW UNIVERSE

2013 ◽  
Vol 28 (37) ◽  
pp. 1350168 ◽  
Author(s):  
K. K. VENKATARATNAM
Keyword(s):  
Scalar Field ◽  
Particle Production ◽  
Gordon Equation ◽  
Frw Universe ◽  
Relative Deviation ◽  
Squeezed Vacuum ◽  
Slow Roll ◽  
Vacuum States ◽  
Klein Gordon ◽  
Klein Gordon Equation

We study the semiclassical Einstein equation and inflaton in the oscillatory region of the FRW Universe. We study the relative deviation of particle production in coherent and squeezed vacuum states for a minimally coupled scalar field in the oscillatory region of flat FRW Universe. We also study the behavior of inflaton field in non-oscillatory region. We examine whether the solution obtained in slow-roll approximation satisfies Klein–Gordon equation and commutation relation as well.

scholarly journals A Central Potential with a Massive Scalar Field in a Lorentz Symmetry Violation Environment

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
R. L. L. Vitória ◽  
H. Belich
Keyword(s):  
Scalar Field ◽  
Gordon Equation ◽  
Mass Term ◽  
Lorentz Symmetry ◽  
Massive Scalar ◽  
Symmetry Violation ◽  
Massive Scalar Field ◽  
Klein Gordon ◽  
Coulomb Type ◽  
Klein Gordon Equation

We investigate the behaviour of a massive scalar field under the influence of a Coulomb-type and central linear central potentials inserted in the Klein-Gordon equation by modifying the mass term in the spacetime with Lorentz symmetry violation. We consider the presence of a background constant vector field which characterizes the breaking of the Lorentz symmetry and show that analytical solutions to the Klein-Gordon equation can be achieved.

scholarly journals Does Inflationary Particle Production Suggest a Low-Density Flat Universe?

1999 ◽  
Vol 183 ◽  
pp. 314-314
Author(s):  
Varun Sahni ◽  
Salman Habib
Keyword(s):  
Scalar Field ◽  
Particle Production ◽  
Gordon Equation ◽  
Low Density ◽  
Frw Universe ◽  
Flat Universe ◽  
Klein Gordon ◽  
Klein Gordon Equation

In a FRW Universe a massless nonminimally coupled scalar field satisfies the Klein-Gordon equation.

scholarly journals Scalar-field theory of dark matter

2014 ◽  
Vol 29 (13) ◽  
pp. 1450074 ◽  
Author(s):  
Kerson Huang ◽  
Chi Xiong ◽  
Xiaofei Zhao
Keyword(s):  
Dark Matter ◽  
Scalar Field ◽  
Gordon Equation ◽  
Galactic Halo ◽  
Galactic Rotation ◽  
Klein Gordon ◽  
External Sources ◽  
Galaxy Collisions ◽  
The Universe ◽  
Klein Gordon Equation

We develop a theory of dark matter based on a previously proposed picture, in which a complex vacuum scalar field makes the universe a superfluid, with the energy density of the superfluid giving rise to dark energy, and variations from vacuum density giving rise to dark matter. We formulate a nonlinear Klein–Gordon equation to describe the superfluid, treating galaxies as external sources. We study the response of the superfluid to the galaxies, in particular, the emergence of the dark-matter galactic halo, contortions during galaxy collisions and the creation of vortices due to galactic rotation.

scholarly journals PHANTOM FIELD FROM CONFORMAL INVARIANCE

2007 ◽  
Vol 22 (04) ◽  
pp. 307-316
Author(s):  
MOKHTAR HASSAÏNE
Keyword(s):  
Scalar Field ◽  
Cosmological Constant ◽  
Gordon Equation ◽  
Complex Scalar ◽  
Conformally Invariant ◽  
Phantom Scalar ◽  
Klein Gordon ◽  
Complex Scalar Field ◽  
Phantom Scalar Field ◽  
Klein Gordon Equation

We establish a correspondence between a conformally invariant complex scalar field action (with a conformal self-interaction potential) and the action of a phantom scalar field minimally coupled to gravity (with a cosmological constant). In this correspondence, the module of the complex scalar field is used to relate conformally the metrics of both systems while its phase is identified with the phantom scalar field. At the level of the equations, the correspondence allows to map solution of the conformally nonlinear Klein–Gordon equation with vanishing energy–momentum tensor to solution of a phantom scalar field minimally coupled to gravity with cosmological constant satisfying a massless Klein–Gordon equation. The converse is also valid with the advantage that it offers more possibilities owing to the freedom of rewriting a metric as the conformal transformation of another metric. In three dimensions, the coupling of this matter action to conformal gravity is put in equivalence with topologically massive gravity with a cosmological constant and with a phantom source. Finally, we provide some examples of this correspondence.

scholarly journals Proper time and conformal problem in Kaluza–Klein theory

2015 ◽  
Vol 12 (05) ◽  
pp. 1550063
Author(s):  
E. Minguzzi
Keyword(s):  
Scalar Field ◽  
Gordon Equation ◽  
Proper Time ◽  
Inertial Mass ◽  
Scalar Fields ◽  
Conformal Factor ◽  
Klein Theory ◽  
Klein Gordon ◽  
Klein Gordon Equation ◽  
Kaluza Klein

In the traditional Kaluza–Klein theory, the cylinder condition and the constancy of the extra-dimensional radius (scalar field) imply that time-like geodesics on the five-dimensional bundle project to solutions of the Lorentz force equation on spacetime. This property is lost for nonconstant scalar fields, in fact there appears new terms that have been interpreted mainly as new forces or as due to a variable inertial mass and/or charge. Here we prove that the additional terms can be removed if we assume that charged particles are coupled with the same spacetime conformal structure of neutral particles but through a different conformal factor. As a consequence, in Kaluza–Klein theory the proper time of the charged particle might depend on the charge-to-mass ratio and the scalar field. Then we show that the compatibility between the equation of the projected geodesic and the classical limit of the Klein–Gordon equation fixes unambiguously the conformal factor of the coupling metric solving the conformal ambiguity problem of Kaluza–Klein theories. We confirm this result by explicitly constructing the projection of the Klein–Gordon equation and by showing that each Fourier mode, even for a variable scalar field, satisfies the Klein–Gordon equation on the base.

scholarly journals Vaidya geometries and scalar fields with null gradients

2021 ◽  
Vol 81 (3) ◽  
Author(s):  
Valerio Faraoni ◽  
Andrea Giusti ◽  
Bardia H. Fahim
Keyword(s):  
Scalar Field ◽  
Gordon Equation ◽  
Plane Waves ◽  
Null Geodesic ◽  
Scalar Fields ◽  
Einstein Gravity ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Klein Gordon ◽  
Klein Gordon Equation

AbstractSince, in Einstein gravity, a massless scalar field with lightlike gradient behaves as a null dust, one could expect that it can act as the matter source of Vaidya geometries. We show that this is impossible because the Klein–Gordon equation forces the null geodesic congruence tangent to the scalar field gradient to have zero expansion, contradicting a basic property of Vaidya solutions. By contrast, exact plane waves travelling at light speed and sourced by a scalar field acting as a null dust are possible.

Zur einheitlichen Feldtheorie

1964 ◽  
Vol 19 (4) ◽  
pp. 401-405
Author(s):  
G. Braunss
Keyword(s):  
Scalar Field ◽  
Gordon Equation ◽  
Field Equations ◽  
Bianchi Identities ◽  
Euclidean Metric ◽  
Klein Gordon ◽  
Klein Gordon Equation

The basic conception of this paper is the assumption, that all quantities characterizing the metric are functionals of one field (worldfield). For the sake of mathematical simplicity a scalar field Φ is considered. The investigations are based on the following system of field equations:Rmn - ½ gmn R=½ gmn [gabΦ, aΦ, b + F(Φ)]-Φ,mΦ, n;F is a functional of Φ. According to the basic conception only such solutions for the gmn are permitted, which for Φ ≡ 0 give the corresponding values of a euclidean metric. Due to the BIANCHI-identities it follows as a consequence of the field equations, that Φ satisfies a nonlinear KLEIN-GORDON-equation :gabΦ;ab-½(dF/dΦ) =0 .The conditions for a nonsingular, static and centralsymmetrical solution are investigated. With regard to cosmological problems the equations for a conformal-flat, timedependent metric are discussed.

SOLUTION OF THE KLEIN–GORDON EQUATION IN A 2 + 1 CURVED SPACE–TIME

2001 ◽  
Vol 16 (18) ◽  
pp. 1151-1156
Author(s):  
TINA A. HARRIOTT ◽  
J. G. WILLIAMS
Keyword(s):  
Scalar Field ◽  
Bessel Functions ◽  
Gordon Equation ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Whittaker Functions ◽  
Curved Space ◽  
Standard Manner ◽  
Klein Gordon ◽  
Klein Gordon Equation

The Klein–Gordon equation for a massless scalar field is considered for an extended matter source in 2 + 1 dimensions. It is shown how a solution can be found using Whittaker functions and can be normalized in the standard manner. In the point source limit, the solution reduces to the usual expression in terms of Bessel functions.

scholarly journals Differences between scalar field and scalar density field solutions

2012 ◽  
Vol 90 (1) ◽  
pp. 91-95
Author(s):  
Nurettin Pirinççiog˜lu ◽  
Ilker Sert
Keyword(s):  
Scalar Field ◽  
Gordon Equation ◽  
Density Field ◽  
Expanding Universe ◽  
Scalar Density ◽  
Newtonian Approximation ◽  
Klein Gordon ◽  
Klein Gordon Equation

Differences between scalar field and scalar density solutions are explored using a Robertson–Walker (RW) metric, and a nonrelativistic Hamiltonian is derived for a scalar density field in the post-newtonian approximation. The results are compared with those of a scalar field. The expanding universe in a RW metric and a post-newtonian solution of the Klein–Gordon equation are discussed separately.

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