scholarly journals Smooth braneworld models possibility in modified gravities

2015 ◽  
Vol 24 (11) ◽  
pp. 1550089 ◽  
Author(s):  
G. P. de Brito ◽  
J. M. Hoff da Silva ◽  
P. Michel L. T. da Silva ◽  
A. de Souza Dutra
Keyword(s):  
Scalar Field ◽  
Extra Dimension ◽  
Field Potential ◽  
Dimensional Case ◽  
Consistency Conditions ◽  
Thick Branes

In this paper, it is shown that the consideration of the braneworld consistency conditions within the framework of bulk modified gravities allows for the existence of thick branes in the five-dimensional case with compact extra dimension. On studying the specific consistency conditions in the Brans–Dicke gravity, we were able to show that the brane generating scalar field potential is relevant for relaxing the gravitational constraints.

A GEOMETRIC WAY TO OBTAIN DE-SITTER SUBSPACES PERPENDICULAR TO A FINITE SIZE EXTRA-DIMENSION IN CURVED 5D UNIVERSES

2004 ◽  
Vol 19 (20) ◽  
pp. 3377-3394 ◽  
Author(s):  
E. GUENDELMAN ◽  
H. RUCHVARGER
Keyword(s):  
Scalar Field ◽  
Extra Dimension ◽  
Special Form ◽  
Separation Of Variables ◽  
Field Potential ◽  
Finite Size ◽  
Flat Space ◽  
Space Time ◽  
De Sitter ◽  
Geodesic Lines

We define curved five-dimensional (5D) space–time from the embedding of 5D surfaces in a 6D flat space. Demanding that the 6D coordinates satisfy a separation of variables form and that the 5D metric is diagonal, we obtain that each curved 5D surface contains 4D hyperboloid de-Sitter subspaces with maximally symmetry SO (4,1). Therefore, we define a very special form for the curved 5D surface where the extra-dimension is perpendicular to the 4D hyperboloid de-Sitter spaces. By relating to a minimally coupled scalar field with a potential which depends on the extra-dimension only, the curved 5D surface's form is satisfied. A mechanism by means of which the extra-dimension can be of a finite size, is found. The borders of the finite extra-dimension are obtained when the scalar field potential goes to infinity for certain finite values of the scalar field. The geodesic lines' equations show that a particle cannot cross such borders.

scholarly journals CHAOTIC INFLATION ON THE RANDALL–SUNDRUM TWO-BRANE MODEL

2010 ◽  
Vol 25 (31) ◽  
pp. 2697-2713
Author(s):  
KOUROSH NOZARI ◽  
SIAMAK AKHSHABI
Keyword(s):  
Scalar Field ◽  
Field Potential ◽  
Friedmann Equation ◽  
Warp Factor ◽  
Model Parameters ◽  
Stabilization Mechanism ◽  
Brane Model ◽  
Inflation Model ◽  
Bulk Scalar Field ◽  
Chaotic Inflation

We construct an inflation model on the Randall–Sundrum I (RSI) brane where a bulk scalar field stabilizes the inter-brane separation. We study impact of the bulk scalar field on the inflationary dynamics on the brane. We proceed in two different approaches: in the first approach, the stabilizing field potential is directly appeared in the Friedmann equation and the resulting scenario is effectively a two-field inflation. In the second approach, the stabilization mechanism is considered in the context of a warp factor so that there is just one field present that plays the roles of both inflaton and stabilizer. We study constraints imposed on the model parameters from recent observations.

PHYSICAL ASPECTS OF SOLITONS IN (4+1) GRAVITY

1995 ◽  
Vol 04 (05) ◽  
pp. 639-659 ◽  
Author(s):  
ANDREW BILLYARD ◽  
PAUL S. WESSON ◽  
DIMITRI KALLIGAS
Keyword(s):  
Physical Properties ◽  
Extra Dimension ◽  
Dimensional Case ◽  
Schwarzschild Solution ◽  
Circular Orbits ◽  
Know How ◽  
Fifth Dimension ◽  
Klein Theory ◽  
Limiting Case ◽  
Kaluza Klein

The augmentation of general relativity’s spacetime by one or more dimensions is described by Kaluza-Klein theory and is within testable limits. Should an extra dimension be observable and significant, it would be beneficial to know how physical properties would differ from “conventional” relativity. In examining the class of five-dimensional solutions analogous to the four-dimensional Schwarzschild solution, we examine where the origin to the system is located and note that it can differ from the four-dimensional case. Furthermore, we study circular orbits and find that the 5D case is much richer; photons can have stable circular orbits in some instances, and stable orbits can exist right to the new origin in others. Finally, we derive both gravitational and inertial masses and find that they do not generally agree, although they can in a limiting case. For all three examinations, it is possible to obtain the four-dimensional results in one limiting case, that of the Schwarzschild solution plus a flat fifth dimension, and that the differences between 4D and 5D occur when the fifth dimension obtains any sort of significance.

scholarly journals Dynamics of scalar potentials in theory of gravity

2019 ◽  
Vol 97 (8) ◽  
pp. 880-894
Author(s):  
M. Zubair ◽  
Farzana Kousar ◽  
Saira Waheed
Keyword(s):  
Scalar Field ◽  
Field Potential ◽  
Graphical Analysis ◽  
Chaplygin Gas ◽  
Field Potentials ◽  
De Sitter ◽  
Field Equations ◽  
Barotropic Fluid ◽  
First Case ◽  
De Sitter Universe

In this paper, we explore the nature of scalar field potential in [Formula: see text] gravity using a well-motivated reconstruction scheme for flat Friedmann–Robertson–Walker (FRW) geometry. The beauty of this scheme lies in the assumption that the Hubble parameter can be expressed in terms of scalar field and vice versa. Firstly, we develop field equations in this gravity and present some general explicit forms of scalar field potential via this technique. In the first case, we take the de Sitter universe model and construct some field potentials by taking different cases for the coupling function. In the second case, we derive some field potentials using the power law model in the presence of different matter sources like barotropic fluid, cosmological constant, and Chaplygin gas for some coupling functions. From graphical analysis, it is concluded that using some specific values of the involved parameters, the reconstructed scalar field potentials are cosmologically viable in both cases.

scholarly journals Isotropic exact solutions in $$F(R,Y,\phi )$$ gravity via Noether symmetries

2021 ◽  
Vol 81 (2) ◽  
Author(s):  
Saira Waheed ◽  
Iqra Nawazish ◽  
M. Zubair
Keyword(s):  
Scalar Field ◽  
Exact Solutions ◽  
Field Potential ◽  
Noether Symmetries ◽  
Dynamical Equations ◽  
Curvature Invariant ◽  
Gauge Symmetries ◽  
Cosmic Evolution ◽  
Fluid Matter ◽  
Alpha Beta

AbstractThe present article investigates the existence of Noether and Noether gauge symmetries of flat Friedman–Robertson–Walker universe model with perfect fluid matter ingredients in a generalized scalar field formulation namely $$f(R,Y,\phi )$$ f ( R , Y , ϕ ) gravity, where R is the Ricci scalar and Y denotes the curvature invariant term defined by $$Y=R_{\alpha \beta }R^{\alpha \beta }$$ Y = R α β R α β , while $$\phi $$ ϕ represents scalar field. For this purpose, we assume different general cases of generic $$f(R,Y,\phi )$$ f ( R , Y , ϕ ) function and explore its possible forms along with field potential $$V(\phi )$$ V ( ϕ ) by taking constant and variable coupling function of scalar field $$\omega (\phi )$$ ω ( ϕ ) . In each case, we find non-trivial symmetry generator and its related first integrals of motion (conserved quantities). It is seen that due to complexity of the resulting system of Lagrange dynamical equations, it is difficult to find exact cosmological solutions except for few simple cases. It is found that in each case, the existence of Noether symmetries leads to power law form of scalar field potential and different new types of generic function. For the acquired exact solutions, we discuss the cosmology generated by these solutions graphically and discuss their physical significance which favors the accelerated expanding eras of cosmic evolution.

scholarly journals PRE-INFLATION IN THE PRESENCE OF CONFORMAL COUPLING

2004 ◽  
Vol 19 (11) ◽  
pp. 807-816
Author(s):  
APOSTOLOS KUIROUKIDIS ◽  
DEMETRIOS B. PAPADOPOULOS
Keyword(s):  
Scalar Field ◽  
Exact Solutions ◽  
Hubble Parameter ◽  
Field Potential ◽  
Critical Value ◽  
Big Bang ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Conformal Parameter ◽  
Flrw Universe

We consider a massless scalar field, conformally coupled to the Ricci scalar curvature, in the pre-inflation era of a closed FLRW Universe. The scalar field potential can be of the form of the Coleman–Weinberg one-loop potential, which is flat at the origin and drives the inflationary evolution. For positive values of the conformal parameter ξ, less than the critical value ξ c =(1/6), the model admits exact solutions with nonzero minimum scale factor and zero initial Hubble parameter. Thus these solutions can be matched smoothly to the so-called Pre-Big-Bang models. At the end of this pre-inflation era one can match inflationary solutions by specifying the form of the potential and the whole solution is of the class C(1).

scholarly journals The Noether–Bessel-Hagen symmetry approach for dynamical systems

2020 ◽  
Vol 17 (14) ◽  
pp. 2050215
Author(s):  
Zbyněk Urban ◽  
Francesco Bajardi ◽  
Salvatore Capozziello
Keyword(s):  
Scalar Field ◽  
Dynamical Systems ◽  
Harmonic Oscillator ◽  
Natural Extension ◽  
Field Potential ◽  
Lagrangian System ◽  
Noether Theorem ◽  
Symmetry Approach ◽  
External Forces ◽  
Shape Of Potential

The Noether–Bessel-Hagen theorem can be considered a natural extension of Noether Theorem to search for symmetries. Here, we develop the approach for dynamical systems introducing the basic foundations of the method. Specifically, we establish the Noether–Bessel-Hagen analysis of mechanical systems where external forces are present. In the second part of the paper, the approach is adopted to select symmetries for a given systems. In particular, we focus on the case of harmonic oscillator as a testbed for the theory, and on a cosmological system derived from scalar–tensor gravity with unknown scalar-field potential [Formula: see text]. We show that the shape of potential is selected by the presence of symmetries. The approach results particularly useful as soon as the Lagrangian of a given system is not immediately identifiable or it is not a Lagrangian system.

scholarly journals ON THE DYNAMICS OF A QUADRATIC SCALAR FIELD POTENTIAL

2009 ◽  
Vol 18 (04) ◽  
pp. 621-634 ◽  
Author(s):  
L. ARTURO UREÑA-LÓPEZ ◽  
MAYRA J. REYES-IBARRA
Keyword(s):  
Scalar Field ◽  
Autonomous System ◽  
Equations Of Motion ◽  
Scalar Potential ◽  
Field Potential ◽  
System Of Equations ◽  
New Formalism ◽  
Slow Roll ◽  
Chaotic Model ◽  
Friedmann Robertson Walker

We review the attractor properties of the simplest chaotic model of inflation, in which a minimally coupled scalar field is endowed with a quadratic scalar potential. The equations of motion in a flat Friedmann–Robertson–Walker universe are written as an autonomous system of equations, and the solutions of physical interest appear as critical points. This new formalism is then applied to the study of inflation dynamics, in which we can go beyond the known slow-roll approximation.

scholarly journals A Riccati equation based approach to isotropic scalar field cosmologies

2014 ◽  
Vol 23 (07) ◽  
pp. 1450063 ◽  
Author(s):  
Tiberiu Harko ◽  
Francisco S. N. Lobo ◽  
M. K. Mak
Keyword(s):  
Scalar Field ◽  
Evolution Equation ◽  
Interaction Potential ◽  
Arbitrary Function ◽  
Field Potential ◽  
Type Equation ◽  
Scalar Fields ◽  
Cosmological Models ◽  
Late Time ◽  
Field Equations

Gravitationally coupled scalar fields ϕ, distinguished by the choice of an effective self-interaction potential V(ϕ), simulating a temporarily nonvanishing cosmological term, can generate both inflation and late time acceleration. In scalar field cosmological models the evolution of the Hubble function is determined, in terms of the interaction potential, by a Riccati type equation. In the present work, we investigate scalar field cosmological models that can be obtained as solutions of the Riccati evolution equation for the Hubble function. Four exact integrability cases of the field equations are presented, representing classes of general solutions of the Riccati evolution equation. The solutions correspond to cosmological models in which the Hubble function is proportional to the scalar field potential plus a linearly decreasing function of time, models with the time variation of the scalar field potential proportional to the potential minus its square, models in which the potential is the sum of an arbitrary function and the square of the function integral, and models in which the potential is the sum of an arbitrary function and the derivative of its square root, respectively. The cosmological properties of all models are investigated in detail, and it is shown that they can describe the inflationary or the late accelerating phase in the evolution of the universe.

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