scholarly journals Modified Hamiltonian Formalism for Regge-Teitelboim Cosmology

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Pinaki Patra ◽  
Md. Raju ◽  
Gargi Manna ◽  
Jyoti Prasad Saha
Keyword(s):  
Cosmological Model ◽  
Tangent Bundle ◽  
Dynamical Equation ◽  
Hamiltonian Formalism ◽  
Equation Of Motion ◽  
Scale Factor ◽  
Correct Equation ◽  
Higher Derivative ◽  
Alternative Approach ◽  
Tangent Manifold

The Ostrogradski approach for the Hamiltonian formalism of higher derivative theory is not satisfactory because the Lagrangian cannot be viewed as a function on the tangent bundle to coordinate manifold. In this paper, we have used an alternative approach which leads directly to the Lagrangian which, being a function on the tangent manifold, gives correct equation of motion; no new coordinate variables need to be added. This approach can be used directly to the singular (in Ostrogradski sense) Lagrangian. We have used this method for the Regge-Teitelboim (RT) minisuperspace cosmological model. We have obtained the Hamiltonian of the dynamical equation of the scale factor of RT model.

scholarly journals Generalized F(R, T) cosmological models with fermionic fields

2021 ◽  
Vol 2090 (1) ◽  
pp. 012063
Author(s):  
Koblandy Yerzhanov ◽  
Gulnur Bauyrzhan ◽  
Ratbay Myrzakulov
Keyword(s):  
Mathematical Model ◽  
Cosmological Model ◽  
Main Idea ◽  
Scale Factor ◽  
Specific Form ◽  
Fermion Field ◽  
Fermionic Fields ◽  
Particular Solution ◽  
The Universe ◽  
Symmetry Method

Abstract We investigated the gravity model F (R, T), which interacts with a fermion field in a uniform and isotropic at spacetime FLRW. The main idea and purpose of the work donewas to create a mathematical model and find a particular solution for the scale factor a, since it describes the dynamics of the evolution of the Universe. The solutions for this universe are obtained using the Noether symmetry method. With its help, a specific form of the Lagrangian is obtained. And the possible types of the scale factor were found. The evolution of the resulting cosmological model has been investigated.

scholarly journals AdS backgrounds and induced gravity

2019 ◽  
Vol 34 (38) ◽  
pp. 2050057
Author(s):  
Hai Lin ◽  
Gaurav Narain
Keyword(s):  
Scalar Field ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Equation Of Motion ◽  
Induced Gravity ◽  
Expectation Value ◽  
Higher Derivative ◽  
Gravity Theories ◽  
Fluctuation Fields ◽  
Ads Geometry

In this paper, we look for AdS solutions to generalized gravity theories in the bulk in various spacetime dimensions. The bulk gravity action includes the action of a non-minimally coupled scalar field with gravity, and a higher-derivative action of gravity. The usual Einstein–Hilbert gravity is induced when the scalar acquires a nonzero vacuum expectation value. The equation of motion in the bulk shows scenarios where AdS geometry emerges on-shell. We further obtain the action of the fluctuation fields on the background at quadratic and cubic orders.

Effect of weak nonlinearities on the plane waves in a plasma stream

1976 ◽  
Vol 54 (1) ◽  
pp. 39-47 ◽  
Author(s):  
S. R. Seshadri
Keyword(s):  
Plane Waves ◽  
Equation Of Motion ◽  
Wave Number ◽  
Plasma Stream ◽  
Electromagnetic Mode ◽  
Correct Equation ◽  
Long Time ◽  
Modulational Stability ◽  
The Waves ◽  
Slow Modulation

The effect of weak nonlinearities on the monochromatic plane waves in a cold infinite plasma stream is investigated for the case in which the waves are progressing parallel to the drift velocity. The fast and the slow space-charge waves undergo amplitude-dependent frequency and wave number shifts. There is a long time slow modulation of the amplitude of the electromagnetic mode which becomes unstable to this nonlinear wave modulation. The importance of using the relativistically correct equation of motion for predicting correctly the modulational stability of the electromagnetic mode is pointed out.

scholarly journals Brans - Dicke Cosmology with Causal Viscous Fluid

1996 ◽  
Vol 49 (5) ◽  
pp. 899 ◽  
Author(s):  
N Banerjee ◽  
A Beesham
Keyword(s):  
Scalar Field ◽  
Cosmological Model ◽  
Viscous Fluid ◽  
Exact Solutions ◽  
Power Function ◽  
Causal Theory ◽  
Scale Factor ◽  
Scalar Tensor Theory ◽  
Equilibrium Thermodynamics ◽  
Tensor Theory

Exact solutions for the spatially flat (k = 0) Robertson–Walker cosmological model in Brans–Dicke scalar tensor theory have been obtained in the presence of a causal viscous fluid. It is found that if the scale factor is a power function of the scalar field, then solutions can be obtained in the full causal theory but not in the truncated theory of non-equilibrium thermodynamics.

scholarly journals QUANTUM EFFECTS AND STABILITY OF CHAMELEON COSMOLOGY

2004 ◽  
Vol 19 (17) ◽  
pp. 1273-1280 ◽  
Author(s):  
SHIN'ICHI NOJIRI ◽  
SERGEI D. ODINTSOV
Keyword(s):  
Quantum Effects ◽  
Equation Of Motion ◽  
Matter Density ◽  
Accelerated Expansion ◽  
Conformal Anomaly ◽  
Tensor Theory ◽  
Higher Derivative ◽  
Expansion Of The Universe ◽  
The Universe ◽  
Principal Possibility

One possibility to explain the current accelerated expansion of the universe may be related with the presence of cosmologically evolving scalar whose mass depends on the local matter density (chameleon cosmology). We point out that matter quantum effects in such scalar–tensor theory produce the chameleon scalar field dependent conformal anomaly. Such conformal anomaly adds higher derivative terms to chameleon field equation of motion. As a result, the principal possibility for instabilities appears. These instabilities seem to be irrelevant at small curvature but may become dangerous in the regions where gravitational field is strong.

The Wheeler–Dewitt Equation for the Superstring World Sheet

1997 ◽  
Vol 06 (01) ◽  
pp. 91-105 ◽  
Author(s):  
M. D. Pollock
Keyword(s):  
Black Hole ◽  
Ground State ◽  
Total Mass ◽  
Equation Of Motion ◽  
Schwarzschild Black Hole ◽  
World Sheet ◽  
Integral Expression ◽  
Higher Derivative ◽  
The World ◽  
The Universe

The Wheeler–DeWitt equation for the wave function ψ is obtained from the two-dimensional world-sheet action for the bosonic string and the superstring, including higher-derivative terms, as the Schrödinger equation i ∂ ψ/ ∂τ = V(τ)ψ. The potential is given by the rate at which the world-sheet area is swept out, V(τ) = dA(τ)/dτ, and is positive semi-definite, allowing the existence of a ground state, corresponding to the absence of the string, with a non-vanishing probability density ψ ψ*. Integration of this equation yields the solution [Formula: see text], where [Formula: see text] is the action, minus the higher-derivative terms [Formula: see text] (and terms involving ∊ab in the case of the superstring), which, however, are constrained to vanish semi-classically, being constructed from the square of the equation of motion for the bosonic coordinates XA derived from [Formula: see text] alone. This path-integral expression for ψ is consistent with the operator replacements for the canonical momenta used in its derivation, and forms the basis of the approach due to Polyakov of summing over random surfaces. Comparison is made with the Schrödinger equations derived previously from the reduced, four-dimensional effective action for the heterotic superstring, and for the Schwarzschild black hole (by Tomimatsu), where the potential is also positive semi-definite, being (twice) the total mass of the Universe and the mass of the black hole, respectively, showing the unity of the method.

scholarly journals Electromagnetic field with induced massive term: Case with scalar field

Open Physics ◽  
2011 ◽  
Vol 9 (5) ◽  
Author(s):  
Yuri Rybakov ◽  
Georgi Shikin ◽  
Yuri Popov ◽  
Bijan Saha
Keyword(s):  
Electromagnetic Field ◽  
Field Equation ◽  
Scalar Field ◽  
Cosmological Model ◽  
Bianchi Type ◽  
Rest Mass ◽  
Additional Term ◽  
Equation Of Motion ◽  
Massless Scalar ◽  
Type I

AbstractWe consider an interacting system of massless scalar and electromagnetic fields, with the Lagrangian explicitly depending on the electromagnetic potentials, i.e., interaction with broken gauge invariance. The Lagrangian for interaction is chosen in such a way that the electromagnetic field equation acquires an additional term, which in some cases is proportional to the vector potential of the electromagnetic field. This equation can be interpreted as the equation of motion of photon with induced nonzero rest-mass. This system of interacting fields is considered within the scope of Bianchi type-I (BI) cosmological model. It is shown that, as a result of interaction the isotropization process of the expansion takes place.

scholarly journals Direct calculation of length contraction and clock retardation

2015 ◽  
pp. 49-58 ◽  
Author(s):  
D.V. Redzic
Keyword(s):  
Electromagnetic Field ◽  
Causal Effect ◽  
Direct Calculation ◽  
Equation Of Motion ◽  
Uniform Motion ◽  
Correct Equation ◽  
Length Contraction ◽  
Inertial Frames ◽  
Electromagnetic Models ◽  
Dynamical Change

For simple electromagnetic models of a rod and a clock, a change of shape of a rod and of the rate of clock when they are set in uniform motion is calculated exactly, employing the correct equation of motion of a charged particle in electromagnetic field and the universal boostability assumption. Thus it is demonstrated that, for the simple system considered, the length contraction and clock retardation can be interpreted as dynamical cause-and-effect phenomena, and not as kinematical effects as usually construed in conventional presentations of Special Relativity. It is argued that the perspective relativistic change of an object (corresponding to observations from two inertial frames), while certainly being an a causal effect, has a dynamical content in the sense that it is tantamount to an actual dynamical change of the object in one frame.

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