126422575
Applying the 'reverse engineering' method in certain cosmologies with scalar field
Modern cosmology is in search for a solution to explain the recent discovered “cosmic-acceleration” effect [1], [2] i.e. the actual universe is in an accelerated inflation period. One of the solutions to this problem is to trigger this acceleration through one or more scalar fields minimally coupled to gravity (“quintessence”). Usually one solves the Friedmann equations (the Einstein equations for cosmological environment – see [3], [4]) for a certain type of potential prescribed within a theoretical background and then one obtains the time behavior of the Universe (the scale factor function R(t)) to be compared with the experimental data. Recently a different method was proposed ([5]–[7]) called today the “reverse engineering” method (REM). Here one starts with a certain type of the scale factor R(t) designed to be as close possible with the experimental data. Then, solving the Einstein-Friedmann equations one obtains the shape of the potential for the scalar field. Different versions of the theory were proposed ([6],[7]) with various final potentials bringing new physical interpretation of the theory. In a recent article [13] was done a systematic use of this method for as many possible examples of initial scale factor functions including also a generalization of REM
120435179
On the Reverse Engineering Method in Cosmologies with Non‐Minimally Coupled Scalar Field
We shall investigate the use of the so called “reverse engineering” method in reconstructing the shape of the potential in cosmologies based on a scalar field non‐minimally coupled with gravity. The main field equations (the new or modified Friedman equations) will be obtained in a cosmology with Robertson‐Walker metric. Then in a similar graphical manner as was introduced recently we shall investigate the particular case of a cosmology with exponential growth of the scale factor. This opens the route for future investigations on other examples and the general case.
120250632
Classical Gaussian bag in (1+1) general relativity
Abstract Relativistic geometric models generated by Gaussian conformally flat (1+1) metrics are considered. These metrics are depending on a fixed parameter and another variable parameter that play the role of coupling constant. It is shown that these models are of open bags where the relativistic massive particles remain confined for energies less than the rest one. By using numeric methods it is pointed out that inside of the bag the motion is close to an harmonic one. The dispersion function is also calculated for different values of the free parameter.
10985262
Doing Numerical Cosmology with the Cactus Code
The article presents some aspects concerning the construction of a new thorn for the Cactus code, a complete 3-dimensional machinery in numerical relativity. This thorn is dedicated to numerical simulations in cosmology, that means it can provide evolutions of different cosmological models, mainly based on Friedman-Robertson-Walker metric. Some numerical results are presented, testing the convergence, stability and the applicability of the code
17884328
Testing The Cactus Code On Exact Solutions Of The Einstein Field Equations
The article presents a series of numerical simulations of exact solutions of the Einstein equations performed using the Cactus code, a complete three-dimensional machinery for numerical relativity. We describe an application ("thorn") for the Cactus code that can be used for evolving a variety of exact solutions, with and without matter, including solutions used in modern cosmology for modeling the early stages of the universe. Our main purpose has been to test the Cactus code on these well-known examples, focusing mainly on the stability and convergence of the code.
2494768
Gravity, torsion, Dirac field and computer algebra using MAPLE and REDUCE
The article presents computer algebra procedures and routines applied to the study of the Dirac field on curved spacetimes. The main part of the procedures is devoted to the construction of Pauli and Dirac matrices algebra on an anholonomic orthonormal reference frame. Then these procedures are used to compute the Dirac equation on curved spacetimes in a sequence of special dedicated routines. A comparative review of such procedures obtained for two computer algebra platforms (REDUCE + EXCALC and MAPLE + GRTensorII) is carried out. Applications for the calculus of Dirac equation on specific examples of spacetimes with or without torsion are pointed out.
11698036
Classical oscillators in general relativity
It is shown that in general relativity some static metrics are able to simulate oscillatory motions. Their form depends on two arbitrary real parameters which determine the specific oscillation modes. The conclusion is that these metrics can be used for new geometric models of closed or even open bags.