scholarly journals COSMOLOGICAL MODELS WITH A VARYING Λ-TERM IN LYRA'S GEOMETRY

2012 ◽  
Vol 27 (29) ◽  
pp. 1250164 ◽  
Author(s):  
V. K. SHCHIGOLEV
Keyword(s):  
Vector Field ◽  
Exact Solutions ◽  
Equations Of State ◽  
Displacement Vector ◽  
Cosmological Models ◽  
Displacement Vector Field ◽  
Varying Λ ◽  
Lyra’S Geometry ◽  
Model Equations ◽  
The Universe

Cosmological models in Lyra's geometry are constructed and investigated with the assumption of a minimal interaction of matter with the displacement vector field and the dynamical Λ-term. Exact solutions of the model equations are obtained for the different equations of state of the matter, that fills the universe, and for the certain assumptions on the decaying law for Λ.

scholarly journals Inhomogeneous cosmology with quasi-vacuum effective equation of state on Lyra manifold

2016 ◽  
Vol 4 (1) ◽  
pp. 15 ◽  
Author(s):  
Victor Shchigolev
Keyword(s):  
Equation Of State ◽  
Displacement Vector ◽  
Cosmological Term ◽  
Cosmological Models ◽  
Minimal Coupling ◽  
Effective Equation ◽  
Displacement Vector Field ◽  
Varying Λ ◽  
Lyra’S Geometry ◽  
Model Equations

<p>A class of inhomogeneous Lemaître-Tolman cosmological models is obtained in the context of Lyra’s geometry. Cosmological models in Lyra’s geometry are studied under the condition of the minimal coupling of matter with the displacement vector field and the varying Λ term. Exact solutions to the model equations are obtained subject to the quasi-vacuum effective equation of state. As a result, the displacement field as well as the cosmological term can be expressed in terms of the energy density of matter. The rate of expansion and the deceleration parameter of the model are also studied</p>

A DARKLESS SPACE–TIME

2008 ◽  
Vol 17 (02) ◽  
pp. 275-299 ◽  
Author(s):  
ANGELO TARTAGLIA ◽  
MONICA CAPONE
Keyword(s):  
Vector Field ◽  
Displacement Vector ◽  
Lagrange Equation ◽  
Empty Space ◽  
Space Time ◽  
Accelerated Expansion ◽  
Displacement Vector Field ◽  
The One ◽  
Internal Viscosity ◽  
The Universe

In cosmology it has become usual to introduce new entities as dark matter and dark energy in order to explain otherwise unexplained observational facts. Here, we propose a different approach treating space–time as a continuum endowed with properties similar to those of ordinary material continua, such as internal viscosity and strain distributions originated by defects in the texture. A Lagrangian modeled on the one valid for simple dissipative phenomena in fluids is built and used for empty space–time. The internal "viscosity" is shown to correspond to a four-vector field. The vector field is shown to be connected with the displacement vector field induced by a point defect in a four-dimensional continuum. Using the known symmetry of the universe, assuming the vector field to be divergenceless and solving the corresponding Euler–Lagrange equation, we directly obtain inflation and a phase of accelerated expansion of space–time. The only parameter in the theory is the "strength" of the defect. We show that it is possible to fix it in such a way as to also quantitatively reproduce the acceleration of the universe. We have finally verified that the addition of ordinary matter does not change the general behavior of the model and that the proper Newtonian limit exists.

Modified f(R,T) cosmology with observational constraints in Lyra’s geometry

2019 ◽  
Vol 17 (01) ◽  
pp. 2050001
Author(s):  
Dinesh Chandra Maurya
Keyword(s):  
Vector Field ◽  
Displacement Vector ◽  
Observational Constraints ◽  
Data Sets ◽  
Type I ◽  
Energy Parameters ◽  
Displacement Vector Field ◽  
Constant Displacement ◽  
Lyra’S Geometry ◽  
Best Fit

In this paper, we have investigated modified [Formula: see text] cosmological models with observational constraints in Lyra’s geometry. We have studied the models in two cases: in the first one it is taken as constant displacement vector field and in second case it is taken as time-dependent. We have established a relationship among energy parameters [Formula: see text], respectively, called as matter, anisotropy and dark energy (DE) density parameters in Bianchi type-I space-time in Lyra’s geometry. We have compared our models with observational data sets with union 2.1 compilation SNe Ia data and [Formula: see text] data sets and have found best fit values of various energy parameters for [Formula: see text]. We have found that the model with constant displacement vector field is the best fit to the study of the whole evolution of the model and the gauge function [Formula: see text] of Lyra geometry behaves like a DE candidate. Also, the various physical and kinematical parameters have been studied in this study.

An obstacle problem for elliptic membrane shells

2018 ◽  
Vol 24 (5) ◽  
pp. 1503-1529 ◽  
Author(s):  
Philippe G. Ciarlet ◽  
Cristinel Mardare ◽  
Paolo Piersanti
Keyword(s):  
Vector Field ◽  
Asymptotic Analysis ◽  
Obstacle Problem ◽  
Displacement Vector ◽  
Middle Surface ◽  
Two Dimensional ◽  
Displacement Vector Field ◽  
Membrane Shells ◽  
Signorini Condition ◽  
Confinement Condition

Our objective is to identify two-dimensional equations that model an obstacle problem for a linearly elastic elliptic membrane shell subjected to a confinement condition expressing that all the points of the admissible deformed configurations remain in a given half-space. To this end, we embed the shell into a family of linearly elastic elliptic membrane shells, all sharing the same middle surface [Formula: see text], where [Formula: see text] is a domain in [Formula: see text] and [Formula: see text] is a smooth enough immersion, all subjected to this confinement condition, and whose thickness [Formula: see text] is considered as a “small” parameter approaching zero. We then identify, and justify by means of a rigorous asymptotic analysis as [Formula: see text] approaches zero, the corresponding “limit” two-dimensional variational problem. This problem takes the form of a set of variational inequalities posed over a convex subset of the space [Formula: see text]. The confinement condition considered here considerably departs from the Signorini condition usually considered in the existing literature, where only the “lower face” of the shell is required to remain above the “horizontal” plane. Such a confinement condition renders the asymptotic analysis substantially more difficult, however, as the constraint now bears on a vector field, the displacement vector field of the reference configuration, instead of on only a single component of this field.

scholarly journals A distance to dose difference tool for estimating the required spatial accuracy of a displacement vector field

2011 ◽  
Vol 38 (5) ◽  
pp. 2318-2323 ◽  
Author(s):  
Nahla K. Saleh-Sayah ◽  
Elisabeth Weiss ◽  
Francisco J. Salguero ◽  
Jeffrey V. Siebers
Keyword(s):  
Vector Field ◽  
Displacement Vector ◽  
Spatial Accuracy ◽  
Displacement Vector Field ◽  
Dose Difference

Cosmological Models in Lyra Geometry with Linearly Varying Deceleration Parameter

2018 ◽  
Author(s):  
Kalyani Desikan
Keyword(s):  
Exact Solutions ◽  
Displacement Field ◽  
Deceleration Parameter ◽  
Lyra Geometry ◽  
Cosmological Models ◽  
Time Dependent ◽  
Linearly Varying Deceleration Parameter ◽  
Frw Model ◽  
Time Periods ◽  
The Universe

Cosmological models with linearly varying deceleration parameter in the cosmological theory based on Lyra&rsquo;s geometry have been discussed. Exact solutions have been obtained for a spatially flat FRW model by considering a time dependent displacement field. We have also obtained the time periods during which the universe undergoes decelerated and accelerated expansions for a matter-dominated universe.

RECONSTRUCTION OF 5D COSMOLOGICAL MODELS FROM THE EQUATION OF STATE OF DARK ENERGY

2006 ◽  
Vol 15 (02) ◽  
pp. 215-224 ◽  
Author(s):  
LI XIN XU ◽  
HONG YA LIU ◽  
CHENG WU ZHANG
Keyword(s):  
Dark Energy ◽  
Equation Of State ◽  
Arbitrary Function ◽  
Equations Of State ◽  
Cosmological Models ◽  
Cosmological Solutions ◽  
The Universe

We consider a class of five-dimensional cosmological solutions which contain two arbitrary function μ(t) and ν(t). We find that the arbitrary function μ(t) contained in the solutions can be rewritten in terms of the redshift z as a new arbitrary function f(z). We further show that this new arbitrary function f(z) can be solved for four known parameterized equations of state of dark energy. Then 5D models can be reconstructed and the evolution of the density and deceleration parameters of the universe can be determined.

Sign in / Sign up

Export Citation Format

Share Document