scholarly journals Hamiltonian Formalism of Bianchi Type I Model for Perfect Fluid

2021 ◽  
Author(s):  
Alokananda Kar ◽  
Shouvik Sadhukhan
Keyword(s):  
Scalar Field ◽  
Perfect Fluid ◽  
Bianchi Type ◽  
Hamiltonian Formalism ◽  
Big Bang ◽  
Type I ◽  
Scale Factors ◽  
Anisotropic Expansion ◽  
Large Anisotropy

We propose the Hamiltonian formalism of Bianchi type 1 cosmological model for perfect fluid. We have considered both the equation of state parameter ω and the cosmological constant Λ as the function of volume V(t) which is defined by the product of three scale factors of the Bianchi type 1 line element. We propose a Lagrangian for the anisotropic Bianchi type-1 model in view of a variable mass moving in a variable potential . We can decompose the anisotropic expansion in terms of expansion and shearing motion by Lagrangian mechanism. We have considered a canonical transformation from expanding scale factor to scalar field ø which helps us to give the proper classical definition of that scalar field in terms of scale factors of the mentioned model. This definition helps us to explain the cosmological inflation. We have used large anisotropy(as in the cases of Bianchi models) and proved that cosmic inflation is not possible in such large anisotropy. Therefore we can conclude that the extent of anisotropy is less in case of our universe. Otherwise the inflation theory which explained the limitations of Big Bang cannot be resolved.Part II is contained with some analysis of the lagrangian ; derived in Part I ; on the quintessence model.

Hamiltonian Formalism of Bianchi Type I Model for Fluid Bulk and Shearing Viscosity

2021 ◽  
Author(s):  
Shouvik Sadhukhan ◽  
Alokananda Kar
Keyword(s):  
Scalar Field ◽  
Viscous Fluid ◽  
Bianchi Type ◽  
Hamiltonian Formalism ◽  
Big Bang ◽  
Type I ◽  
Scale Factors ◽  
Anisotropic Expansion ◽  
Large Anisotropy

In this paper we will consider the cosmic fluid to be dissipating i.e it has both bulk and shearing viscosity. We propose the Hamiltonian formalism of Bianchi type 1 cosmological model for cosmic fluid which is dissipating i.e it has both shearing and bulk viscosity. We have considered both the equation of state parameter ω and the cosmological constant Λ as the function of volume V(t) which is defined by the product of three scale factors of the Bianchi type 1 line element. We propose a Lagrangian for the anisotropic Bianchi type-1 model in view of a variable mass moving in a variable potential . We can decompose the anisotropic expansion of Bianchi type 1 in terms of expansion and shearing motion by Lagrangian mechanism. We have considered a canonical transformation from expanding scale factor to scalar field ø which helps us to give the proper classical definition of that scalar field in terms of scale factors of the mentioned model. By this transformation we can express the mass to be moving in a scalar potential field. This definition helps us to explain the nature of expansion of universe during cosmological inflation. We have used large anisotropy(as in the cases of Bianchi models) and proved that cosmic inflation is not possible in such large anisotropy. Therefore we can conclude that the extent of anisotropy is less in case of our universe. Otherwise the inflation theory which explained the limitations of Big Bang cannot be resolved. In the case of bulk and shearing viscous fluid we get the solution of damped harmonic oscillator after the cosmological inflation.Part I contains the calculations of bulk viscous fluids and Part II contains the calculations of bulk and shearing viscous fluid.At the end we have also provided the relation of shearing and expansion.Part III will give the approximation of low viscosity to solve the viscous fluid problem.

scholarly journals Decoupling of the general scalar field mode and the solution space for Bianchi type I and V cosmologies coupled to perfect fluid sources

2006 ◽  
Vol 47 (4) ◽  
pp. 042505 ◽  
Author(s):  
T. Christodoulakis ◽  
Th. Grammenos ◽  
Ch. Helias ◽  
P. G. Kevrekidis ◽  
A. Spanou
Keyword(s):  
Scalar Field ◽  
Perfect Fluid ◽  
Bianchi Type ◽  
Solution Space ◽  
Type I ◽  
Field Mode ◽  
Bianchi Type I ◽  
General Scalar ◽  
Fluid Sources

scholarly journals Anisotropic quantum cosmology with minimally coupled scalar field

2019 ◽  
Vol 34 (34) ◽  
pp. 1950283 ◽  
Author(s):  
Saumya Ghosh ◽  
Sunandan Gangopadhyay ◽  
Prasanta K. Panigrahi
Keyword(s):  
Scalar Field ◽  
Wave Packet ◽  
Quantum Cosmology ◽  
Hamiltonian Formalism ◽  
Big Bang ◽  
Type I ◽  
The Big Bang ◽  
The Universe ◽  
Big Bang Singularity

In this paper, we perform the Wheeler–DeWitt quantization for Bianchi type I anisotropic cosmological model in the presence of a scalar field minimally coupled to the Einstein–Hilbert gravity theory. We also consider the cosmological (perfect) fluid to construct the matter sector of the model whose dynamics plays the role of time. After obtaining the Wheeler–DeWitt equation from the Hamiltonian formalism, we then define the self-adjointness relations properly. Doing that, we proceed to get a solution for the Wheeler–DeWitt equation and construct a well-behaved wave function for the universe. The wave packet is next constructed from a superposition of the wave functions with different energy eigenvalues together with a suitable weight factor which renders the norm of the wave packet finite. It is then concluded that the Big-Bang singularity can be removed in the context of quantum cosmology.

scholarly journals Mesonic Stiff Fluid Distribution in Bianchi Type Space-Times

2007 ◽  
Vol 14 (2) ◽  
pp. 84-89 ◽  
Author(s):  
G. Mohanty ◽  
S. K. Sahu ◽  
P. K. Sahoo
Keyword(s):  
Scalar Field ◽  
Perfect Fluid ◽  
Bianchi Type ◽  
Fluid Distribution ◽  
Type I ◽  
Stiff Fluid ◽  
Geometrical Properties ◽  
Zero Mass ◽  
Type V ◽  
Bianchi Type V

The distributions of stiff perfect fluid coupled with zero mass scalar field in LRS Bianchi type-I & Bianchi type-V space times are investigated. Some physical and geometrical properties of the models are discussed.

Classical and quantum cosmological solutions in Bianchi type-I metric with fermionic field and relativistic fluid in Schutz’s formalism

2019 ◽  
Vol 34 (33) ◽  
pp. 1950271 ◽  
Author(s):  
Marlos O. Ribas ◽  
Fernando P. Devecchi ◽  
Gilberto M. Kremer
Keyword(s):  
Degrees Of Freedom ◽  
Bianchi Type ◽  
Hamiltonian Formalism ◽  
Inflationary Universe ◽  
Type I ◽  
Conformal Time ◽  
Fermionic Field ◽  
Bianchi Type I ◽  
Relativistic Fluid ◽  
Scale Factors

A model for an anisotropic pre-inflationary universe described by the Bianchi type-I metric is developed. A relativistic fluid of the Schutz formalism and a self-interacting fermionic field are considered as sources of the gravitational field. The classical analysis is based on the Hamiltonian formalism written in terms of the Misner variables and it is shown that the fluid degrees of freedom can be embodied by a conformal time variable. The three classical scale factors are obtained as functions of the conformal time. The quantum analysis follows from the de Broglie–Bohm formalism applied to the wave function which is a solution of the Wheeler–DeWitt equation and the three scale factors are also determined as functions of the conformal time. While the classical expressions for the scale factors show a singularity when the conformal time vanishes, their quantum expressions exhibit bouncing behavior. It is possible to adjust the behavior of the classical and quantum scale factors as functions of the conformal time so that they have a common isotropic behavior at late times with a dilution of the quantum effects.

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