Cosmology with fermionic sources and relativistic fluid in Schutz’s formalism: Classical and quantum solutions

2017 ◽  
Vol 32 (40) ◽  
pp. 1750220 ◽  
Author(s):  
Marlos O. Ribas ◽  
Fernando P. Devecchi ◽  
Gilberto M. Kremer
Keyword(s):  
Degrees Of Freedom ◽  
Hamiltonian Formalism ◽  
Expected Value ◽  
Scale Factor ◽  
Inflationary Universe ◽  
Conformal Time ◽  
Classical Analysis ◽  
Relativistic Fluid ◽  
The Universe ◽  
Quantum Solution

In this work, a model for the pre-inflationary universe is developed where the sources of the gravitational field are a relativistic fluid and a self-interacting fermionic field. The inclusion of the relativistic fluid is based on Schutz’s model. From the classical analysis based on the Hamiltonian formalism, it is shown that the fluid degrees of freedom can be embodied by a conformal time variable and an expression for the scale factor as function of the conformal time is obtained. From the Wheeler–DeWitt equation, the expected value for the scale factor as function of the conformal time is determined. It is shown that contrary to the classical solution, the expected value of the scale factor does not have a singularity, since it is preceded by a contracted phase up to a minimum value from which the universe begins to expand. Furthermore, from the plots of the classical and quantum solutions for the scale factor as functions of the conformal time it is shown that a decoherence of the quantum solution occurs for late times and both solutions coincide.

Quantum Bohmian description of a primordial universe with Fermionic and Bosonic sources

2021 ◽  
pp. 2150103
Author(s):  
Marlos O. Ribas ◽  
Fernando P. Devecchi ◽  
Gilberto M. Kremer
Keyword(s):  
Scalar Field ◽  
Degrees Of Freedom ◽  
Hamiltonian Formalism ◽  
Bohmian Mechanics ◽  
Smooth Transition ◽  
Conformal Time ◽  
Classical Analysis ◽  
Fermionic Field ◽  
Relativistic Fluid ◽  
The Universe

We present a model of an early universe where the sources of gravitational effects are a scalar field, a relativistic fluid based on Schutz’s model and a self-interacting fermionic field. From the classical analysis based on the Hamiltonian formalism we show that the scale factor of the universe can be expressed in terms of a conformal time that emerges from the fluid’s degrees of freedom. From the Wheeler–DeWitt equation, a wave packet solution as function of the conformal time is determined. It is shown that the combination of the scalar and the fermionic field furnishes a consistent quantum regime and a smooth transition to the classical description, working with the aid of the Bohmian mechanics and in particular with the concept of quantum potential. The influence of the presence of the scalar field is also 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.

scholarly journals Hamiltonian formalism for nonlocal gravity models

2022 ◽  
Author(s):  
Pawan Joshi ◽  
Utkarsh Kumar ◽  
Sukanta Panda
Keyword(s):  
Ricci Tensor ◽  
Degrees Of Freedom ◽  
Hamiltonian Formalism ◽  
Riemann Tensor ◽  
Ricci Scalar ◽  
Gravity Models ◽  
Lagrangian Formalism ◽  
Acceleration Of The Universe ◽  
Nonlocal Action ◽  
The Universe

Nonlocal gravity models are constructed to explain the current acceleration of the universe. These models are inspired by the infrared correction appearing in Einstein–Hilbert action. Here, we develop the Hamiltonian formalism of a nonlocal model by considering only terms to quadratic order in Riemann tensor, Ricci tensor and Ricci scalar. We show how to count degrees of freedom using Hamiltonian formalism including Ricci tensor and Ricci scalar terms. In this model, we have also worked out with a choice of a nonlocal action which has only two degrees of freedom equivalent to GR. Finally, we find the existence of additional constraints in Hamiltonian required to remove the ghosts in our full action. We also compare our results with that of obtained using Lagrangian formalism.

THE STABILITY OF THE MINISUPERSPACE

1993 ◽  
Vol 08 (36) ◽  
pp. 3413-3427 ◽  
Author(s):  
ATUSHI ISHIKAWA ◽  
TOSHIKI ISSE
Keyword(s):  
Scalar Field ◽  
Early Universe ◽  
Degrees Of Freedom ◽  
Einstein Gravity ◽  
Scale Factor ◽  
Planck Length ◽  
Inhomogeneous Wave ◽  
The Stability ◽  
The Universe ◽  
Wave Modes

The stability of the minisuperspace model of the early universe is studied by solving the Wheeler-DeWitt equation numerically. We consider a system of Einstein gravity with a scalar field. When we solve the Wheeler-DeWitt equation, we pick up some inhomogeneous wave modes from infinite wave modes adequately: degrees of freedom of the superspace are restricted to finite. We show that the minisuperspace is stable when a scale factor (a) of the universe is a few times larger than the Planck length, while it becomes unstable when a is comparable to the Planck length.

scholarly journals IMPLICATIONS OF A QUANTUM MECHANICAL TREATMENT OF THE UNIVERSE

1998 ◽  
Vol 13 (05) ◽  
pp. 347-351 ◽  
Author(s):  
MURAT ÖZER
Keyword(s):  
Quantum Mechanics ◽  
Wave Packet ◽  
Early Universe ◽  
Mechanical Treatment ◽  
Correspondence Principle ◽  
Scale Factor ◽  
Quantum Mechanical ◽  
Quantum Mechanical Treatment ◽  
The Standard Model ◽  
The Universe

We attempt to treat the very early Universe according to quantum mechanics. Identifying the scale factor of the Universe with the width of the wave packet associated with it, we show that there cannot be an initial singularity and that the Universe expands. Invoking the correspondence principle, we obtain the scale factor of the Universe and demonstrate that the causality problem of the standard model is solved.

DARK GEOMETRY

2004 ◽  
Vol 13 (10) ◽  
pp. 2275-2279 ◽  
Author(s):  
J. A. R. CEMBRANOS ◽  
A. DOBADO ◽  
A. L. MAROTO
Keyword(s):  
Dark Matter ◽  
Extra Dimensions ◽  
Degrees Of Freedom ◽  
Planck Scale ◽  
Point Of View ◽  
Missing Mass ◽  
Brane Worlds ◽  
Mass Problem ◽  
Extra Space ◽  
The Universe

Extra-dimensional theories contain additional degrees of freedom related to the geometry of the extra space which can be interpreted as new particles. Such theories allow to reformulate most of the fundamental problems of physics from a completely different point of view. In this essay, we concentrate on the brane fluctuations which are present in brane-worlds, and how such oscillations of the own space–time geometry along curved extra dimensions can help to resolve the Universe missing mass problem. The energy scales involved in these models are low compared to the Planck scale, and this means that some of the brane fluctuations distinctive signals could be detected in future colliders and in direct or indirect dark matter searches.

scholarly journals A New Inflationary Universe Scenario with Inhomogeneous Quantum Vacuum

2018 ◽  
Vol 2018 ◽  
pp. 1-15
Author(s):  
Yilin Chen ◽  
Jin Wang
Keyword(s):  
Green’S Function ◽  
Potential Barrier ◽  
Green's Function ◽  
Inflationary Universe ◽  
Quantum Vacuum ◽  
Vacuum Fluctuations ◽  
Inflationary Scenario ◽  
Slowing Down ◽  
The Universe ◽  
Inhomogeneous Quantum

We investigate the quantum vacuum and find that the fluctuations can lead to the inhomogeneous quantum vacuum. We find that the vacuum fluctuations can significantly influence the cosmological inhomogeneity, which is different from what was previously expected. By introducing the modified Green’s function, we reach a new inflationary scenario which can explain why the Universe is still expanding without slowing down. We also calculate the tunneling amplitude of the Universe based on the inhomogeneous vacuum. We find that the inhomogeneity can lead to the penetration of the Universe over the potential barrier faster than previously thought.

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 Augustine of Hippo’s Philosophy of Time Meets General Relativity

KronoScope ◽  
2014 ◽  
Vol 14 (1) ◽  
pp. 71-89 ◽  
Author(s):  
Ettore Minguzzi
Keyword(s):  
General Relativity ◽  
Cosmological Model ◽  
Degrees Of Freedom ◽  
Big Bang ◽  
Null Hypersurface ◽  
Philosophy Of Time ◽  
The Big Bang ◽  
The Universe

Abstract This paper proposes a cosmological model that uses a causality argument to solve the homogeneity and entropy problems of cosmology. In this model, a chronology violating region of spacetime causally precedes the remainder of the Universe, and a theorem establishes the existence of time functions precisely outside the chronology violating region. This model is shown to nicely reproduce Augustine of Hippo’s thought on time and the beginning of the Universe. In the model, the spacelike boundary representing the Big Bang is replaced by a null hypersurface at which the gravitational degrees of freedom are almost frozen while the matter and radiation content is highly homogeneous and thermalized.

scholarly journals Inflation with explicit parametric connection between general relativity and scalar–tensor gravity

2018 ◽  
Vol 33 (28) ◽  
pp. 1850161 ◽  
Author(s):  
I. V. Fomin ◽  
S. V. Chervon
Keyword(s):  
General Relativity ◽  
Scale Factor ◽  
Cosmological Inflation ◽  
The Difference ◽  
The Universe

We consider the cosmological inflation with scalar–tensor gravity and compare it with standard inflation based on General Relativity. The difference is determined by the value of the parameter [Formula: see text]. This approach is associated with using the special ansatz which links a function that defines a type of gravity with a scale factor of the universe.

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