scholarly journals AN EARLY UNIVERSE MODEL WITH STIFF MATTER AND A COSMOLOGICAL CONSTANT

2011 ◽  
Vol 03 ◽  
pp. 254-265 ◽  
Author(s):  
G. OLIVEIRA-NETO ◽  
G. A. MONERAT ◽  
E. V. CORRÊA SILVA ◽  
C. NEVES ◽  
L. G. FERREIRA FILHO
Keyword(s):  
Cosmological Constant ◽  
Perfect Fluid ◽  
Scale Factor ◽  
Initial Singularity ◽  
Discrete Energy ◽  
Classical Level ◽  
Stiff Matter ◽  
Expectation Value ◽  
Variational Formalism ◽  
Friedmann Robertson Walker

In the present work, we study the quantum cosmology description of a Friedmann-Robertson-Walker model in the presence of a stiff matter perfect fluid and a negative cosmological constant. We work in the Schutz's variational formalism and the spatial sections have constant negative curvature. We quantize the model and obtain the appropriate Wheeler-DeWitt equation. In this model the states are bounded therefore we compute the discrete energy spectrum and the corresponding eigenfunctions. In the present work, we consider only the negative eigenvalues and their corresponding eigenfunctions. This choice implies that the energy density of the perfect fluid is negative. A stiff matter perfect fluid with this property produces a model with a bouncing solution, at the classical level, free from an initial singularity. After that, we use the eigenfunctions in order to construct wave packets and evaluate the time-dependent expectation value of the scale factor. We find that it oscillates between maximum and minimum values. Since the expectation value of the scale factor never vanishes, we confirm that this model is free from an initial singularity, also, at the quantum level.

scholarly journals CANONICAL TRANSFORMATION FOR STIFF MATTER MODELS IN QUANTUM COSMOLOGY

2011 ◽  
Vol 03 ◽  
pp. 324-328 ◽  
Author(s):  
C. NEVES ◽  
G. A. MONERAT ◽  
E. V. CORRÊA SILVA ◽  
L. G. FERREIRA FILHO ◽  
G. OLIVEIRA-NETO
Keyword(s):  
Cosmological Constant ◽  
Perfect Fluid ◽  
Canonical Transformation ◽  
Quantum Cosmology ◽  
Symplectic Method ◽  
Coordinate Transformations ◽  
Stiff Matter ◽  
Variational Formalism ◽  
Quantum Operators ◽  
Friedmann Robertson Walker

In the present work we consider Friedmann-Robertson-Walker models in the presence of a stiff matter perfect fluid and a cosmological constant. We write the superhamiltonian of these models using the Schutz's variational formalism. We notice that the resulting superhamiltonians have terms that will lead to factor ordering ambiguities when they are written as quantum operators. In order to remove these ambiguities, we introduce appropriate coordinate transformations and prove that these transformations are canonical using the symplectic method.

Quantum cosmology on (k = −1)-Friedmann–Robertson–Walker Universe evolving from stiff matter era to the dust dominated one

2016 ◽  
Vol 32 (01) ◽  
pp. 1750003 ◽  
Author(s):  
Marina-Aura Dariescu ◽  
Ciprian Dariescu
Keyword(s):  
Wave Function ◽  
Quantum Cosmology ◽  
Friedmann Equation ◽  
Scale Function ◽  
Frw Universe ◽  
Classical Level ◽  
Stiff Matter ◽  
Quantum Analysis ◽  
Functional Relations ◽  
Friedmann Robertson Walker

This work is devoted to the spatially open Friedmann–Robertson–Walker (FRW) Universe evolving from the stiff matter era to the dust dominated one. Within the quantum analysis based on the Wheeler–DeWitt equation, we derive the wave function of the [Formula: see text]-FRW Universe with combined matter sources. On the classical level, one has to deal with the Friedmann equation which leads on a dependence of the scale function on time generally expressed from functional relations involving elliptic integrals.

Quantization of Friedmann-Robertson-Walker Spacetimes in the Presence of a Cosmological Constant and Stiff Matter

2013 ◽  
Vol 52 (9) ◽  
pp. 2991-3006 ◽  
Author(s):  
G. Oliveira-Neto ◽  
G. A. Monerat ◽  
E. V. Corrêa Silva ◽  
C. Neves ◽  
L. G. Ferreira Filho
Keyword(s):  
Cosmological Constant ◽  
Stiff Matter ◽  
Friedmann Robertson Walker

The effect of backreaction on inflationary Starobinsky cosmology

2017 ◽  
Vol 14 (10) ◽  
pp. 1750134 ◽  
Author(s):  
Mohammad Reza Setare ◽  
Mitra Sahraee
Keyword(s):  
Energy Momentum Tensor ◽  
Dimensional Regularization ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Momentum Tensor ◽  
Scale Factor ◽  
Quantum Energy ◽  
Expectation Value ◽  
Trace Anomaly ◽  
Friedmann Robertson Walker

In this paper, we would like to obtain the effect of the quantum backreaction on inflationary Starobinsky cosmology in spatially flat [Formula: see text]-dimensional Friedmann–Robertson–Walker universe. For this purpose, first, we obtain the vacuum expectation value of energy–momentum tensor, which is separated into two parts, UV and IR. To calculate the UV contribution, we use the WKB approximation of the mode function of the equation of motion. Since the obtained value of this contribution of the vacuum expectation value of energy–momentum tensor is divergent, we should renormalize it. Therefore, by using the dimensional regularization and introducing a counterterm action, we eliminate divergences. After that, we calculate the contributions of IR part and trace anomaly. Thus, we obtain the quantum energy density and pressure during inflation era in this model. Finally, we can find the effect of backreaction on scale factor in inflation era, which leads to the new scale factor.

scholarly journals Noncommutativity in the early universe

2017 ◽  
Vol 26 (02) ◽  
pp. 1750011 ◽  
Author(s):  
G. Oliveira-Neto ◽  
M. Silva de Oliveira ◽  
G. A. Monerat ◽  
E. V. Corrêa Silva
Keyword(s):  
Energy Spectrum ◽  
Present Model ◽  
Scale Factor ◽  
Matter Content ◽  
Quantum Level ◽  
Discrete Energy ◽  
Noncommutative Version ◽  
The Universe ◽  
Friedmann Robertson Walker ◽  
Noncommutative Parameter

In the present work, we study the noncommutative version of a quantum cosmology model. The model has a Friedmann–Robertson–Walker (FRW) geometry, the matter content is a radiative perfect fluid and the spatial sections have zero constant curvature. In this model, the scale factor takes values in a bounded domain. Therefore, its quantum mechanical version has a discrete energy spectrum. We compute the discrete energy spectrum and the corresponding eigenfunctions. The energies depend on a noncommutative parameter [Formula: see text]. We compute the scale factor expected value ([Formula: see text]) for several values of [Formula: see text]. For all of them, [Formula: see text] oscillates between maxima and minima values and never vanishes. It gives an initial indication that those models are free from singularities, at the quantum level. We improve this result by showing that if we subtract a quantity proportional to the standard deviation of [Formula: see text] from [Formula: see text], this quantity is still positive. The [Formula: see text] behavior, for the present model, is a drastic modification of the [Formula: see text] behavior in the corresponding commutative version of the present model. There, [Formula: see text] grows without limits with the time variable. Therefore, if the present model may represent the early stages of the universe, the results of the present paper give an indication that [Formula: see text] may have been, initially, bounded due to noncommutativity. We also compute the Bohmian trajectories for [Formula: see text], which are in accordance with [Formula: see text], and the quantum potential [Formula: see text]. From [Formula: see text], we may understand why that model is free from singularities, at the quantum level.

scholarly journals Can noncommutativity affect the whole history of the universe?

2017 ◽  
Vol 26 (03) ◽  
pp. 1750022 ◽  
Author(s):  
G. A. Monerat ◽  
E. V. Corrêa Silva ◽  
C. Neves ◽  
G. Oliveira-Neto ◽  
L. G. Rezende Rodrigues ◽  
...  
Keyword(s):  
Perfect Fluid ◽  
Scale Factor ◽  
Matter Content ◽  
The Other ◽  
General Situation ◽  
Canonical Variables ◽  
History Of ◽  
Frw Cosmological Model ◽  
The Universe ◽  
Friedmann Robertson Walker

We study a classical, noncommutative (NC), Friedmann–Robertson–Walker (FRW) cosmological model. The spatial sections may have positive, negative or zero constant curvatures. The matter content is a generic perfect fluid. The initial noncommutativity between some canonical variables is rewritten, such that, we end up with commutative variables and a NC parameter. Initially, we derive the scale factor dynamic equations for the general situation, without specifying the perfect fluid or the curvature of the spatial sections. Next, we consider two concrete situations: a radiation perfect fluid and dust. We study all possible scale factor behaviors, for both cases. We compare them with the corresponding commutative cases and one with the other. We obtain, some cases, where the NC model predicts a scale factor expansion which may describe the present expansion of our universe. Those cases are not present in the corresponding commutative models. Finally, we compare our model with another NC model, where the noncommutativity is between different canonical variables. We show that, in general, it leads to a scale factor behavior that is different from our model.

scholarly journals COASTING COSMOLOGIES WITH TIME DEPENDENT COSMOLOGICAL CONSTANT

1999 ◽  
Vol 14 (10) ◽  
pp. 1523-1529 ◽  
Author(s):  
LUIS O. PIMENTEL ◽  
LUZ M. DIAZ-RIVERA
Keyword(s):  
Cosmological Constant ◽  
Perfect Fluid ◽  
Gravitational Constant ◽  
Linear Expansion ◽  
Cosmological Models ◽  
Time Dependent ◽  
Expansion Factor ◽  
Fluid Matter ◽  
Friedmann Robertson Walker

The effect of a time dependent cosmological constant is considered in a family of scalar-tensor theories. Friedmann–Robertson–Walker cosmological models for vacuum and perfect fluid matter are found. They have a linear expansion factor, the so-called coasting cosmology, the gravitational "constant" decreases inversely with time; that is these models satisfy the Dirac Hypotheses. The cosmological "constant" decreases inversely with the square of time, therefore we can have a very small value for it at present time.

WAVE-FUNCTION OF AN ASYMPTOTICALLY DE SITTER UNIVERSE

2007 ◽  
Vol 16 (09) ◽  
pp. 3014-3018 ◽  
Author(s):  
L. G. FERREIRA FILHO ◽  
J. ACACIO DE BARROS ◽  
E. V. CORRÊA SILVA ◽  
G. A. MONERAT ◽  
G. OLIVEIRA-NETO ◽  
...  
Keyword(s):  
Wave Function ◽  
Cosmological Constant ◽  
Scale Factor ◽  
De Sitter ◽  
Positive Cosmological Constant ◽  
Initial Wave ◽  
Frw Model ◽  
De Sitter Universe ◽  
Friedmann Robertson Walker ◽  
Initial Wave Function

In the present work, we quantize a closed Friedmann–Robertson–Walker (FRW) model in the presence of a positive cosmological constant and radiation. It gives rise to a Wheeler–DeWitt equation for the scale factor which has the form of a Schrödinger equation for a potential with a barrier. We solve it numerically and determine the evolution of an initial wave-function.

scholarly journals EXACT INFLATIONARY SOLUTIONS

1998 ◽  
Vol 07 (03) ◽  
pp. 443-454 ◽  
Author(s):  
GABRIELLA PICCINELLI ◽  
TONATIUH MATOS ◽  
MERCED MONTESINOS-VELÁSQUEZ
Keyword(s):  
Scalar Field ◽  
Cosmological Constant ◽  
Perfect Fluid ◽  
Physical Meaning ◽  
Scale Factor ◽  
Spatial Curvature ◽  
New Class ◽  
Negative Cosmological Constant

We present a new class of exact inflationary solutions for the evolution of a universe with spatial curvature, filled with a perfect fluid, a scalar field with potential V±(ϕ) = λ(ϕ2 ± δ2)2 and a cosmological constant Λ. With the V+(ϕ) potential and a negative cosmological constant, the scale factor experiments a graceful exit. We give a brief discussion about the physical meaning of the solutions.

Weakly Ricci symmetric spacetimes

2017 ◽  
Vol 15 (01) ◽  
pp. 1850007
Author(s):  
Avik De ◽  
Pradip Majhi
Keyword(s):  
Field Equation ◽  
Cosmological Constant ◽  
Perfect Fluid ◽  
Petrov Type ◽  
Stiff Matter ◽  
Type Formula ◽  
Dark Fluid ◽  
Symmetric Spacetimes ◽  
Perfect Fluid Spacetime ◽  
Symmetric Spacetime

The objective of the present paper is to study weakly Ricci symmetric spacetimes. Among others, we prove that a weakly Ricci symmetric spacetime obeying Einstein’s field equation without cosmological constant represents stiff matter. Moreover, it is shown that the local cosmological structure of a weakly Ricci symmetric perfect fluid spacetime can be identified as Petrov type [Formula: see text], [Formula: see text] or [Formula: see text]. Next, we prove that a dust and dark fluid weakly Ricci symmetric spacetime satisfying Einstein’s field equation without cosmological constant is vacuum. Finally, we show the non-existence of radiation era in such a spacetime.

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