scholarly journals THE VALUE OF THE COSMOLOGICAL CONSTANT

2011 ◽  
Vol 20 (14) ◽  
pp. 2875-2880 ◽  
Author(s):  
JOHN D. BARROW ◽  
DOUGLAS J. SHAW
Keyword(s):  
Wave Function ◽  
Cosmological Constant ◽  
Classical Limit ◽  
Constraint Equation ◽  
Einstein Equations ◽  
Spatial Curvature ◽  
Self Consistent ◽  
Curvature Parameter ◽  
The Universe ◽  
Planck Satellite

We make the cosmological constant, Λ, into a field and restrict the variations of the action with respect to it by causality. This creates an additional Einstein constraint equation. It restricts the solutions of the standard Einstein equations and is the requirement that the cosmological wave function possess a classical limit. When applied to the Friedmann metric it requires that the cosmological constant measured today, tU, be [Formula: see text], as observed. This is the classical value of Λ that dominates the wave function of the universe. Our new field equation determines Λ in terms of other astronomically measurable quantities. Specifically, it predicts that the spatial curvature parameter of the universe is [Formula: see text], which will be tested by Planck Satellite data. Our theory also creates a new picture of self-consistent quantum cosmological history.

scholarly journals INFLATION INDUCED BY VACUUM ENERGY AND GRACEFUL EXIT FROM IT

2001 ◽  
Vol 16 (40) ◽  
pp. 2545-2555 ◽  
Author(s):  
E. PAPANTONOPOULOS ◽  
I. PAPPA
Keyword(s):  
Cosmological Constant ◽  
Vacuum Energy ◽  
Einstein Equations ◽  
Time Dependent ◽  
Brane Cosmology ◽  
Fast Growing ◽  
Early Epoch ◽  
The Universe ◽  
Natural Way

Motivated by brane cosmology, we solve the Einstein equations with a time-dependent cosmological constant. Assuming that at an early epoch the vacuum energy scales as 1/log t, we show that the universe passes from a fast growing phase (inflation) to an expanding phase in a natural way.

QUANTUM COSMOLOGY IN ANISOTROPIC COSMOLOGICAL MODELS WITH SCALAR–TENSOR THEORIES

2001 ◽  
Vol 10 (06) ◽  
pp. 943-956
Author(s):  
SUBENOY CHAKRABORTY
Keyword(s):  
Wave Function ◽  
Quantum Cosmology ◽  
Classical Limit ◽  
Cosmological Models ◽  
Integral Formulation ◽  
Causal Interpretation ◽  
Anisotropic Cosmological Models ◽  
Bohmian Trajectories ◽  
The Universe ◽  
Method Of Steepest Descent

This paper deals with quantum cosmological phenomena in anisotropic cosmological models with nonminimally coupled scalor field. With proper transformation of the field variables, the Wheeler–Dewitt (WD) equation looks simple in form and solutions are obtained using separable form of the wave function. Using part integral formulation, the wave function of the Universe has been evaluated by the method of steepest descent. Finally, the causal interpretation has been done using quantum Bohmian trajectories and also we study the classical limit of some particular solutions of these quantum models.

scholarly journals THE EFFECT OF SPATIAL CURVATURE ON CLASSICAL AND QUANTUM STRINGS

1996 ◽  
Vol 11 (21) ◽  
pp. 4005-4030 ◽  
Author(s):  
A.L. LARSEN ◽  
N. SÁNCHEZ
Keyword(s):  
Center Of Mass ◽  
Elliptic Functions ◽  
Space Time ◽  
Einstein Equations ◽  
Back Reaction ◽  
Level Spacing ◽  
Spatial Curvature ◽  
Curvature Index ◽  
Self Consistent ◽  
Consistent Solution

We study the effects of spatial curvature on classical and quantum string dynamics. We find the general solution of the circular string motion in static Robertson–Walker space-times with closed or open sections. This is given closely and completely in terms of elliptic functions. The physical properties, string length, energy and pressure are computed and analyzed. We find the back-reaction effect of these strings on the space-time: the self-consistent solution to the Einstein equations is a spatially closed (K>0) space-time with a selected value of the curvature index K (the scale factor is normalized to unity). No self-consistent solutions with K≤0 exist. We semiclassically quantize the circular strings and find the mass m in each case. For K>0, the very massive strings, oscillating on the full hypersphere, have m2~Kn2(n∈N0)independent of α' and the level spacing grows with n, while the strings oscillating on one hemisphere (without crossing the equator) have m2α′~n and a finite number of states N~1/Kα′. For K<0, there are infinitely many string states with masses m log m ~ n, i.e. the level spacing grows slower than n. The stationary string solutions as well as the generic string fluctuations around the center of mass are also found and analyzed in closed form.

scholarly journals Wave function of the universe from a matrix-valued first-order formalism

2015 ◽  
Vol 12 (04) ◽  
pp. 1550050
Author(s):  
Sergey I. Kruglov ◽  
Mir Faizal
Keyword(s):  
Wave Function ◽  
Partition Function ◽  
Cosmological Constant ◽  
Eigenvalue Equation ◽  
Cosmological Constant Problem ◽  
First Order ◽  
Superspace Formalism ◽  
Statistical Mechanical ◽  
The Universe ◽  
Spacetime Foam

In this paper, the Wheeler–DeWitt equation in full superspace formalism will be written in a matrix-valued first-order formalism. We will also analyze the Wheeler–DeWitt equation in minisuperspace approximation using this matrix-valued first-order formalism. We will note that this Wheeler–DeWitt equation, in this minisuperspace approximation, can be expressed as an eigenvalue equation. We will use this fact to analyze the spacetime foam in this formalism. This will be done by constructing a statistical mechanical partition function for the Wheeler–DeWitt equation in this matrix-valued first-order formalism. This will lead to a possible solution for the cosmological constant problem.

THE WAVE FUNCTION OF THE UNIVERSE AND p-ADIC GRAVITY

1991 ◽  
Vol 06 (24) ◽  
pp. 4341-4358 ◽  
Author(s):  
I. YA. AREF’EVA ◽  
B. DRAGOVICH ◽  
P.H. FRAMPTON ◽  
I.V. VOLOVICH
Keyword(s):  
Wave Function ◽  
Correspondence Principle ◽  
Number Fields ◽  
Gravitational Theory ◽  
Einstein Equations ◽  
Field Equations ◽  
Gravitation Field ◽  
New Approach ◽  
Algebraic Manifolds ◽  
The Universe

A new approach to the wave function of the universe is suggested. The key idea is to take into account fluctuating number fields and present the wave function in the form of a Euler product. For this purpose we define a p-adic generalization of both classical and quantum gravitational theory. Elements of p-adic differential geometry are described. The action and gravitation field equations over the p-adic number field are investigated. p-adic analogs of some known solutions to the Einstein equations are presented. It follows that in quantum cosmology one should consider summation only over algebraic manifolds. The correspondence principle with the standard approach is considered.

ON THE COSMOLOGICAL CONSTANT IN QUANTUM COSMOLOGY OF THE BRANS–DICKE THEORY

1998 ◽  
Vol 13 (17) ◽  
pp. 1333-1337 ◽  
Author(s):  
ZONG-HONG ZHU ◽  
YUAN-ZHONG ZHANG ◽  
XIANG-PING WU
Keyword(s):  
Boundary Condition ◽  
Wave Function ◽  
Cosmological Constant ◽  
Quantum Cosmology ◽  
Gravitational Theory ◽  
Wkb Approximation ◽  
Expanding Universe ◽  
The Universe

We study the issue of the cosmological constant in quantum cosmology combined with the Brans–Dicke gravitational theory. Using the minisuperspace approximation, we build up the Wheeler–De Witt equation and then obtain the wave function of the universe by further assuming the WKB approximation under the boundary condition proposed by Vilenkin. It is shown that the amplitude of the resulting wave function, which represents an expanding universe, reaches its peaks if the cosmological constant vanishes.

Multiscalar field models: Interaction potentials, wave functions and cosmological solutions

2020 ◽  
Vol 29 (07) ◽  
pp. 2050046
Author(s):  
Sameerah Jamal
Keyword(s):  
Wave Function ◽  
Wave Functions ◽  
Scalar Interaction ◽  
Coordinate Transformations ◽  
Spatial Curvature ◽  
Field Equations ◽  
Interaction Potentials ◽  
Cosmological Solutions ◽  
The Universe ◽  
Friedmann Robertson Walker

We consider a multiscalar tensor cosmology model described by Friedmann–Robertson–Walker (FRW) spacetime with zero spatial curvature. Three specific scalar interaction potentials that characterize the model are analyzed under a set of coordinate transformations. By implication, we solve for the wave function of the universe, reduce the dimension of the underlying Hamiltonian system and consequently, establish analytical solutions of the multiscalar model’s field equations.

scholarly journals From General Relativity to A Simple-Harmonically Oscillating Universe, and Vice-Versa: A Review

2017 ◽  
Vol 9 (1) ◽  
pp. 86 ◽  
Author(s):  
Carmine Cataldo
Keyword(s):  
General Relativity ◽  
Cosmological Constant ◽  
Gravitational Constant ◽  
Spatial Dimension ◽  
Global Symmetry ◽  
Mass Energy ◽  
Fluid Equation ◽  
Energy Equivalence ◽  
Curvature Parameter ◽  
The Universe

In this paper two different lines of reasoning are followed in order to discuss a Universe that belongs to the so-called oscillatory class. In the first section, we start from the general writing of the first Friedmann – Lemaître equation. Taking into account mass – energy equivalence, the so-called fluid equation is immediately deduced, with the usual hypotheses of homogeneity and isotropy, once identified the evolution of the Universe with an isentropic process. Considering equal to zero the curvature parameter, and carrying out an opportune position concerning the so-called cosmological constant, we obtain an oscillating class, to which a simple-harmonically oscillating Universe evidently belongs. In the second section, we start from a simple-harmonically oscillating Universe, hypothesized globally flat and characterized by at least a further spatial dimension. Once defined the density, taking into account a global symmetry elsewhere postulated, we carry out a simple but noteworthy position concerning the gravitational constant. Then, once established the dependence between pressure and density, we deduce, by means of simple mathematical passages, the equations of Friedmann – Lemaître, without using Einstein’s Relativity.

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