scholarly journals TIME IN THE CHAOTIC INFLATION MODEL AND NUMERICAL CALCULATIONS

1995 ◽  
Vol 10 (16) ◽  
pp. 2317-2332
Author(s):  
YOSHIAKI OHKUWA ◽  
TETSURO KITAZOE ◽  
YOSHIHIKO MIZUMOTO
Keyword(s):  
Quantum Gravity ◽  
Perturbation Method ◽  
Orbital Motion ◽  
Semiclassical Approximation ◽  
Natural Extension ◽  
Matter Field ◽  
Time Variable ◽  
Inflation Model ◽  
Scalar Matter ◽  
Scalar Mass

The time variable is considered in the quantum gravity theory and calculated explicitly in the framework of the chaotic inflationary scenario where the scalar matter field has a contribution to the time variable in addition to the gravity field. The time formulated under the semiclassical approximation is a natural extension of that in the classical orbital motion. A perturbation method is introduced in terms of the scalar mass to obtain analytically solvable expressions for the time. The Wheeler-DeWitt equation is solved numerically to ensure that the semiclassical approximation is well justified. We examine the obtained time in detail and find that it is reasonable to consider it as time in the region where the semiclassical approximation is well justified.

scholarly journals TIME IN THE SEMICLASSICAL APPROXIMATION TO QUANTUM GRAVITY COUPLED WITH A BACKGROUND SCALAR FIELD AND KALUZA-KLEIN THEORY

1995 ◽  
Vol 10 (13) ◽  
pp. 1905-1915
Author(s):  
YOSHIAKI OHKUWA
Keyword(s):  
Scalar Field ◽  
Quantum Gravity ◽  
Semiclassical Approximation ◽  
Matter Field ◽  
Time Variable ◽  
Time Coordinate ◽  
Quantum Matter ◽  
Klein Theory ◽  
Original Time ◽  
Kaluza Klein

We consider the semiclassical approximation to quantum gravity coupled with a background scalar field and a quantum matter field. We define the semiclassical time variable and write down the Schrödinger equation for the quantum matter field. This can be rewritten into the form whose time variable is the original time coordinate, when the relation of Hamilton-Jacobi holds. It is shown that the four-dimensional semiclassical time with a background scalar field is related to the five-dimensional semiclassical time without it by means of the Kaluza-Klein dimensional reduction.

scholarly journals Quantum gravity, dynamical phase-space and string theory

2014 ◽  
Vol 23 (12) ◽  
pp. 1442006 ◽  
Author(s):  
Laurent Freidel ◽  
Robert G. Leigh ◽  
Djordje Minic
Keyword(s):  
Quantum Theory ◽  
Phase Space ◽  
String Theory ◽  
Quantum Gravity ◽  
Momentum Space ◽  
Symplectic Geometry ◽  
Complex Geometry ◽  
Hamiltonian Dynamics ◽  
Natural Extension ◽  
Dynamical Phase

In a natural extension of the relativity principle, we speculate that a quantum theory of gravity involves two fundamental scales associated with both dynamical spacetime as well as dynamical momentum space. This view of quantum gravity is explicitly realized in a new formulation of string theory which involves dynamical phase-space and in which spacetime is a derived concept. This formulation naturally unifies symplectic geometry of Hamiltonian dynamics, complex geometry of quantum theory and real geometry of general relativity. The spacetime and momentum space dynamics, and thus dynamical phase-space, is governed by a new version of the renormalization group (RG).

scholarly journals THE VIRTUAL BLACK HOLE IN 2D QUANTUM GRAVITY AND ITS RELEVANCE FOR THE S-MATRIX

2002 ◽  
Vol 17 (06n07) ◽  
pp. 989-992 ◽  
Author(s):  
DANIEL GRUMILLER
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Wave Scattering ◽  
Black Hole Mass ◽  
Hole Formation ◽  
S Wave ◽  
Scalar Matter ◽  
S Matrix ◽  
Tree Vertex ◽  
Classical Mechanism

As shown recently 2d quantum gravity theories — including spherically reduced Einstein-gravity — after an exact path integral of its geometric part can be treated perturbatively in the loops of (scalar) matter. Obviously the classical mechanism of black hole formation should be contained in the tree approximation of the theory. This is shown to be the case for the scattering of two scalars through an intermediate state which by its effective black hole mass is identified as a "virtual black hole". We discuss the lowest order tree vertex for minimally and non-minimally coupled scalars and find a non-trivial finite S-matrix for gravitational s-wave scattering in the latter case.

scholarly journals The Quantum Cosmological Constant

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1130 ◽  
Author(s):  
Stephon Alexander ◽  
Joao Magueijo ◽  
Lee Smolin
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Uncertainty Relation ◽  
Time Variable ◽  
Transition Functions ◽  
New Interpretation ◽  
Chern Simons

We present an extension of general relativity in which the cosmological constant becomes dynamical and turns out to be conjugate to the Chern–Simons invariant of the Ashtekar connection on a spatial slicing. The latter has been proposed Soo and Smolin as a time variable for quantum gravity: the Chern–Simons time. In the quantum theory, the inverse cosmological constant and Chern–Simons time will then become conjugate operators. The “Kodama state” gets a new interpretation as a family of transition functions. These results imply an uncertainty relation between Λ and Chern–Simons time; the consequences of which will be discussed elsewhere.

scholarly journals The Casimir effect with quantized charged scalar matter in background magnetic field

2014 ◽  
Vol 29 (09) ◽  
pp. 1450052 ◽  
Author(s):  
Yu. A. Sitenko ◽  
S. A. Yushchenko
Keyword(s):  
Magnetic Field ◽  
Boundary Condition ◽  
Boundary Conditions ◽  
Casimir Force ◽  
Matter Field ◽  
Particle Energy ◽  
Parallel Plates ◽  
Charged Scalar ◽  
Scalar Matter ◽  
Background Magnetic Field

We study the influence of a background uniform magnetic field and boundary conditions on the vacuum of a quantized charged massive scalar matter field confined between two parallel plates; the magnetic field is directed orthogonally to the plates. The admissible set of boundary conditions at the plates is determined by the requirement that the operator of one-particle energy squared be self-adjoint and positive-definite. We show that, in the case of a weak magnetic field and a small separation of the plates, the Casimir force is either attractive or repulsive, depending on the choice of a boundary condition. In the case of a strong magnetic field and a large separation of the plates, the Casimir force is repulsive, being independent of the choice of a boundary condition, as well as of the distance between the plates.

scholarly journals On Gauge Invariant Cosmological Perturbations in UV-modified Hořava Gravity: A Brief Introduction

2018 ◽  
Vol 168 ◽  
pp. 08003 ◽  
Author(s):  
Mu-In Park
Keyword(s):  
Detailed Balance ◽  
Big Bang ◽  
Matter Field ◽  
Cosmological Perturbations ◽  
Scale Invariant ◽  
Gauge Invariant ◽  
Four Dimensions ◽  
Detailed Balance Condition ◽  
Scalar Matter ◽  
Horava Gravity

We revisit gauge invariant cosmological perturbations in UV-modified, z = 3 Hořava gravity with one scalar matter field, which has been proposed as a renormalizable gravity theory without the ghost problem in four dimensions. We confirm that there is no extra graviton modes and general relativity is recovered in IR, which achieves the consistency of the model. From the UV-modification terms which break the detailed balance condition in UV, we obtain scale-invariant power spectrums for non-inflationary backgrounds, like the power-law expansions, without knowing the details of early expansion history of Universe. This could provide a new framework for the Big Bang cosmology.

scholarly journals CASIMIR ENERGY AND FORCE INDUCED BY AN IMPENETRABLE FLUX TUBE OF FINITE RADIUS

2013 ◽  
Vol 28 (31) ◽  
pp. 1350161 ◽  
Author(s):  
VOLODYMYR M. GORKAVENKO ◽  
YURII A. SITENKO ◽  
OLEXANDER B. STEPANOV
Keyword(s):  
Magnetic Flux ◽  
Vacuum Polarization ◽  
Dirichlet Boundary ◽  
Topological Defect ◽  
Casimir Energy ◽  
Matter Field ◽  
Tube Radius ◽  
Finite Radius ◽  
Polarization Effects ◽  
Scalar Matter

A perfectly reflecting (Dirichlet) boundary condition at the edge of an impenetrable magnetic-flux-carrying tube of nonzero transverse size is imposed on the charged massive scalar matter field which is quantized outside the tube. We show that the vacuum polarization effects outside the tube give rise to a macroscopic force acting at the increase of the tube radius (if the magnetic flux is held steady). The Casimir energy and force are periodic in the value of the magnetic flux, being independent of the coupling to the space–time curvature scalar. We conclude that a topological defect of the vortex type can polarize the vacuum of only those quantum fields that have masses which are much less than a scale of the spontaneous symmetry breaking.

Sign in / Sign up

Export Citation Format

Share Document