scholarly journals No smooth beginning for spacetime

2019 ◽  
Vol 28 (02) ◽  
pp. 1930005 ◽  
Author(s):  
Jean-Luc Lehners
Keyword(s):  
Cosmological Constant ◽  
Gravitational Wave ◽  
Path Integral ◽  
Quantum Cosmology ◽  
Path Integrals ◽  
Mathematical Tool ◽  
Positive Cosmological Constant ◽  
Quantum Amplitude ◽  
The Universe

In this paper, I will review an obstruction for theories of the beginning of the universe which can be formulated as semiclassical path integrals. Hartle and Hawking’s no boundary proposal and Vilenkin’s tunneling proposal are examples of such theories. Each may be formulated as the quantum amplitude for obtaining a final 3-geometry by integrating over 4-geometries. The result is obtained using a new mathematical tool — Picard–Lefschetz theory — for defining the semiclassical path integral for gravity. The Lorentzian path integral for quantum cosmology with a positive cosmological constant is mathematically meaningful in this approach, but the Euclidean version is not. Framed in this way, the resulting framework and predictions are unique. Unfortunately, the outcome is that primordial gravitational wave fluctuations are unsuppressed.

scholarly journals Relationship between Bondi–Sachs quantities and source of gravitational radiation in asymptotically de Sitter spacetime

2018 ◽  
Vol 27 (04) ◽  
pp. 1850046 ◽  
Author(s):  
Xiaokai He ◽  
Jiliang Jing ◽  
Zhoujian Cao
Keyword(s):  
Cosmological Constant ◽  
Gravitational Wave ◽  
Gravitational Radiation ◽  
The Other ◽  
Perturbation Approach ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Positive Cosmological Constant ◽  
Sitter Spacetime ◽  
Explicit Expressions

Gravitational radiation plays an important role in astrophysics. Based on the fact that our universe is expanding, the gravitational radiation when a positive cosmological constant is presented has been studied along with two different ways recently, one is the Bondi–Sachs (BS) framework in which the result is shown by BS quantities in the asymptotic null structure, the other is the perturbation approach in which the result is presented by the quadrupoles of source. Therefore, it is worth to interpret the quantities in asymptotic null structure in terms of the information of the source. In this paper, we investigate this problem and find the explicit expressions of BS quantities in terms of the quadrupoles of source in asymptotically de Sitter spacetime. We also estimate how far away the source is, the cosmological constant may affect the detection of the gravitational wave.

scholarly journals Asymptotically equivalent functions and ultrafilters applied to noncommutative quantum cosmology

2019 ◽  
Vol 65 (5 Sept-Oct) ◽  
pp. 519
Author(s):  
J.A. Astorga-Moreno ◽  
E.A. Mena Barboza ◽  
And M.A. García-Aspeitia
Keyword(s):  
Dynamical System ◽  
Cosmological Constant ◽  
Commutation Relation ◽  
Quantum Cosmology ◽  
Positive Cosmological Constant ◽  
Classical Approximation ◽  
Noncommutative Quantum

Using the semi-classical approximation to the Wheeler-DeWitt equation obtained via Arnowitt-Deser-Misner (ADM) formalism in the Friedmann-Lemaitre-Robertson-Walker (FLRW) model coupled to a scalar eld and positive cosmological constant, and in the Kantowski-Sachs (KS) Universe, we introduced a deformation on the commutation relation for the minisuperspace variables and find an explicit semiclassical expression equivalent, in an adequate limit, to the solution with the aid of asymptotically equal functions and the theory of Ultralters, oering a suggestive alternative to sketch the behavior of the dynamical system involved without the need to solve it numerically.

scholarly journals The Effect of a Positive Cosmological Constant on the Bounce of Loop Quantum Cosmology

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 186
Author(s):  
Mercedes Martín-Benito ◽  
Rita B. Neves
Keyword(s):  
Scalar Field ◽  
Cosmological Constant ◽  
Quantum Cosmology ◽  
Quantum Dynamics ◽  
Solvable Model ◽  
Massless Scalar ◽  
Loop Quantum Cosmology ◽  
Massless Scalar Field ◽  
Positive Cosmological Constant ◽  
Semiclassical States

We provide an analytical solution to the quantum dynamics of a flat Friedmann-Lemaître- Robertson-Walker model with a massless scalar field in the presence of a small and positive cosmological constant, in the context of Loop Quantum Cosmology. We use a perturbative treatment with respect to the model without a cosmological constant, which is exactly solvable. Our solution is approximate, but it is precisely valid at the high curvature regime where quantum gravity corrections are important. We compute explicitly the evolution of the expectation value of the volume. For semiclassical states characterized by a Gaussian spectral profile, the introduction of a positive cosmological constant displaces the bounce of the solvable model to lower volumes and to higher values of the scalar field. These displacements are state dependent, and in particular, they depend on the peak of the Gaussian profile, which measures the momentum of the scalar field. Moreover, for those semiclassical states, the bounce remains symmetric, as in the vanishing cosmological constant case. However, we show that the behavior of the volume is more intricate for generic states, leading in general to a non-symmetric bounce.

COSMIC TIME IN QUANTUM COSMOLOGY: INFLATION-COMPACTIFICATION AS A QUANTUM EFFECT

1993 ◽  
Vol 02 (02) ◽  
pp. 221-247 ◽  
Author(s):  
E.I. GUENDELMAN ◽  
A.B. KAGANOVICH
Keyword(s):  
Cosmological Constant ◽  
Quantum Cosmology ◽  
Quantum Effect ◽  
Cosmic Time ◽  
Expectation Values ◽  
Cosmological Singularity ◽  
Inflationary Phase ◽  
Definition Of ◽  
The Universe ◽  
Kaluza Klein

We consider 1+D-dimensional, toroidally compact Kaluza-Klein theories. In the context of the minisuperspace approach of quantum cosmology, we solve the Wheeler-DeWitt equation in the presence of a negative cosmological constant and dust. Then, it is found that the quantum effects stabilize the volume of the Universe, so that there can be an avoidance of the cosmological singularity. Although cosmic time does not appear explicitly in the Wheeler-DeWitt equation, we find that a cosmic time dependence appears for the expectation values of certain variables. This result is obtained when proper care of some subtle points concerning the definition of averages in this model is taken. The stabilization of the volume, when there is anisotropy in the evolution of the Universe (which turns out to be quantized), is consistent with another effect we find: the existence of a “quantum inflationary phase” for some dimensions and simultaneously the existence of a “quantum deflationary contraction” for the rest.

THE CONFORMAL FACTOR AND THE COSMOLOGICAL CONSTANT

1990 ◽  
Vol 05 (19) ◽  
pp. 3811-3829 ◽  
Author(s):  
STEVEN B. GIDDINGS
Keyword(s):  
Quantum Gravity ◽  
Cosmological Constant ◽  
Path Integral ◽  
Conformal Factor ◽  
Positive Cosmological Constant ◽  
Lorentzian Signature ◽  
Wrong Sign ◽  
Euclidean Signature

The issue of the conformal factor in quantum gravity is examined for Lorentzian signature spacetimes. In Euclidean signature, the “wrong” sign of the conformal action makes the path integral undefined, but in Lorentzian signature this sign is tied to the instability of gravity and once this is accounted for the path integral should be well-defined. In this approach it is not obvious that the Baum-Hawking-Coleman mechanism for suppression of the cosmological constant functions. It is conceivable that since the multiuniverse system exhibits an instability for positive cosmological constant, the dynamics should force the system to zero cosmological constant.

scholarly journals High-order quantum back-reaction and quantum cosmology with a positive cosmological constant

2011 ◽  
Vol 84 (4) ◽  
Author(s):  
Martin Bojowald ◽  
David Brizuela ◽  
Hector H. Hernández ◽  
Michael J. Koop ◽  
Hugo A. Morales-Técotl
Keyword(s):  
Cosmological Constant ◽  
Quantum Cosmology ◽  
High Order ◽  
Back Reaction ◽  
Positive Cosmological Constant

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.

scholarly journals On the Geometry of No-Boundary Instantons in Loop Quantum Cosmology

Universe ◽  
2019 ◽  
Vol 5 (1) ◽  
pp. 22 ◽  
Author(s):  
Suddhasattwa Brahma ◽  
Dong-han Yeom
Keyword(s):  
Cosmological Constant ◽  
Path Integral ◽  
Quantum Cosmology ◽  
Einstein Gravity ◽  
Peculiar Feature ◽  
Loop Quantum Cosmology ◽  
Quantum Geometry

We study the geometry of Euclidean instantons in loop quantum cosmology (LQC) such as those relevant for the no-boundary proposal. Confining ourselves to the simplest case of a cosmological constant in minisuperspace cosmologies, we analyze solutions of the semiclassical (Euclidean) path integral in LQC. We find that the geometry of LQC instantons have the peculiar feature of an infinite tail which distinguishes them from Einstein gravity. Moreover, due to quantum-geometry corrections, the small-a behaviour of these instantons seem to naturally favor a closing-off of the geometry in a regular fashion, as was originally proposed for the no-boundary wavefunction.

Sign in / Sign up

Export Citation Format

Share Document