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.

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.

scholarly journals CAUSAL LOOP QUANTUM COSMOLOGY IN MOMENTUM SPACE

2009 ◽  
Vol 18 (01) ◽  
pp. 83-93
Author(s):  
ALI SHOJAI ◽  
FATIMAH SHOJAI
Keyword(s):  
Cosmological Constant ◽  
Momentum Space ◽  
Quantum Cosmology ◽  
Cosmological Solution ◽  
Dynamical Variable ◽  
Loop Quantum Cosmology ◽  
Causal Interpretation ◽  
Causal Loop ◽  
Bohmian Trajectories

We shall show that it is possible to make a causal interpretation of loop quantum cosmology using the momentum as the dynamical variable. We shall show that one can derive Bohmian trajectories. For a sample cosmological solution with cosmological constant, the trajectory is plotted.

scholarly journals Universe’s memory and spontaneous coherence in loop quantum cosmology

2016 ◽  
Vol 25 (08) ◽  
pp. 1642013 ◽  
Author(s):  
Tomasz Pawłowski
Keyword(s):  
Cosmological Constant ◽  
Present State ◽  
Quantum Cosmology ◽  
A Priori ◽  
Loop Quantum Cosmology ◽  
Positive Cosmological Constant ◽  
Isotropic Universe ◽  
Constant Of Motion ◽  
Universe Evolution

The quantum bounce a priori connects several (semi)classical epochs of universe evolution, however determining if and how well the semiclassicality is preserved in this transition is highly nontrivial. We review the present state of knowledge in that regards in the isotropic sector of loop quantum cosmology (LQC). This knowledge is next extended by studies of an isotropic universe admitting positive cosmological constant (featuring an infinite chain of large universe epochs). It is also shown, that such universe always admits a semiclassical epoch thanks to spontaneous coherence, provided it is semiclassical in certain constant of motion playing the role of energy.

scholarly journals The status of quantum geometry in the dynamical sector of loop quantum cosmology

2008 ◽  
Vol 25 (5) ◽  
pp. 055003 ◽  
Author(s):  
Wojciech Kamiński ◽  
Jerzy Lewandowski ◽  
Łukasz Szulc
Keyword(s):  
Quantum Cosmology ◽  
Loop Quantum Cosmology ◽  
Quantum Geometry ◽  
The Status

scholarly journals Inconsistencies of the New No-Boundary Proposal

Universe ◽  
2018 ◽  
Vol 4 (10) ◽  
pp. 100 ◽  
Author(s):  
Job Feldbrugge ◽  
Jean-Luc Lehners ◽  
Neil Turok
Keyword(s):  
Boundary Condition ◽  
Perturbation Theory ◽  
Strong Coupling ◽  
Path Integral ◽  
Quantum Cosmology ◽  
Einstein Gravity ◽  
Strong Coupling Regime ◽  
Recent Modification ◽  
Circular Contour ◽  
Made In

In previous works, we have demonstrated that the path integral for real, Lorentzian four-geometries in Einstein gravity yields sensible results in well-understood physical situations, but leads to uncontrolled fluctuations when the “no boundary” condition proposed by Hartle and Hawking is imposed. In order to circumvent our result, new definitions for the gravitational path integral have been sought, involving specific choices for a class of complex four-geometries to be included. In their latest proposal, Diaz Dorronsoro et al. advocate for integrating the lapse over a complex circular contour enclosing the origin. In this note, we show that, like their earlier proposal, this leads to mathematical and physical inconsistencies and thus cannot be regarded as a basis for quantum cosmology. We also comment on Vilenkin and Yamada’s recent modification of the “tunneling" proposal, made in order to avoid the same problems. We show that it leads to the breakdown of perturbation theory in a strong coupling regime.

scholarly journals Path integral of Bianchi I models in loop quantum cosmology

2013 ◽  
Vol 30 (6) ◽  
pp. 065010 ◽  
Author(s):  
Xiao Liu ◽  
Fei Huang ◽  
Jian-Yang Zhu
Keyword(s):  
Path Integral ◽  
Quantum Cosmology ◽  
Loop Quantum Cosmology ◽  
Bianchi I

scholarly journals The Vacuum State of Primordial Fluctuations in Hybrid Loop Quantum Cosmology

Universe ◽  
2018 ◽  
Vol 4 (10) ◽  
pp. 98 ◽  
Author(s):  
Beatriz Elizaga Navascués ◽  
Daniel Martín de Blas ◽  
Guillermo Mena Marugán
Keyword(s):  
General Relativity ◽  
Kinetic Energy ◽  
Quantum Cosmology ◽  
Power Spectra ◽  
Mass Term ◽  
Vacuum State ◽  
Initial Time ◽  
Loop Quantum Cosmology ◽  
Quantum Geometry ◽  
Effective Dynamics

We investigate the role played by the vacuum of the primordial fluctuations in hybrid Loop Quantum Cosmology. We consider scenarios where the inflaton potential is a mass term and the unperturbed quantum geometry is governed by the effective dynamics of Loop Quantum Cosmology. In this situation, the phenomenologically interesting solutions have a preinflationary regime where the kinetic energy of the inflaton dominates over the potential. For these kind of solutions, we show that the primordial power spectra depend strongly on the choice of vacuum. We study in detail the case of adiabatic states of low order and the non-oscillating vacuum introduced by Martín de Blas and Olmedo, all imposed at the bounce. The adiabatic spectra are typically suppressed at large scales, and display rapid oscillations with an increase of power at intermediate scales. In the non-oscillating vacuum, there is power suppression for large scales, but the rapid oscillations are absent. We argue that the oscillations are due to the imposition of initial adiabatic conditions in the region of kinetic dominance, and that they would also be present in General Relativity. Finally, we discuss the sensitivity of our results to changes of the initial time and other data of the model.

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