scholarly journals Quantization ambiguities and the robustness of effective descriptions of primordial perturbations in hybrid Loop Quantum Cosmology

2021 ◽  
Author(s):  
Beatriz Elizaga Navascués ◽  
Guillermo A Mena Marugan
Keyword(s):  
Quantum Theory ◽  
Quantum Cosmology ◽  
Hamiltonian Structure ◽  
Initial Conditions ◽  
Loop Quantum Cosmology ◽  
Quantum Field Theories ◽  
Primordial Power Spectrum ◽  
Starting Point ◽  
Hamiltonian Operators ◽  
Positive Frequency

Abstract We study the imprint that certain quantization ambiguities may leave in effective regimes of the hybrid loop quantum description of cosmological perturbations. More specifically, in the case of scalar perturbations we investigate how to reconstruct the Mukhanov-Sasaki field in the effective regime of Loop Quantum Cosmology, taking as starting point for the quantization a canonical formulation in terms of other perturbative gauge invariants that possess different dynamics. This formulation of the quantum theory, in terms of variables other than the Mukhanov-Sasaki ones, is crucial to arrive at a quantum Hamiltonian with a good behavior, elluding the problems with ill defined Hamiltonian operators typical of quantum field theories. In the reconstruction of the Mukhanov-Sasaki field, we ask that the effective Mukhanov-Sasaki equations adopt a similar form and display the same Hamiltonian structure as the classical ones, a property that has been widely assumed in Loop Quantum Cosmology studies over the last decade. This condition actually restricts the freedom inherent to certain quantization ambiguities. Once these ambiguities are removed, the reconstruction of the Mukhanov-Sasaki field naturally identifies a set of positive-frequency solutions to the effective equations, and hence a choice of initial conditions for the perturbations. Our analysis constitutes an important and necessary test of the robustness of standard effective descriptions in Loop Quantum Cosmology, along with their observational predictions on the primordial power spectrum, taking into account that they should be the consequence of a more fundamental quantum theory with a well-defined Hamiltonian, in the spirit of Dirac’s long-standing ideas.

scholarly journals Phenomenology analysis of duration inflation for tachyon field in loop quantum cosmology

2014 ◽  
Vol 23 (11) ◽  
pp. 1450087 ◽  
Author(s):  
Kui Xiao ◽  
Xiao-Kai He ◽  
Fei Huang ◽  
Jian-Yang Zhu
Keyword(s):  
Quantum Cosmology ◽  
Initial Conditions ◽  
Scale Factor ◽  
Loop Quantum Cosmology ◽  
Tachyon Field ◽  
Exponential Potential ◽  
Quadratic Potential ◽  
Slow Rolling

Assuming that the e-folding number is just determined by the change of the scale factor, the tachyonic inflation theory in loop quantum cosmology (LQC) has been discussed. Considering the tachyon field with exponential potential and inverse quadratic potential, we find that the evolutionary pictures of super inflation are affected by the potentials and the initial conditions. However it cannot provide enough e-folding number, no matter which condition is chosen. Therefore a slow-rolling inflation is necessary. The e-folding number for slow-rolling inflation depends on the values of the parameter α of the exponential potential and the initial conditions. To get enough e-folding number, α should be small. Based on the slow-rolling inflation happens immediately when the super inflation ends, and the scale factor continuously grows during the whole inflation stage, we consider an e-folding number provided by the whole inflationary stage, and we find that it is easier to get enough e-folding number when the scale factor increases during all the inflation phase.

scholarly journals Pre-inflation dynamical behavior of warm inflation in loop quantum cosmology

2020 ◽  
Vol 35 (35) ◽  
pp. 2050293
Author(s):  
Kui Xiao ◽  
Sheng-Qin Wang
Keyword(s):  
Quantum Cosmology ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Loop Quantum Cosmology ◽  
Warm Inflation ◽  
Dynamical Behaviors ◽  
Slow Roll ◽  
Dissipative Coefficient ◽  
Slow Roll Inflation ◽  
Three Phases

Considering a constant dissipative coefficient [Formula: see text], the pre-inflation dynamical behaviors of warm inflation in the loop quantum cosmology scenario are discussed. We consider three sets of initial conditions. The evolution of the background can always be divided into three phases, namely super-inflation, damping, and slow-roll inflation phases, with the duration of each phase depending on the initial conditions. As an example, we compare the background evolution between [Formula: see text] and [Formula: see text] under special initial conditions and find that there is no slow-roll inflation phase for [Formula: see text] while the number of e-folds is about 60.209 for [Formula: see text].

scholarly journals Non-Oscillatory Power Spectrum From States of Low Energy in Kinetically Dominated Early Universes

2021 ◽  
Vol 8 ◽  
Author(s):  
Mercedes Martín-Benito ◽  
Rita B. Neves ◽  
Javier Olmedo
Keyword(s):  
Power Spectrum ◽  
Quantum Cosmology ◽  
Initial Conditions ◽  
Power Spectra ◽  
Low Energy ◽  
Loop Quantum Cosmology ◽  
Test Function ◽  
Vacuum States ◽  
Oscillatory Power ◽  
Definition Of

Recently, States of Low Energy (SLEs) have been proposed as viable vacuum states of primordial perturbations within Loop Quantum Cosmology (LQC). In this work we investigate the effect of the high curvature region of LQC on the definition of SLEs. Shifting the support of the test function that defines them away from this regime results in primordial power spectra of perturbations closer to those of the so-called Non-oscillatory (NO) vacuum, which is another viable choice of initial conditions previously introduced in the LQC context. Furthermore, through a comparison with the Hadamard-like SLEs, we prove that the NO vacuum is of Hadamard type as well.

scholarly journals The perturbed universe in the deformed algebra approach of loop quantum cosmology

2016 ◽  
Vol 25 (08) ◽  
pp. 1642003 ◽  
Author(s):  
Julien Grain
Keyword(s):  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Initial Conditions ◽  
Power Spectra ◽  
Quantum Corrections ◽  
Loop Quantum Cosmology ◽  
Algebra Approach ◽  
Deformed Algebra ◽  
Contracting Phase ◽  
The Universe

Loop Quantum Cosmology (LQC) is a tentative approach to model the universe down to the Planck era where quantum gravity settings are needed. The quantization of the universe as a dynamical spacetime is inspired by Loop Quantum Gravity (LQG) ideas. In addition, LQC could bridge contact with astronomical observations, and thus potentially investigate quantum cosmology modelings in the light of observations. To do so however, modeling both the background evolution and its perturbations is needed. The latter described cosmic inhomogeneities that are the main cosmological observables. In this context, we present the so-called deformed algebra approach implementing the quantum corrections to the perturbed universe at an effective level by taking great care of gauge issues. We particularly highlight that in this framework, the algebra of hypersurface deformation receives quantum corrections, and we discuss their meaning. The primordial power spectra of scalar and tensor inhomogeneities are then presented, assuming initial conditions are set in the contracting phase preceding the quantum bounce and the well-known expanding phase of the cosmic history. These spectra are subsequently propagated to angular power spectra of the anisotropies of the cosmic microwave background. It is then shown that regardless of the choice for the initial conditions inside the effective approach for the background evolution (except that they are set in the contracting phase), the predicted angular power spectra of the polarized [Formula: see text]-modes exceed the upper bound currently set by observations. The exclusion of this specific version of LQC establishes the falsifiability of the approach, though one shall not conclude here that either LQC or LQG excluded.

scholarly journals Oscillatory universes in loop quantum cosmology and initial conditions for inflation

2004 ◽  
Vol 70 (6) ◽  
Author(s):  
James E. Lidsey ◽  
David J. Mulryne ◽  
N. J. Nunes ◽  
Reza Tavakol
Keyword(s):  
Quantum Cosmology ◽  
Initial Conditions ◽  
Loop Quantum Cosmology

scholarly journals INFLATIONARY COSMOLOGY AND OSCILLATING UNIVERSES IN LOOP QUANTUM COSMOLOGY

2005 ◽  
Vol 20 (11) ◽  
pp. 2347-2357 ◽  
Author(s):  
DAVID J. MULRYNE ◽  
N. J. NUNES ◽  
REZA TAVAKOL ◽  
JAMES E. LIDSEY
Keyword(s):  
Comparative Study ◽  
Quantum Cosmology ◽  
Initial Conditions ◽  
Scalar Fields ◽  
Inflationary Cosmology ◽  
Loop Quantum Cosmology ◽  
Oscillatory Dynamics ◽  
Slow Roll ◽  
Positively Curved ◽  
Slow Roll Inflation

We study oscillatory universes within the context of Loop Quantum Cosmology. We make a comparative study of flat and positively curved universes sourced by scalar fields with either positive or negative potentials. We investigate how oscillating universes can set the initial conditions for successful slow-roll inflation, while ensuring that the semi-classical bounds are satisfied. We observe rich oscillatory dynamics with negative potentials, although it is difficult to respect the semi-classical bounds in models of this type.

scholarly journals A Brief Overview of Results about Uniqueness of the Quantization in Cosmology

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 299
Author(s):  
Jerónimo Cortez ◽  
Guillermo A. Mena Marugán ◽  
José M. Velhinho
Keyword(s):  
Quantum Theory ◽  
Quantum Cosmology ◽  
Loop Quantum Cosmology ◽  
Linear Transformations ◽  
Time Direction ◽  
Uniqueness Criteria ◽  
Inhomogeneous Cosmologies

The purpose of this review is to provide a brief overview of recent conceptual developments regarding possible criteria to guarantee the uniqueness of the quantization in a variety of situations that are found in cosmological systems. These criteria impose certain conditions on the representation of a group of physically relevant linear transformations. Generally, this group contains any existing symmetry of the spatial sections. These symmetries may or may not be sufficient for the purpose of uniqueness and may have to be complemented with other remaining symmetries that affect the time direction or with dynamical transformations that are, in fact, not symmetries. We discuss the extent to which a unitary implementation of the resulting group suffices to fix the quantization—a demand that can be seen as a weaker version of the requirement of invariance. In particular, a strict invariance under certain transformations may eliminate some physically interesting possibilities in the passage to the quantum theory. This is the first review in which this unified perspective is adopted to discuss otherwise different uniqueness criteria proposed either in homogeneous loop quantum cosmology or in the Fock quantization of inhomogeneous cosmologies.

Stability analysis of Einstein’s universe in loop quantum cosmology

2020 ◽  
Vol 35 (28) ◽  
pp. 2050166
Author(s):  
Eamon Mc Caughey
Keyword(s):  
General Relativity ◽  
Stability Analysis ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Hamiltonian Structure ◽  
Loop Quantum Cosmology ◽  
Universe Model ◽  
Integrals Of Motion ◽  
Cyclic Universe ◽  
The Stability

A stability analysis of Einstein’s universe in both classical general relativity and semiclassical loop quantum cosmology regimes is presented. The stability properties of the general relativity model are significantly altered due to loop quantum gravity corrections. Comparisons between both dynamical systems are considered on the basis of these modifications. The loop quantum cosmology solutions are restricted to an open universe model [Formula: see text] and represent a cyclic universe. The integrals of motion for both systems are found and their Hamiltonian structure determined.

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