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 Quantum reduced loop gravity and the foundation of loop quantum cosmology

2016 ◽  
Vol 25 (08) ◽  
pp. 1642005 ◽  
Author(s):  
Emanuele Alesci ◽  
Francesco Cianfrani
Keyword(s):  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Loop Quantum Cosmology ◽  
Quantum Description ◽  
Semiclassical Dynamics ◽  
Loop Gravity ◽  
The Universe

Quantum reduced loop gravity is a promising framework for linking loop quantum gravity and the effective semiclassical dynamics of loop quantum cosmology. We review its basic achievements and its main perspectives, outlining how it provides a quantum description of the Universe in terms of a cuboidal graph which constitutes the proper framework for applying loop techniques in a cosmological setting.

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 Comparison of primordial tensor power spectra from the deformed algebra and dressed metric approaches in loop quantum cosmology

2015 ◽  
Vol 91 (8) ◽  
Author(s):  
Boris Bolliet ◽  
Julien Grain ◽  
Clément Stahl ◽  
Linda Linsefors ◽  
Aurélien Barrau
Keyword(s):  
Quantum Cosmology ◽  
Power Spectra ◽  
Loop Quantum Cosmology ◽  
Tensor Power ◽  
Deformed Algebra

scholarly journals Preinflationary Dynamics of Power-Law Potential in Loop Quantum Cosmology †

Universe ◽  
2018 ◽  
Vol 4 (8) ◽  
pp. 87 ◽  
Author(s):  
M. Shahalam
Keyword(s):  
Quantum Cosmology ◽  
Initial Conditions ◽  
Big Bang ◽  
Loop Quantum Cosmology ◽  
Inflationary Universe ◽  
Slow Roll ◽  
Wide Range ◽  
The Big Bang ◽  
The Universe ◽  
Big Bang Singularity

In this article, I mainly discuss the dynamics of the pre-inflationary Universe for the potential V ( ϕ ) ∝ ϕ n with n = 5 / 3 in the context of loop quantum cosmology, in which the big bang singularity is resolved by a non-singular quantum bounce. In the case of the kinetic energy-dominated initial conditions of the scalar field at the bounce, the numerical evolution of the Universe can be split up into three regimes: bouncing, transition, and slow-roll inflation. In the bouncing regime, the numerical evolution of the scale factor does not depend on a wide range of initial values, or on the inflationary potentials. I calculate the number of e-folds in the slow-roll regime, by which observationally identified initial conditions are obtained. Additionally, I display the phase portrait for the model under consideration.

scholarly journals An Overview on the Nature of the Bounce in LQC and PQM

Universe ◽  
2021 ◽  
Vol 7 (9) ◽  
pp. 327
Author(s):  
Gabriele Barca ◽  
Eleonora Giovannetti ◽  
Giovanni Montani
Keyword(s):  
Energy Density ◽  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Critical Energy ◽  
Loop Quantum Cosmology ◽  
Isotropic Universe ◽  
Bianchi I ◽  
Critical Energy Density ◽  
The Universe

We present a review on some of the basic aspects concerning quantum cosmology in the presence of cut-off physics as it has emerged in the literature during the last fifteen years. We first analyze how the Wheeler–DeWitt equation describes the quantum Universe dynamics, when a pure metric approach is concerned, showing how, in general, the primordial singularity is not removed by the quantum effects. We then analyze the main implications of applying the loop quantum gravity prescriptions to the minisuperspace model, i.e., we discuss the basic features of the so-called loop quantum cosmology. For the isotropic Universe dynamics, we compare the original approach, dubbed the μ0 scheme, and the most commonly accepted formulation for which the area gap is taken as physically scaled, i.e., the so-called μ¯ scheme. Furthermore, some fundamental results concerning the Bianchi Universes are discussed, especially with respect to the morphology of the Bianchi IX model. Finally, we consider some relevant criticisms developed over the last ten years about the real link existing between the full theory of loop quantum gravity and its minisuperspace implementation, especially with respect to the preservation of the internal SU(2) symmetry. In the second part of the review, we consider the dynamics of the isotropic Universe and of the Bianchi models in the framework of polymer quantum mechanics. Throughout the paper, we focus on the effective semiclassical dynamics and study the full quantum theory only in some cases, such as the FLRW model and the Bianchi I model in the Ashtekar variables. We first address the polymerization in terms of the Ashtekar–Barbero–Immirzi connection and show how the resulting dynamics is isomorphic to the μ0 scheme of loop quantum cosmology with a critical energy density of the Universe that depends on the initial conditions of the dynamics. The following step is to analyze the polymerization of volume-like variables, both for the isotropic and Bianchi I models, and we see that if the Universe volume (the cubed scale factor) is one of the configurational variables, then the resulting dynamics is isomorphic to that one emerging in loop quantum cosmology for the μ¯ scheme, with the critical energy density value being fixed only by fundamental constants and the Immirzi parameter. Finally, we consider the polymer quantum dynamics of the homogeneous and inhomogeneous Mixmaster model by means of a metric approach. In particular, we compare the results obtained by using the volume variable, which leads to the emergence of a singularity- and chaos-free cosmology, to the use of the standard Misner variable. In the latter case, we deal with the surprising result of a cosmology that is still singular, and its chaotic properties depend on the ratio between the lattice steps for the isotropic and anisotropic variables. We conclude the review with some considerations of the problem of changing variables in the polymer representation of the minisuperspace dynamics. In particular, on a semiclassical level, we consider how the dynamics can be properly mapped in two different sets of variables (at the price of having to deal with a coordinate dependent lattice step), and we infer some possible implications on the equivalence of the μ0 and μ¯ scheme of loop quantum cosmology.

scholarly journals A first step towards the inflationary trans-Planckian problem treatment in loop quantum cosmology

2018 ◽  
Vol 27 (07) ◽  
pp. 1850067 ◽  
Author(s):  
Killian Martineau ◽  
Aurélien Barrau ◽  
Julien Grain
Keyword(s):  
Observational Data ◽  
Quantum Cosmology ◽  
Initial Conditions ◽  
Power Spectra ◽  
Dispersion Relations ◽  
Loop Quantum Cosmology ◽  
Modified Dispersion Relations

For most initial conditions, cosmologically relevant physical modes were trans-Planckian at the bounce time, often by many magnitude orders. We improve the usual loop quantum cosmology calculation of the primordial power spectra — in the inflationary framework — by accounting for those trans-Planckian effects through modified dispersion relations. This can induce drastic changes in the spectrum, making it either compatible or incompatible with observational data, depending on the details of the choices operated.

Tomographic analysis of quantum and classical de Sitter cosmological models

2019 ◽  
Vol 28 (16) ◽  
pp. 2040009 ◽  
Author(s):  
Cosimo Stornaiolo
Keyword(s):  
Quantum Cosmology ◽  
Classical Limit ◽  
Initial Conditions ◽  
Quantum Tomography ◽  
Wave Functions ◽  
Hamiltonian Constraint ◽  
De Sitter ◽  
Quantum Universe ◽  
Tomographic Analysis ◽  
The Universe

In this work, we show the importance of introducing the quantum tomography formalism to analyze the properties of wave functions in quantum cosmology. In particular, we examine the initial conditions of the universe proposed by various authors in the context of de Sitter’s cosmology studying their classical limit and comparing it with the classical tomogram obtained from the Hamiltonian constraint in General Relativity. This comparison gives us the opportunity to find under which conditions there is a transition from the quantum universe to the classical one. A relevant result is that in these models the decay of the cosmological constant is a sufficient condition for this transition.

Polymer quantization effects on gauge-flation

2018 ◽  
Vol 15 (10) ◽  
pp. 1850169
Author(s):  
M. Mardaani ◽  
K. Nozari
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Gauge Field ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Loop Quantum Cosmology ◽  
Abelian Gauge ◽  
Friedmann Equations ◽  
Cosmological Inflation

Polymer quantum mechanics, as a non-standard representation of quantum mechanics, is based on a symmetric sector of loop quantum gravity known as loop quantum cosmology. In this work, by analyzing the Hamiltonian and Friedmann equations in the standard Hilbert space and polymer Hilbert space, we show that polymer quantization is a successful formalism for a non-Abelian gauge field driving the cosmological inflation, the so-called gauge-flation, in order to remove initial singularity and also keeping the inflationary trajectories in this model as attractors of dynamics after the bounce.

The evolutionary pictures for phantom field in loop quantum cosmology

2019 ◽  
Vol 28 (15) ◽  
pp. 1950170
Author(s):  
Kui Xiao
Keyword(s):  
Dark Matter ◽  
Quantum Cosmology ◽  
Scalar Fields ◽  
Chaplygin Gas ◽  
Loop Quantum Cosmology ◽  
Phantom Field ◽  
Dynamical Behaviors ◽  
Slow Roll ◽  
The Universe ◽  
Slow Roll Inflation

The evolutionary pictures for phantom field in loop quantum cosmology are discussed in this paper. Comparing the dynamical behaviors of the phantom field with one of the canonical scalar fields in loop quantum cosmology scenario, we found that the [Formula: see text] phase trajectories are the same, but the [Formula: see text] phase-spaces are very different, and the phantom field with considering potentials can drive neither super inflation nor slow-roll inflation in loop quantum cosmology (LQC) scenario. While the universe is filled with multiple dark fluids, to ensure that the condition [Formula: see text] does not violate, the energy density of dark matter [Formula: see text] and the equation-of-state of phantom field [Formula: see text] should satisfy the condition [Formula: see text] at the bounce point. If this constraint condition holds, the universe can enter an inflationary stage, and it is possible to unify the description of phantom field, dark matter and inflation. We introduced a toy model which has the same form of the general Chaplygin gas to unify the dark energy, dark matter and slow-roll inflation, and the slow-roll inflation of the toy model has also been discussed.

SEARCHING FOR QUANTUM GRAVITY EFFECTS IN COSMOLOGICAL DATA

1994 ◽  
Vol 03 (01) ◽  
pp. 257-263 ◽  
Author(s):  
D.S. SALOPEK
Keyword(s):  
Quantum Gravity ◽  
Initial Conditions ◽  
Microwave Background ◽  
Nonlinear Quantum ◽  
Gravity Effects ◽  
Cosmological Data ◽  
Clustering Data ◽  
Non Gaussian ◽  
Excess Power ◽  
The Universe

If the inflationary scenario describes our Universe, then it is possible that quantum gravity phenomena could be observed in anisotropy experiments of the microwave background as well as in galaxy clustering data. Primordial gravitational radiation arising from inflation is a consequence of quantum gravity. Moreover, the wavefunction of the Universe is currently being measured by the COBE satellite. A non-Gaussian distribution could be a signature of nonlinear quantum gravity. In fact, the excess power power seen in the APM survey of galaxies can arise from non-Gaussian initial conditions generated during inflation.

Sign in / Sign up

Export Citation Format

Share Document