Quantum Nature of the Big Bang

Loop quantum cosmology provides a nice solution of avoiding the big bang singularity through a big bounce mechanism in the high energy region. In loop quantum cosmology an inflationary universe is emergent after the big bounce, no matter what matter component is filled in the universe. A super-inflation phase without phantom matter will appear in a certain way in the initial stage after the bounce; then the universe will undergo a normal inflation stage. We discuss the condition of inflation in detail in this framework. Also, for slow-roll inflation, we expect the imprint from the effects of the loop quantum cosmology should be left in the primordial perturbation power spectrum. However, we show that this imprint is too weak to be observed.

Section: Effective Dynamics In Loop Quantum Cosmology and Big Bounce mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Inflationary universe in loop quantum cosmology

Zhang

Ling

2007

“…This model has been successfully quantized in LQC and its physics has been well understood [4]. The underlying quantum constraint is non-local and uniformly discrete in volume.…”

mentioning

confidence: 99%

“…In recent years, extensive analytical work and numerical simulations have shown that the big bang singularity can be resolved in LQC. The non-perturbative quantum geometric effects result in a quantum bounce to a pre-big bang branch when the energy density of the universe reaches close to the Planck scale [4]. Further, analysis from exactly solvable models show that the bounce is generic [5].…”

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confidence: 99%

Covariant effective action for loop quantum cosmology à la Palatini

Olmo

Singh

2009

Self Cite

123

130

In loop quantum cosmology, non-perturbative quantum gravity effects lead to the resolution of the big bang singularity by a quantum bounce without introducing any new degrees of freedom. Though fundamentally discrete, the theory admits a continuum description in terms of an effective Hamiltonian. Here we provide an algorithm to obtain the corresponding effective action, establishing in this way the covariance of the theory for the first time. This result provides new insights on the continuum properties of the discrete structure of quantum geometry and opens new avenues to extract physical predictions such as those related to gauge invariant cosmological perturbations.Understanding the nature of gravity and spacetime at high energies is one of the most interesting open issues in theoretical physics. In it lie the answers to various questions which Einstein's theory of general relativity (GR) fails to address, such as the origin of our Universe and the resolution of the big bang singularity. This is also deeply connected with our understanding of the way various dynamical and structural properties of the spacetime and the field equations, such as covariance, emerge from a more fundamental description.It is generally believed that limitations of GR would be overcome in a quantum theory of gravity, which is expected to cure the big bang singularity and provide modifications to the Friedman dynamics in the early universe. An approach in this direction is to find a renormalizable perturbative theory of quantum gravity which agrees with GR at low energies. This inspired modifications of the Einstein-Hilbert action via addition of terms involving higher curvature invariants and higher derivatives of the metric, motivating ansatzes to potentially tame the initial singularity (see for example [1]). They inevitably have more degrees of freedom than GR and often face limitations such as lack of unitarity, ghosts, and instabilities. These effective theories are based on a classical continuum spacetime and are covariant by construction.To faithfully capture the dynamical nature of spacetime, however, we need to go beyond the perturbative methods. One such approach is loop quantum gravity, which is background independent and non-perturbative [2]. It is a canonical quantization of gravity with classical phase space given by the Ashtekar variables: the connection A i a and the triad E a i . A key prediction of the theory is the discreteness of the eigenvalues of geometrical operators such as volume and area. Thus, the classical notion of a smooth differentiable geometry is replaced by a discrete quantum geometry. Techniques of LQG have been successfully applied to formulate loop quantum cosmology (LQC) which is a non-perturbative quantization of cosmological spacetimes [3]. In recent years, extensive analytical work and numerical simulations have shown that the big bang singularity can be resolved in LQC. The non-perturbative quantum geometric effects result in a quantum bounce to a pre-big bang branch when the energy density o...

“…Loop quantisation of the homogeneous and isotropic FRW models have been performed in Ref. [3,4,5] (K = 0), Ref. [6,7] (K = 1) and Ref.…”

Section: Introductionmentioning

confidence: 99%

Effective dynamics of the closed loop quantum cosmology

Mielczarek

Hrycyna

Szydłowski

2009

In this paper we study dynamics of the closed FRW model with holonomy corrections coming from loop quantum cosmology. We consider models with a scalar field and cosmological constant. In case of the models with cosmological constant and free scalar field, dynamics reduce to 2D system and analysis of solutions simplify. If only free scalar field is included then universe undergoes non-singular oscillations. For the model with cosmological constant, different behaviours are obtained depending on the value of Λ. If the value of Λ is sufficiently small, bouncing solutions with asymptotic de Sitter stages are obtained. However if the value of Λ exceeds critical value Λ c = √ 3m 2 Pl 2πγ 3 ≃ 21m 2 Pl then solutions become oscillatory. Subsequently we study models with a massive scalar field. We find that this model possess generic inflationary attractors. In particular field, initially situated in the bottom of the potential, is driven up during the phase of quantum bounce. This subsequently leads to the phase of inflation. Finally we find that, comparing with the flat case, effects of curvature do not change qualitatively dynamics close to the phase of bounce. Possible effects of inverse volume corrections are also briefly discussed.