One-loop quantum gravity repulsion in the early Universe

Perturbative quantum gravity formalism is applied to compute the lowest order corrections to the classical spatially flat cosmological Friedmann-Lema?tre-Robertson-Walker solution (for the radiation). The presented approach is analogous to the approach applied to compute quantum corrections to the Coulomb potential in electrodynamics, or rather to the approach applied to compute quantum corrections to the Schwarzschild solution in gravity. In the framework of the standard perturbative quantum gravity, it is shown that the corrections to the classical deceleration, coming from the one-loop graviton vacuum polarization (self-energy), have (UV cutoff free) opposite to the classical repulsive properties which are not negligible in the very early Universe. The repulsive "quantum forces" resemble those known from loop quantum cosmology.     

Loop quantum modified gravity and its cosmological application

A general nonperturvative loop quantization procedure for metric modified gravity is reviewed. As an example, this procedure is applied to scalar-tensor theories of gravity. The quantum kinematical framework of these theories is rigorously constructed. Both the Hamiltonian and master constraint operators are well defined and proposed to represent quantum dynamics of scalar-tensor theories. As an application to models, we set up the basic structure of loop quantum Brans-Dicke cosmology. The effective dynamical equations of loop quantum Brans-Dicke cosmology are also obtained, which lay a foundation for the phenomenological investigation to possible quantum gravity effects in cosmology.     

Surface tension and the cosmological constant

One of the few predictions from quantum gravity models is Sorkin's observation that the cosmological constant has quantum fluctuations originating in the fundamental discreteness of spacetime at the Planck scale. Here we present a compelling analogy between the cosmological constant of the Universe and the surface tension of fluid membranes. The discreteness of spacetime on the Planck scale translates into the discrete molecular structure of a fluid membrane. We propose an analog quantum gravity experiment which realizes Sorkin's idea in the laboratory. We also notice that the analogy sheds light on the cosmological constant problem, suggesting a mechanism for dynamically generating a vanishingly small cosmological constant. We emphasize the generality of Sorkin's idea and suggest that similar effects occur generically in quantum gravity models.     

Modified Friedmann Equations on the Brane from Entropic Force

The well-known area relation of the black hole entropy can be modified from the inclusion of quantum effects, motivated from the loop quantum gravity. Applying this modified entropy-area relation to brane cosmology, we derive the modified cosmological equations governing the evolution of the universe on the brane. We adopt the viewpoint that interprets gravity as an entropic force caused by the changes in the information when a material body moves away from the holographic screen.     

Consequences of a Cosmological Phase Transition at the TeV Scale

A finite vacuum energy density implies the existence of a UV scale for gravitational modes. This gives a phenomenological scale to the dynamical equations governing the cosmological expansion that must satisfy constraints consistent with quantum measurability and spatial flatness. Examination of these constraints for the observed dark energy density establishes a time interval from the transition to the present, suggesting major modifications from the thermal equations of state far from Planck density scales. The assumption that a phase transition initiates the radiation dominated epoch is shown under several scenarios to be able to produce fluctuations to the CMB of the order observed. Quantum measurability constraints (eg. uncertainly relations) define cosmological scales bounded by luminal expansion rates. It is shown that the dark energy can consistently be interpreted as being due to the vacuum energy of collective gravitational modes which manifest as the zero-point motions of coherent Planck scale mass units prior to the UV scale onset of gravitational quantum de-coherence for the cosmology. A cosmological model with multiple scales, one of which replaces an apparent cosmological “constant”, is shown to reproduce standard cosmology during intermediate times, while making the exploration of the early and late time cosmology more accessible. Talk presented at the 2006 biennial conference of the International Association for Relativistic Dynamics, June 12–14, University of Connecticut (Storrs).     

Absence of preclassical solutions in Bianchi I loop quantum cosmology

Loop quantum cosmology, the symmetry reduction of quantum geometry for the study of various cosmological situations, leads to a difference equation for its quantum evolution equation. To ensure that solutions of this equation act in the expected classical manner far from singularities, additional restrictions are imposed on the solution. In this Letter, we consider the Bianchi I model, both the vacuum case and the addition of a cosmological constant, and show using generating function techniques that only the zero solution satisfies these constraints. This implies either that there are technical difficulties with the current method of quantizing the evolution equation, or else loop quantum gravity imposes strong restrictions on the physically allowed solutions.     

Formation and evolution of structure in loop cosmology

Inhomogeneous cosmological perturbation equations are derived in loop quantum gravity, taking into account corrections, in particular, in gravitational parts. This provides a framework for calculating the evolution of modes in structure formation scenarios related to inflationary or bouncing models. Applications here are corrections to the Newton potential and to the evolution of large scale modes which imply nonconservation of curvature perturbations possibly noticeable in a running spectral index. These effects are sensitive to quantization procedures and test the characteristic behavior of correction terms derived from quantum gravity.     

Some aspects of gravitational quantum mechanics

String theory, quantum geometry, loop quantum gravity and black hole physics all indicate the existence of a minimal observable length on the order of Planck length. This feature leads to a modification of Heisenberg uncertainty principle. Such a modified Heisenberg uncertainty principle is referred as gravitational uncertainty principle(GUP) in literatures. This proposal has some novel implications on various domains of theoretical physics. Here, we study some consequences of GUP in the spirit of Quantum mechanics. We consider two problem: a particle in an one-dimensional box and free particle wave function. In each case we will solve corresponding perturbational equations and compare the results with ordinary solutions.     

Inflation and late-time acceleration in braneworld cosmological models with varying brane tension

Braneworld models with variable brane tension λ introduce a new degree of freedom that allows for evolving gravitational and cosmological constants, the latter being a natural candidate for dark energy. We consider a thermodynamic interpretation of the varying brane tension models, by showing that the field equations with variable λ can be interpreted as describing matter creation in a cosmological framework. The particle creation rate is determined by the variation rate of the brane tension, as well as by the brane–bulk energy-matter transfer rate. We investigate the effect of a variable brane tension on the cosmological evolution of the Universe, in the framework of a particular model in which the brane tension is an exponentially dependent function of the scale factor. The resulting cosmology shows the presence of an initial inflationary expansion, followed by a decelerating phase, and by a smooth transition towards a late accelerated de Sitter type expansion. The varying brane tension is also responsible for the generation of the matter in the Universe (reheating period). The physical constraints on the model parameters, resulting from the observational cosmological data, are also investigated.     

Alternative quantization of the Hamiltonian in loop quantum cosmology

Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology are robust against the ambiguities. In this Letter, we quantize the Lorentz term of the gravitational Hamiltonian constraint in the spatially flat FRW model by two approaches different from that of the Euclidean term. One of the approaches is very similar to the treatment of the Lorentz part of Hamiltonian in loop quantum gravity and hence inherits more features from the full theory. Two symmetric Hamiltonian constraint operators are constructed respectively in the improved scheme. Both of them are shown to have the correct classical limit by the semiclassical analysis. In the loop quantum cosmological model with a massless scalar field, the effective Hamiltonians and Friedmann equations are derived. It turns out that the classical big bang is again replaced by a quantum bounce in both cases. Moreover, there are still great possibilities for the expanding universe to recollapse due to the quantum gravity effect.     

量子纠缠与宇宙学弗里德曼方程

量子纠缠作为量子信息理论中最核心的部分,代表量子态一种内在的特性,是微观物质的一种根本的性质,它是以非定域的形式存在于多子量子系统中的一种神奇的物理现象.熵也是量子信息理论的重要概念之一,纠缠熵作为量子信息的一个测度已经成为一种重要的理论工具,为物理学中的各类课题提供了新的研究方法.本文主要考虑量子纠缠的宇宙学应用,试图更好地从纠缠的角度来理解宇宙动力学.本文研究了量子信息理论的概念和宇宙学之间的深层联系,利用费米正则坐标和共形费米坐标构建了弗里德曼- 勒梅特-罗伯逊-沃尔克宇宙学弗里德曼方程和纠缠之间的联系.假设小测地球（a geodesic ball）的纠缠熵在给定体积下是最大的,可以从量子纠缠第一定律推导出弗里德曼方程.研究表明引力与量子纠缠之间存在着某种深刻的联系,这种联系对引力场方程的解是成立的.     

Notes on dark energy interacting with dark matter and unparticle in loop quantum cosmology

We investigate the behavior of dark energy interacting with dark matter and unparticle in the framework of loop quantum cosmology. In four toy models, we study the interaction between the cosmic components by choosing different coupling functions representing the interaction. We found that there are only two attractor solutions namely dark energy dominated and dark matter dominated Universe. The other two models are unstable, as they predict either a dark energy filled Universe or one completely devoid of it.     

Cosmological Plebanski theory

We consider the cosmological symmetry reduction of the Plebanski action as a toy-model to explore, in this simple framework, some issues related to loop quantum gravity and spin-foam models. We make the classical analysis of the model and perform both path integral and canonical quantizations. As for the full theory, the reduced model admits two disjoint types of classical solutions: topological and gravitational ones. The quantization mixes these two solutions, which prevents the model from being equivalent to standard quantum cosmology. Furthermore, the topological solution dominates at the classical limit. We also study the effect of an Immirzi parameter in the model.     

Path Integrals and Alternative Effective Dynamics in Loop Quantum Cosmology

The alternative dynamics of loop quantum cosmology is examined by the path integral formulation.We consider the spatially flat FRW models with a massless scalar field,where the alternative quantizations inherit more features from full loop quantum gravity.The path integrals can be formulated in both timeless and deparameterized frameworks.It turns out that the effective Hamiltonians derived from the two different viewpoints are equivalent to each other.Moreover,the first-order modified Friedmann equations are derived and predict quantum bounces for contracting universe,which coincide with those obtained in canonical theory.     

Loop quantum cosmology and inhomogeneities

Inhomogeneities are introduced in loop quantum cosmology using regular lattice states, with a kinematical arena similar to that in homogeneous models considered earlier. The framework is intended to encapsulate crucial features of background independent quantizations in a setting accessible to explicit calculations of perturbations on a cosmological background. It is used here only for qualitative insights but can be extended with further more detailed input. One can thus see how several parameters occuring in homogeneous models appear from an inhomogeneous point of view. Their physical roles in several cases then become much clearer, often making previously unnatural choices of values look more natural by providing alternative physical roles. This also illustrates general properties of symmetry reduction at the quantum level and the roles played by inhomogeneities. Moreover, the constructions suggest a picture for gravitons and other metric modes as collective excitations in a discrete theory, and lead to the possibility of quantum gravity corrections in large universes.     

Towards the map of quantum gravity

In this paper we point out some possible links between different approaches to quantum gravity and theories of the Planck scale physics. In particular, connections between loop quantum gravity, causal dynamical triangulations, Ho?ava–Lifshitz gravity, asymptotic safety scenario, Quantum Graphity, deformations of relativistic symmetries and nonlinear phase space models are discussed. The main focus is on quantum deformations of the Hypersurface Deformations Algebra and Poincaré algebra, nonlinear structure of phase space, the running dimension of spacetime and nontrivial phase diagram of quantum gravity. We present an attempt to arrange the observed relations in the form of a graph, highlighting different aspects of quantum gravity. The analysis is performed in the spirit of a mind map, which represents the architectural approach to the studied theory, being a natural way to describe the properties of a complex system. We hope that the constructed graphs (maps) will turn out to be helpful in uncovering the global picture of quantum gravity as a particular complex system and serve as a useful guide for the researchers.     

Dark energy interacting with dark matter in classical Einstein and loop quantum cosmology

The cosmological model of dark energy interacting with cold dark matter without coupling to the baryonic matter is studied in the background of both classical Einstein and loop quantum cosmology. We consider two types of interacting models. In the former model, the interaction is a linear combination of the densities of two dark sectors, while in the latter model, the interaction with a constant transfer rate depends only on the density of cold dark matter. It is shown that the dynamical results in loop quantum cosmology are different from those in classical Einstein cosmology for both of the two kinds of interacting models. Moreover, the form of the interaction significantly affects the dynamical results in both kinds of cosmology.