Background Independent Approach Research Articles

Measuring Hubble constant in an anisotropic extension of [formula omitted]CDM model

Cosmic Microwave Background (CMB) independent approaches are frequently used in the literature to provide estimates of Hubble constant (H0). In this work, we report CMB independent constraints on H0 in an anisotropic extension of ΛCDM model using the Big Bang Nucleosynthesis (BBN), Baryonic Acoustic Oscillations (BAOs), Cosmic Chronometer (CC), and Pantheon+ (PP) compilation of Type Ia supernovae and SH0ES Cepheid host distance anchors data. In the anisotropic model, we find H0=70.1−1.5+1.2(72.67±0.85)kms−1Mpc−1 both with 68% CL from BAO+BBN+CC+PP (BAO+BBN+CC+PPSH0ES) data. The analyses of the anisotropic model with the two combinations of datasets reveal that anisotropy is positively correlated with H0, and an anisotropy of the order 10−14 in the anisotropic model reduces the H0 tension by ∼2σ.

Entanglement negativity on random spin networks

We investigate multipartite entanglement for quantum states of $3D$ space geometry, described via generalized random spin networks with fixed areas, in the context of background independent approaches to quantum gravity. We focus on entanglement negativity as a well defined witness of quantum correlations for mixed states, in our setting describing generic subregions of the boundary of a quantum $3D$ region of space. In particular, we consider a generic tripartition of the boundary of an open spin network state and we compute the typical R\'enyi negativity of two boundary subregions $A$ and $B$ immersed in the environment $C$, explicitly for a set of simple open random spin network states. We use the random character of the spin network to exploit replica and random average techniques to derive the typical R\'enyi negativty via a classical generalized Ising model correspondence generally used for random tensor networks in the large bond regime. For trivially correlated random spin network states, with only local entanglement between spins located on the network edges, we find that typical log negativity displays a holographic character, in agreement with the results for random tensor networks, in large spin limit. When nonlocal bulk entanglement between intertwiners at the vertices is considered the negativity increases, while at the same time the holographic scaling is generally perturbed by the bulk contribution.

Properties of a proposed background independent exact renormalization group

We explore the properties of a recently proposed background independent exact renormalization group approach to gauge theories and gravity. In the process we also develop the machinery needed to study it rigorously. The proposal comes with some advantages. It preserves gauge invariance manifestly, avoids introducing unphysical fields, such as ghosts and Pauli-Villars fields, and does not require gauge-fixing. However, we show that in the simple case of $SU(N)$ Yang-Mills it does not completely regularize the longitudinal part of vertex functions already at one loop, invalidating certain methods for extracting universal components. Moreover, we demonstrate a kind of no-go theorem: within the proposed structure, whatever choice is made for covariantization and cutoff profiles, the two-point vertex flow equation at one loop cannot be both transverse, as required by gauge invariance, and fully regularized.

Space–Time Physics in Background-Independent Theories of Quantum Gravity

Background independence is often emphasized as an important property of a quantum theory of gravity that takes seriously the geometrical nature of general relativity. In a background-independent formulation, quantum gravity should determine not only the dynamics of space–time but also its geometry, which may have equally important implications for claims of potential physical observations. One of the leading candidates for background-independent quantum gravity is loop quantum gravity. By combining and interpreting several recent results, it is shown here how the canonical nature of this theory makes it possible to perform a complete space–time analysis in various models that have been proposed in this setting. In spite of the background-independent starting point, all these models turned out to be non-geometrical and even inconsistent to varying degrees, unless strong modifications of Riemannian geometry are taken into account. This outcome leads to several implications for potential observations as well as lessons for other background-independent approaches.

Background independent exact renormalisation

A geometric formulation of Wilson’s exact renormalisation group is presented based on a gauge invariant ultraviolet regularisation scheme without the introduction of a background field. This allows for a manifestly background independent approach to quantum gravity and gauge theories in the continuum. The regularisation is a geometric variant of Slavnov’s scheme consisting of a modified action, which suppresses high momentum modes, supplemented by Pauli–Villars determinants in the path integral measure. An exact renormalisation group flow equation for the Wilsonian effective action is derived by requiring that the path integral is invariant under a change in the cutoff scale while preserving quasi-locality. The renormalisation group flow is defined directly on the space of gauge invariant actions without the need to fix the gauge. We show that the one-loop beta function in Yang–Mills and the one-loop divergencies of General Relativity can be calculated without fixing the gauge. As a first non-perturbative application we find the form of the Yang–Mills beta function within a simple truncation of the Wilsonian effective action.

Typicality in spin-network states of quantum geometry

In this work, we extend the so-called typicality approach, originally formulated in statistical mechanics contexts, to $SU(2)$-invariant spin-network states. Our results do not depend on the physical interpretation of the spin network; however, they are mainly motivated by the fact that spin-network states can describe states of quantum geometry, providing a gauge-invariant basis for the kinematical Hilbert space of several background-independent approaches to quantum gravity. The first result is, by itself, the existence of a regime in which we show the emergence of a typical state. We interpret this as the proof that in that regime there are certain (local) properties of quantum geometry which are "universal". Such a set of properties is heralded by the typical state, of which we give the explicit form. This is our second result. In the end, we study some interesting properties of the typical state, proving that the area law for the entropy of a surface must be satisfied at the local level, up to logarithmic corrections which we are able to bound.

Exact renormalization group and loop variables: A background independent approach to string theory

This paper is a self-contained review of the loop variable approach to string theory. The Exact Renormalization Group is applied to a world sheet theory describing string propagation in a general background involving both massless and massive modes. This gives interacting equations of motion for the modes of the string. Loop variable techniques are used to obtain gauge invariant equations. Since this method is not tied to flat space–time or any particular background metric, it is manifestly background independent. The technique can be applied to both open and closed strings. Thus gauge invariant and generally covariant interacting equations of motion can be written for massive higher spin fields in arbitrary backgrounds. Some explicit examples are given.

Localization and diffusion in polymer quantum field theory

Polymer quantization is a nonstandard approach to quantizing a classical system inspired by background-independent approaches to quantum gravity such as loop quantum gravity. When applied to field theory it introduces a characteristic polymer scale at the level of the fields' classical configuration space. Compared with models with space-time discreteness or noncommutativity, this is an alternative way in which a characteristic scale can be introduced in a field theoretic context. Motivated by this comparison we study here localization and diffusion properties associated with polymer field observables and dispersion relation in order to shed some light on the novel physical features introduced by polymer quantization. While localization processes seems to be only mildly affected by polymer effects, we find that polymer diffusion differs significantly from the ``dimensional reduction'' picture emerging in other Planck-scale models beyond local quantum field theory.

Towards Loop Quantum Supergravity (LQSG)

Should nature be supersymmetric, then it will be described by Quantum Supergravity at least in some energy regimes. The currently most advanced description of Quantum Supergravity and beyond is Superstring Theory/M-Theory in 10/11 dimensions. String Theory is a top-to-bottom approach to Quantum Supergravity in that it postulates a new object, the string, from which classical Supergravity emerges as a low energy limit. On the other hand, one may try more traditional bottom-to-top routes and apply the techniques of Quantum Field Theory. Loop Quantum Gravity (LQG) is a manifestly background independent and non-perturbative approach to the quantisation of classical General Relativity, however, so far mostly without supersymmetry. The main obstacle to the extension of the techniques of LQG to the quantisation of higher dimensional Supergravity is that LQG rests on a specific connection formulation of General Relativity which exists only in D+1=4 dimensions. In this Letter we introduce a new connection formulation of General Relativity which exists in all space–time dimensions. We show that all LQG techniques developed in D+1=4 can be transferred to the new variables in all dimensions and describe how they can be generalised to the new types of fields that appear in Supergravity theories as compared to standard matter, specifically Rarita–Schwinger and p-form gauge fields.

Comments on Background Independence and Gauge Redundancies

We describe the definition and the role background independence and the closely related notion of diffeomorphism invariance play in modern string theory. These important concepts are transformed by a new understanding of gauge redundancies and their implementation in non-perturbative quantum field theory and quantum gravity. This new understanding also suggests a new role for the so-called background-independent approaches to directly quantize the gravitational field. This article is intended for a general audience, and is based on a plenary talk given in the Loops 2007 conference in Morelia, Mexico.

FUNDAMENTAL STRUCTURE OF LOOP QUANTUM GRAVITY

In the recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is to construct a mathematically rigorous, background independent, non-perturbative quantum theory for a Lorentzian gravitational field on a four-dimensional manifold. In the approach, the principles of quantum mechanics are combined with those of general relativity naturally. Such a combination provides us a picture of, so-called, quantum Riemannian geometry, which is discrete on the fundamental scale. Imposing the quantum constraints in analogy from the classical ones, the quantum dynamics of gravity is being studied as one of the most important issues in loop quantum gravity. On the other hand, the semi-classical analysis is being carried out to test the classical limit of the quantum theory. In this review, the fundamental structure of loop quantum gravity is presented pedagogically. Our main aim is to help non-experts to understand the motivations, basic structures, as well as general results. It may also be beneficial to practitioners to gain insights from different perspectives on the theory. We will focus on the theoretical framework itself, rather than its applications, and do our best to write it in modern and precise langauge while keeping the presentation accessible for beginners. After reviewing the classical connection dynamical formalism of general relativity, as a foundation, the construction of the kinematical Ashtekar–Isham–Lewandowski representation is introduced in the content of quantum kinematics. The algebraic structure of quantum kinematics is also discussed. In the content of quantum dynamics, we mainly introduce the construction of a Hamiltonian constraint operator and the master constraint project. At last, some applications and recent advances are outlined. It should be noted that this strategy of quantizing gravity can also be extended to obtain other background-independent quantum gauge theories. There is no divergence within this background-independent and diffeomorphism-invariant quantization program of matter coupled to gravity.

Dynamics of a scalar field in a polymer-like representation

In the last 20 years, loop quantum gravity, a background-independent approach to unify general relativity and quantum mechanics, has been widely investigated. We consider the quantum dynamics of a real massless scalar field coupled to gravity in this framework. A Hamiltonian operator for the scalar field can be well defined in the coupled diffeomorphism-invariant Hilbert space, which is both self-adjoint and positive. On the other hand, the Hamiltonian constraint operator for the scalar field coupled to gravity can be well defined in the coupled kinematical Hilbert space. There are one-parameter ambiguities due to scalar field in the construction of both operators. The results heighten our confidence that there is no divergence within this background-independent and diffeomorphism-invariant quantization approach of matter coupled to gravity. Moreover, to avoid possible quantum anomaly, the master constraint programme can be carried out in this coupled system by employing a self-adjoint master constraint operator on the diffeomorphism-invariant Hilbert space.

From 3-geometry transition amplitudes to graviton states

In various background independent approaches, quantum gravity is defined in terms of a field propagation kernel: a sum over paths interpreted as a transition amplitude between 3-geometries, expected to project quantum states of the geometry on the solutions of the Wheeler–deWitt equation. We study the relation between this formalism and conventional quantum field theory methods. We consider the propagation kernel of 4d Lorentzian general relativity in the temporal gauge, defined by a conventional formal Feynman path integral, gauge fixed à la Faddeev–Popov. If space is compact, this turns out to depend only on the initial and final 3-geometries, while in the asymptotically flat case it depends also on the asymptotic proper time. We compute the explicit form of this kernel at first order around flat space, and show that it projects on the solutions of all quantum constraints, including the Wheeler–DeWitt equation, and yields the correct vacuum and n-graviton states. We also illustrate how the Newtonian interaction is coded into the propagation kernel, a key open issue in the spinfoam approach.

Addressing Challenges of Quantum Gravity Through Quantum Geometry: Black holes and Big-bang

In this article I present a brief review of some of the recent advances in loop quantum gravity - a non-perturbative, background independent approach to quantum gravity based on quantum geometry. The emphasis is on physical issues.

On exact tachyon potential in open string field theory

In these notes we revisit the tachyon lagrangian in the open string field theory using background independent approach of Witten from 1992. We claim that the tree level lagrangian (up to second order in derivatives and modulo some class of field redefinitions) is given by $L = e^{-T} (\partial T)^2 + (1+T)e^{-T}$. Upon obvious change of variables this leads to the potential energy $-\phi^2 \log {\phi^2 \over e}$ with canonical kinetic term. This lagrangian may be also obtained from the effective tachyon lagrangian of the p-adic strings in the limit $p\to 1$. Applications to the problem of tachyon condensation are discussed.

Towards a background independent approach to [formula omitted] theory

Work in progress is described which aims to construct a background independent formulation of M theory by extending results about background independent states and observables from quantum general relativity and supergravity to string theory. A list of principles for such a theory is proposed which is drawn from results of both string theory and non-perturbative approaches to quantum gravity. Progress is reported on a background independent membrane field theory and on a realization of the holographic principle based on finite surfaces.