Making classical and quantum canonical general relativity computable through a power series expansion in the inverse cosmological constant

We consider general relativity with a cosmological constant as a perturbative expansion around a completely solvable diffeomorphism invariant field theory. This theory is the lambda --> infinity limit of general relativity. This allows an explicit perturbative computational setup in which the quantum states of the theory and the classical observables can be explicitly computed. An unexpected relationship arises at a quantum level between the discrete spectrum of the volume operator and the allowed values of the cosmological constant.     

Operators with Large R-Charge in N=4 Yang-Mills Theory

It has been recently proposed that string theory in the background of a plane wave corresponds to a certain subsector of the N=4 supersymmetric Yang-Mills theory. This correspondence follows as a limit of the AdS/CFT duality. As a particular case of the AdS/CFT correspondence, it is a priori a strong-weak coupling duality. However, the predictions for the anomalous dimensions which follow from this particular limit are analytic functions of the 't Hooft coupling constant λ and have a well-defined expansion in the weak coupling regime. This allows one to conjecture that the correspondence between the strings on the plane wave background and the Yang-Mills theory works at the level of perturbative expansions. In our paper we perform perturbative computations in the Yang-Mills theory that confirm this conjecture. We calculate the anomalous dimension of the operator corresponding to the elementary string excitation. We verify at the two-loop level that the anomalous dimension has a finite limit when the R-charge J→∞ keeps λ/J² finite. We conjecture that this is true at higher orders of perturbation theory. We show, by summing an infinite subset of Feynman diagrams, under the above assumption, that the anomalous dimensions arising from the Yang-Mills perturbation theory are in agreement with the anomalous dimensions following from the string worldsheet sigma-model.     

Taming the cosmological constant in 2D causal quantum gravity with topology change

As shown in previous work, there is a well-defined nonperturbative gravitational path integral including an explicit sum over topologies in the setting of causal dynamical triangulations in two dimensions. In this paper we derive a complete analytical solution of the quantum continuum dynamics of this model, obtained uniquely by means of a double-scaling limit. We show that the presence of infinitesimal wormholes leads to a decrease in the effective cosmological constant, reminiscent of the suppression mechanism considered by Coleman and others in the four-dimensional Euclidean path integral. Remarkably, in the continuum limit we obtain a finite spacetime density of microscopic wormholes without assuming fundamental discreteness. This shows that one can in principle make sense of a gravitational path integral which includes a sum over topologies, provided suitable causality restrictions are imposed on the path integral histories.     

Cosmological constant from degenerate vacua

Under the hypothesis that the cosmological constant vanishes in the true ground state with lowest possible energy density, we argue that the observed small but finite vacuumlike energy density can be explained if we consider a theory with two or more degenerate perturbative vacua, which are unstable due to quantum tunneling, and if we still live in one of such states. An example is given making use of the topological vacua in non-Abelian gauge theories.     

Bekenstein-Hawking Cosmological Entropy and Correction Term Corresponding Cosmological Horizon of Rotating and Charged Black String

Utilizing the quantum statistical method and applying the new state density equation motivated by generalized uncertainty principle in quantum gravitaty, we avoid the difficulty in solving wave equation and directly calculate the partition function ofbosonic and fermionic field on the background of rotating and charged black string. Then near the cosmological horizon, entropies of bosonic and fermionic field are calculated on the background of black string. When constant λ introduced ingeneralized uncertainty principle takes a proper value, we derive Bekenstein-Hawking entropy and the correction value corresponding cosmological horizon on the background of rotating and charged black string. Because we use the new state density equation, in our calculation there are not divergent term and small massapproximation in the original brick-wall method. From the view of quantum statistic mechanics, the correction value to Bekenstein-Hawking entropy of the black string is derived. It makes people deeply understand the correction value to the entropyof the black string cosmological horizon in non-spherical coordinate spacetime.     

Universality near zero virtuality

In this paper we study a random matrix model with the chiral and flavor structure of the QCD Dirac operator and a temperature dependence given by the lowest Matsubara frequency. Using the supersymmetric method for random matrix theory, we obtain an exact, analytic expression for the average spectral density. In the large-n limit, the spectral density can be obtained from the solution to a cubic equation. This spectral density is nonzero in the vicinity of eigenvalue zero only for temperatures below the critical temperature of this model. Our main result is the demonstration that the microscopic limit of the spectral density is independent of temperature (apart from a temperature dependent scale factor expressed in terms of the chiral condensate) up to the critical temperature. This is due to a number of remarkable cancellations. This result provides strong support for the conjecture that the microscopic spectral density is universal. In our derivation, we emphasize the symmetries of the partition function and show that this universal behavior is closely related to the existence of an invariant saddle-point manifold.     

Vertex Operators in 4D Quantum Gravity Formulated as CFT

We study vertex operators in 4D conformal field theory derived from quantized gravity, whose dynamics is governed by the Wess-Zumino action by Riegert and the Weyl action. Conformal symmetry is equal to diffeomorphism symmetry in the ultraviolet limit, which mixes positive-metric and negative-metric modes of the gravitational field and thus these modes cannot be treated separately in physical operators. In this paper, we construct gravitational vertex operators such as the Ricci scalar, defined as space-time volume integrals of them are invariant under conformal transformations. Short distance singularities of these operator products are computed and it is shown that their coefficients have physically correct signs. Furthermore, we show that conformal algebra holds even in the system perturbed by the cosmological constant vertex operator as in the case of the Liouville theory shown by Curtright and Thorn.     

Chern-Simons Theory,Matrix Integrals,and Perturbative Three-Manifold Invariants

The universal perturbative invariants of rational homology spheres can be extracted from the Chern-Simons partition function by combining perturbative and nonperturbative results. We spell out the general procedure to compute these invariants, and we work out in detail the case of Seifert spaces. By extending some previous results of Lawrence and Rozansky, the Chern-Simons partition function with arbitrary simply-laced group for these spaces is written in terms of matrix integrals. The analysis of the perturbative expansion amounts to the evaluation of averages in a Gaussian ensemble of random matrices. As a result, explicit expressions for the universal perturbative invariants of Seifert homology spheres up to order five are presented.     

宇宙常数的Bulk流形的起源

关于宇宙常数问题是个至今没有解决的问题, 它的来源至今还没有一个共识. 从额外维的流形出发, 给出了宇宙常数的,bulk,流形起源的理论, 得到了不同情况下宇宙常数的取值和宇宙常数随时间演化的函数, 并且得到了可拟合现代天文观测的宇宙常数.     

Models of the universe

In this paper a theory of models of the universe is proposed. We refer to such models ascosmological models, where a cosmological model is defined as an Einstein-inextendible Einstein spacetime. A cosmological model isabsolute if it is a Lorentz-inextendible Einstein spacetime,predictive if it is globally hyperbolic, andnon-predictive if it is nonglobally-hyperbolic. We discuss several features of these models in the study of cosmology. As an example, any compact Einstein spacetime is always a non-predictive absolute cosmological model, whereas a noncompact complete Einstein spacetime is an absolute cosmological model which may be either predictive or non-predictive. We discuss the important role played by maximal Einstein spacetimes. In particular, we examine the possible proper Lorentz-extensions of such spacetimes, and show that a spatially compact maximal Einstein spacetime is exclusively either a predictive cosmological model or a proper sub-spacetime of a non-predictive cosmological model. Provided that the Strong Cosmic Censorship conjecture is true, a generic spatially compact maximal Einstein spacetime must be a predictive cosmological model. It isconjectured that the Strong Cosmic Censorship conjecture isnot true, and converting a vice to a virtue it is argued that the failure of the Strong Cosmic Censorship conjecture would point to what may be general relativity's greatest prediction of all, namely,that general relativity predicts that general relativity cannot predict the entire history of the universe.     

Time-Dependent Density of Modified Cosmic Chaplygin Gas with Variable Cosmological Constant in Non-Flat Universe

In this paper we study modified cosmic Chaplygin cosmology with non-zero cosmological constant in non-flat Universe. By using well-known forms of scale factor we obtain time-dependent dark energy density by numerical analysis of non-linear differential equation and fitting curves. We use observational data to fix solution and discuss about stability of our system. First of all we consider cosmological constant as a constant in Einstein equation, and then study possibility of variable cosmological constant.     

A class of stationary rotating string cosmological models

We obtain a one parameter class of stationary rotating string cosmological models of which the well-known Gödel universe is a particular case. By suitably choosing the free parameter function, it is always possible to satisfy the energy conditions. The rotation of the model hinges on the cosmological constant which turns out to be negative. String-dust distribution in Gödel-type universes is also briefly discussed.     

Relating hard QCD processes through universality of mass singularities (II)

Extending previous techniques we obtain at all orders the factorization of mass singularities for every hard QCD process. These appear in a universal factor that can be reabsorbed into the standard parton density. Thus suitable ratios of cross sections can be computed by a perturbative expansion in the running coupling constant. Moreover, at the leading log level we obtain, after explicit cancellation of infrared divergences, the scaling violation of the operator product expansion.     

Quantum holonomy theory

We present quantum holonomy theory, which is a non‐perturbative theory of quantum gravity coupled to fermionic degrees of freedom. The theory is based on a ‐algebra that involves holonomy‐diffeo‐morphisms on a 3‐dimensional manifold and which encodes the canonical commutation relations of canonical quantum gravity formulated in terms of Ashtekar variables. Employing a Dirac type operator on the configuration space of Ashtekar connections we obtain a semi‐classical state and a kinematical Hilbert space via its GNS construction. We use the Dirac type operator, which provides a metric structure over the space of Ashtekar connections, to define a scalar curvature operator, from which we obtain a candidate for a Hamilton operator. We show that the classical Hamilton constraint of general relativity emerges from this in a semi‐classical limit and we then compute the operator constraint algebra. Also, we find states in the kinematical Hilbert space on which the expectation value of the Dirac type operator gives the Dirac Hamiltonian in a semi‐classical limit and thus provides a connection to fermionic quantum field theory. Finally, an almost‐commutative algebra emerges from the holonomy‐diffeomorphism algebra in the same limit.     

Effects of the quantization ambiguities on the Big Bounce dynamics

In this paper, we investigate dynamics of the modified loop quantum cosmology models using dynamical systems methods. Modifications considered come from the choice of the different field strength operator F̂ and result in different forms of the effective Hamiltonian. Such an ambiguity of the choice of this expression from some class of functions is allowed in the framework of loop quantization. Our main goal is to show how such modifications can influence the bouncing universe scenario in the loop quantum cosmology. In effective models considered we classify all evolutional paths for all admissible initial conditions. The dynamics is reduced to the form of a dynamical system of the Newtonian type on a two-dimensional phase plane. These models are equivalent dynamically to the FRW models with the decaying effective cosmological term parameterized by the canonical variable p (or by the scale factor a). We demonstrate that the evolutional scenario depends on the geometrical constant parameter Λ as well as the model parameter n. We find that for the positive cosmological constant there is a class of oscillating models without the initial and final singularities. The new phenomenon is the appearance of curvature singularities for the finite values of the scale factor, but we find that for the positive cosmological constant these singularities can be avoided. The values of the parameter n and the cosmological constant differentiate asymptotic states of the evolution. For the positive cosmological constant the evolution begins at the asymptotic state in the past represented by the de Sitter contracting (deS₋) spacetime or the static Einstein universe H = 0 or H =  − ∞ state and reaches the de Sitter expanding state (deS₊), the state H = 0 or H =  + ∞ state. In the case of the negative cosmological constant we obtain the past and future asymptotic states as the Einstein static universes.     

Entropy of higher-dimensional charged Gauss–Bonnet black hole in de Sitter space

The fundamental equation of the thermodynamic system gives the relation between the internal energy, entropy and volume of two adjacent equilibrium states. Taking a higher-dimensional charged Gauss–Bonnet black hole in de Sitter space as a thermodynamic system, the state parameters have to meet the fundamental equation of thermodynamics. We introduce the effective thermodynamic quantities to describe the black hole in de Sitter space. Considering that in the lukewarm case the temperature of the black hole horizon is equal to that of the cosmological horizon, we conjecture that the effective temperature has the same value. In this way, we can obtain the entropy formula of spacetime by solving the differential equation. We find that the total entropy contains an extra term besides the sum of the entropies of the two horizons. The corrected term of the entropy is a function of the ratio of the black hole horizon radius to the cosmological horizon radius, and is independent of the charge of the spacetime.     

Superstrings on hyperelliptic surfaces and the two-loop vanishing of the cosmological constant

We calculate the supersymmetric type II string partition function in a flat background for the situation where the world-sheet is hyperelliptic. We show explicitly that the contribution to the cosmological constant from hyperelliptic world-surfaces vanishes for genus ⩽ 20. This implies, in particular, that the cosmological constant vanishes completely to two loops. Due to the decoupling of the holomorphic and antiholomorphic sectors, this conclusion holds equally well for the heterotic string.