119270462
Stress-energy tensor correlators of a quantum field in Euclidean R N and AdS N spaces via the generalized zeta-function method
In this paper we calculate the vacuum expectation values of the stress-energy bitensor of a massive quantum scalar field with general coupling to $N$-dimensional Euclidean spaces and hyperbolic spaces which are Euclidean sections of the anti-de Sitter spaces. These correlators, also known as the noise kernel, act as sources in the Einstein-Langevin equations of stochastic gravity [B. L. Hu and E. Verdaguer, Living Rev. Relativity 11, 3 (2008).][B. L. Hu and E. Verdaguer, Classical Quantum Gravity 20, R1 (2003).] which govern the induced metric fluctuations beyond the mean-field dynamics described by the semiclassical Einstein equations of semiclassical gravity. Because these spaces are maximally symmetric the eigenmodes have analytic expressions which facilitate the computation of the zeta function [J. S. Dowker and R. Critchley, Phys. Rev. D 13, 224 (1976); J. S. DowkerR. Critchley, Phys. Rev. D 13, 3224 (1976).][S. W. Hawking, Commun. Math. Phys. 55, 133 (1977).]. Upon taking the second functional variation of the generalized zeta function introduced in [N. G. Phillips and B. L. Hu, Phys. Rev. D 55, 6123 (1997).] we obtain the correlators of the stress tensor for these two classes of spacetimes. Both the short and the large geodesic distance limits of the correlators are presented for dimensions up to 11. We mention current research problems in early universe cosmology, black hole physics and gravity-fluid duality where these results can be usefully applied to.
118267306
Cosmology as `Condensed Matter' Physics
We note that in general there exist two basic aspects in any branch of physics, including cosmology - one dealing with the attributes of basic constituents and forces of nature, the other dealing with how structures arise from them and how they evolve. Current research in quantum and superstring cosmology is directed mainly towards the first aspect, even though a viable theory of the underlying interactions is lacking. We call the attention to the development of the second aspect, i.e., on the organization and processing of the basic constituents of matter (in classical cosmology) and spacetime (in quantum cosmology). Many newly developed concepts and techniques in condensed matter physics stemming from the investigation of disordered, dynamical and complex systems can guide us in asking the right questions and formulating new solutions to existing and developing cosmological issues, thereby broadening our view of the universe both in its formative and present state.
119407258
Quantum statistical processes in the early universe
We show how the concept of quantum open system and the methods in non-equilibrium statistical mechanics can be usefully applied to studies of quantum statistical processes in the early universe. We first sketch how noise, fluctuation, dissipation and decoherence processes arise in a wide range of cosmological problems. We then focus on the origin and nature of noise in quantum fields and spacetime dynamics. We introduce the concept of geometrodynamic noise and suggest a statistical mechanical definition of gravitational entropy. We end with a brief discussion of the theoretical appropriateness to view the physical universe as an open system.
18511662
Noise and fluctuations in semiclassical gravity.
We continue our earlier investigation of the back reaction problem in semiclassical gravity with the Schwinger-Keldysh or closed-time-path (CTP) functional formalism using the language of the decoherent history formulation of quantum mechanics. Making use of its intimate relation with the Feynman-Vernon influence functional method, we examine the statistical mechanical meaning and show the interrelation of the many quantum processes involved in the back reaction problem, such as particle creation, decoherence, and dissipation. We show how noise and fluctuation arise naturally from the CTP formalism. We derive an expression for the CTP effective action in terms of the Bogoliubov coefficients and show how noise is related to the fluctuations in the number of particles created. In so doing we have extended the old framework of semiclassical gravity, based on the mean field theory of Einstein equation with a source given by the expectation value of the energy-momentum tensor, to that based on a Langevin-type equation, where the dynamics of the fluctuations of spacetime is driven by the quantum fluctuations of the matter field. This generalized framework is useful for the investigation of quantum processes in the early Universe involving fluctuations, vacuum instability, and phase transition phenomena as well as the nonequilibrium thermodynamics of black holes. It is also essential to an understanding of the transition from any quantum theory of gravity to classical general relativity.
22366791
Noise kernel in stochastic gravity and stress energy bitensor of quantum fields in curved spacetimes
The noise kernel is the vacuum expectation value of the (operator-valued) stress-energy bi-tensor which describes the fluctuations of a quantum field in curved spacetimes. It plays the role in stochastic semiclassical gravity based on the Einstein-Langevin equation similar to the expectation value of the stress-energy tensor in semiclassical gravity based on the semiclassical Einstein equation. According to the stochastic gravity program, this two point function (and by extension the higher order correlations in a hierarchy) of the stress energy tensor possesses precious statistical mechanical information of quantum fields in curved spacetime and, by the self-consistency required of Einstein's equation, provides a probe into the coherence properties of the gravity sector (as measured by the higher order correlation functions of gravitons) and the quantum nature of spacetime. It reflects the low and medium energy (referring to Planck energy as high energy) behavior of any viable theory of quantum gravity, including string theory. It is also useful for calculating quantum fluctuations of fields in modern theories of structure formation and for backreaction problems in cosmological and black holes spacetimes. 
We discuss the properties of this bi-tensor with the method of point-separation, and derive a regularized expression of the noise-kernel for a scalar field in general curved spacetimes. One collorary of our finding is that for a massless conformal field the trace of the noise kernel identically vanishes. We outline how the general framework and results derived here can be used for the calculation of noise kernels for Robertson-Walker and Schwarzschild spacetimes.
17830761
Correlation entropy of an interacting quantum field and H theorem for the O(N) model
Following the paradigm of Boltzmann-BBGKY we propose a correlation entropy (of the nth order) for an interacting quantum field, obtained by `slaving' (truncation with causal factorization) of the higher (n+1 th) order correlation functions in the Schwinger-Dyson system of equations. This renders an otherwise closed system effectively open where dissipation arises. The concept of correlation entropy is useful for addressing issues related to thermalization. As a small yet important step in that direction we prove an H-theorem for the correlation entropy of a quantum mechanical O(N) model with a Closed Time Path Two Particle Irreducible Effective Action at the level of Next-to-Leading-Order large N approximation. This model may be regarded as a field theory in $0$ space dimensions.
118679381
Dynamical scalar degree of freedom in Horava-Lifshitz gravity
We investigate the linear cosmological perturbations of Horcava-Lifshitz gravity in a Friedmann-Robertson-Walker universe without any matter. Our results show that a new gauge-invariant dynamical scalar mode emerges, due to the gauge transformation under the "foliation-preserving" diffeomorphism and "projectability condition," and it can produce a scale invariant power spectrum. In the infrared regime with lambda=1, the dynamical scalar degree of freedom turns to be a nondynamical one at the linear order level.
119229799
Cosmological parameter estimation from CMB and X-ray cluster after Planck
. We investigate constraints on cosmological parameters in three 8-parameter models with the summed neutrino mass as a free parameter, by a joint analysis of CCCP X-ray cluster data, the newly released Planck CMB data as well as some external data sets including baryon acoustic oscillation measurements from the 6dFGS, SDSS DR7 and BOSS DR9 surveys, and Hubble Space Telescope Ho measurement. We find that the combined data strongly favor a non-zero neutrino masses at more than 3 sigma confidence level in these non-vanilla models. Allowing the CMB lensing amplitude A(L) to vary, we find A(L) > 1 at 3 sigma confidence level. For dark energy with a constant equation of state w, we obtain w < -1 at 3 sigma confidence level. The estimate of the matter power spectrum amplitude 08 is discrepant with the Planck value at 2 sigma confidence level, which reflects some tension between X-ray cluster data and Planck data in these non-vanilla models. The tension can be alleviated by adding a 9% systematic shift in the cluster mass function.
119185851
Timelike vector field dynamics in the early universe
We study the dynamics of a timelike vector field when the background spacetime is in an accelerating phase in the early universe. With a timelike vector field, an inflationary phase is shown to be difficult to realize, so we investigate the evolution of a vector field within a scalar field-driven inflation model. Also, we calculate the power spectrum of the vector field without considering the metric perturbations. While the time component of the vector field perturbations provides a scale invariant spectrum when ζ = 0, where ζ is a nonminimal coupling parameter, both the longitudinal and the transverse perturbations give a scale invariant spectrum when ζ = 1/6 in the absence of the coupling terms. The deviation of the power spectrum due to the coupling terms is calculated by use of the Greens’ function.
120519307
Introduction to real-space renormalization-group methods in critical and chaotic phenomena
Abstract The methods of the real-space renormalization group, and their application to critical and chaotic phenomena are reviewed. The article consists of two parts: the first part deals with phase transitions and critical phenomena; the second part, bifurcations and transitions to chaos. We begin with an introduction to the phenomenology of phase transitions and critical phenomena. Seminal concepts such as scaling and universality, and their characterization by critical exponents are discussed. The basic ideas of the renormalization group are then explained. A survey of real-space renormalization-group methods: decimation, Migdal-Kadanoff approximation, cumulant and cluster expansions, is given. The Hamiltonian formulation of classical statistical systems into quantum mechanical systems by the method of the transfer matrix is introduced. Quantum renormalization-group methods of truncation and projection, and their application to the transcribed quantum mechanical Ising model in a transverse field are illustrated. Finally, the quantum cumulant-expansion method as applied to the one-dimensional quantum mechanical XY model is discussed. The second part of the article is devoted to the subject of bifurcations and transitions to chaos. The three most commonly discussed kinds of bifurcations: the pitchfork, tangent and Hopf bifurcations, and the associated routes to chaos: period doubling, intermittency and quasiperiodicity are discussed. Period doubling based on the logistic map is explained in detail. Universality and its expression in terms of functional renormalization-group equations is discussed. The Liapunov characteristic exponent and its analogy to the order parameter are introduced. The effect of external noise and its universal scaling feature are shown. The simplest characterizations of the Henon strange attractor are intuitively illustrated. The purpose of this article is primarily pedagogical. The similarity between critical and chaotic phenomena is a recurrent theme that underlines the importance and usefulness of such concepts as scaling, renormalization and universality.
118528998
Note on self-gravitating radiation in AdS spacetime
Recently Vaganov and Hammersley investigated independently the equilibrium self-gravitating radiation in higher (d >= 4)-dimensional, spherically symmetric anti-de Sitter space. It was found that in 4 = 11, the temperature, mass, and entropy of the self-gravitating configuration are monotonic functions of the central energy density, asymptoting to their maxima as the central density goes to infinity. In this paper we investigate the equilibrium self-gravitating radiation in higher-dimensional, plane-symmetric anti-de Sitter space. We find that there exist essential differences from the spherically syrnmetric case: In each dimension (d >= 4), there are maximal mass (density), maximal entropy (density), and maximal temperature configurations; they do not appear at the same central energy density; the oscillation behavior appearing in the spherically symmetric case does not happen in this case; and the mass (density), as a function of the central energy density, increases first and reaches its maximum at a certain central energy density and then decreases monotonically in 4 = 8, besides the maximum, the mass (density) of the equilibrium configuration has a minimum: the mass (density) first increases and reaches its maximum, then decreases to its minimum, and then increases to its asymptotic value monotonically. The reason causing the difference is discussed.