17360462
Minisuperspace as a quantum open system
We trace the development of ideas on dissipative processes in chaotic cosmology and on minisuperspace quantum cosmology from the time Misner proposed them to current research. We show 1) how the effect of quantum processes like particle creation in the early universe can address the issues of the isotropy and homogeneity of the observed universe, 2) how viewing minisuperspace as a quantum open system can address the issue of the validity of such approximations customarily adopted in quantum cosmology, and 3) how invoking statistical processes like decoherence and correlation when considered together can help to establish a theory of quantum fields in curved spacetime as the semiclassical limit of quantum gravity. {\it Dedicated to Professor Misner on the occasion of his sixtieth birthday, June 1992.} To appear in the Proceedings of a Symposium on {\it Directions in General Relativity}, College Park, May 1993, Volume 1, edited by B. L. Hu, M. P. Ryan and C. V. Vishveshwara (Cambridge University Press 1993)~~~~umdpp 93-60
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.
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.
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.
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.
119229309
Non-Gaussian features from the inverse volume corrections in loop quantum cosmology
In this paper we study the non-Gaussian features of the primordial fluctuations in loop quantum cosmology with the inverse volume corrections. The detailed analysis is performed in the single field slow-roll inflationary models. However, our results reflect the universal characteristics of bispectrum in loop quantum cosmology. The main corrections to the scalar bispectrum come from two aspects: one is the modifications to the standard Bunch-Davies vacuum, and the other is the corrections to the background dependent variables, such as slow-roll parameters. Our calculations show that the loop quantum corrections make f(NL) of the inflationary models increase 0.1%. Moreover, we find that two new shapes of non-Gaussian signal arise, which we name F-1 and F-2. The former gives a unique loop quantum feature, which is less correlated with the local, equilateral, and single types, while the latter is highly correlated with the local one.
118426631
Acoustic signatures in the Cosmic Microwave Background bispectrum from primordial magnetic fields
Using the full radiation transfer function, we numerically calculate the CMB angular bispectrum seeded by the compensated magnetic scalar density mode. We find that, for the string inspired primordial magnetic fields characterized by index nB = −2.9 and mean-field amplitude Bλ = 9nG, the angular bispectrum is dominated by two primordial magnetic shapes. The first magnetic shape looks similar to the one from local-type primordial curvature perturbations, so both the amplitude and profile of the Komatsu-Spergel estimator (reduced bispectrum) seeded by this shape are almost the same as those of the primary CMB anisotropies. However, for different parameter sets (l1,l2), this ``local-type'' reduced bispectrum oscillates around different asymptotic values in the high-l3 regime because of the effect of the Lorentz force, which is exerted by the primordial magnetic fields on the charged baryons. This feature is different from the standard case where all modes approach to zero asymptotically in the high-l limit. On the other hand, the second magnetic shape appears only in the primordial magnetic field model. The amplitude of the Komatsu-Spergel estimator sourced by the second shape diverges in the low-l regime because of the negative slope of shape. In the high-l regime, this amplitude is approximately equal to that of the first estimator, but with a reversal phase.
14771278
Nonadiabatic geometric phase for the cyclic evolution of a time-dependent Hamiltonian system
The geometric phases of the cyclic states of a generalized harmonic oscillator with nonadiabatic timeperiodic parameters are discussed in the framework of squeezed state. It is shown that the cyclic and quasicyclic squeezed states correspond to the periodic and quasiperiodic solutions of an effective Hamiltonian defined on an extended phase space, respectively. The geometric phase of the cyclic squeezed state is found to be a phase-space area swept out by a periodic orbit. Furthermore, a class of cyclic states is expressed as a superposition of an infinite number of squeezed states. Their geometric phases are found to be independent of \, and equal to 2(n11/2) times the classical nonadiabatic Hannay angle. @S1050-2947~98!03311-3# The Berry phase is one of the most important findings on the fundamental problem of quantum mechanics in recent years @1#. It reveals the gauge structure associated with a phase shift in adiabatic processes in quantum mechanics. This quantal phase is connected with a classical angle, namely, the Hannay angle, by a simple and elegant expression in the semiclassical limit @2#. The next important advance was the relaxation of the adiabatic approximation @3,4#. Aharanov and Anandan studied the phase associated with a cyclic evolution in quantum mechanics, which occurs when a state returns to its initial condition. They showed that the phase is a geometrical property of the curve in the projective Hilbert space which is naturally associated with the motion @3#. For the special case of an adiabatic evolution, this phase factor is a gauge-invariant generalization of the Berry phase. The significance of Aharanov and Anandan’s generalization lies in the following: ~i! the cyclic evolution of a physical system is of the most interest in physics both experimentally and theoretically; ~ii! the universal existence of the cyclic evolution is guaranteed for any quantum system. The second point can be easily recognized by considering the eigenvectors of the unitary evolution operator for a quantum system. An explicit example is a time-periodic Hamiltonian system where the Floquet theorem applies. The eigenfunctions of the Floquet operator, which are the socalled Bloch wave functions in condensed-matter physics, are obviously cyclic solutions and are of great interest in physics. However, unlike the adiabatic case, in the nonadiabatic case calculating the eigenvectors and extracting the nonadiabatic geometric phase from the quasienergy term for a time-dependent Hamiltonian is far from a trivial task, except in the special case of the spin particle in a magnetic field. Recent works of Ge and Child@5# made a further step in this direction. They found a special cyclic state of the Gaussian wave packet’s form for a generalized harmonic oscillator. The nonadiabatic geometric phase is explicitly calculated and found to be one-half of the classical nonadiabatic Hannay angle. In this paper, we would like to suggest an alternative approach—the squeezed-state approach to study the general cyclic evolutions of the generalized harmonic oscillator. In particular, we shall construct a class of quantum states based on the superposition of an infinite number of squeezed states. We find that the condition for them to be cyclic evolutions is nothing but the quantization rule without Maslov-Morse correction. The nonadiabatic geometric phases are obtained analytically, and found to be related to the classical Hannay angle by an explicit expression.
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.
121095182
Period doubling: Universality and critical-point order
The dependence of the universal bifurcation ratio on the order of the local maximum is studied for a family of maps $f(x)=1\ensuremath{-}a{x}^{z}$($z=2,4,6,8$). Although these maps all exhibit period doubling, the precise bifurcation ratio depends on the order $z$, and seems to be an increasing function of $z$. We have employed a renormalization-group method to calculate $\ensuremath{\delta}(z)$ to second order. They agree very well with the exact values.