118352317
GRAVITY AND NONEQUILIBRIUM THERMODYNAMICS OF CLASSICAL MATTER
Happy Birthday Mario, the philosopher, the king and the philosopher king! — This was explained in the first few slides of my talk at Mariofest. In an earlier, different occasion I had compared Mario, in his capacity of an inspiring mentor and a chief architect, in building up an eminent school of theoretical physics and astrophysics in Argentina, to my own Ph.D. advisor, the late Professor John Archibald Wheeler, in the USA. The nature of this meeting could perhaps allow me to also relate some of my past experience with Wheeler, and to pay homage to his influence on me in the same capacity as is done here by many young researchers, leaders in their own rights in different fields of physics and astrophysics, with Mario. So please forgive me if you find me delving at times into the past, referring to what I was thinking when I was a graduate student, some 40 years ago, on certain topics, some still of current interest. One of these ideas bears on the present theme of gravity in relation to thermodynamics, another on the philosophy I use for understanding it.
11606437
Fluctuation-dissipation relation for semiclassical cosmology.
Using the concept of open systems where the classical geometry is treated as the system and the quantum matter field as the environment, we derive a fluctuation-dissipation theorem for semiclassical cosmology. This theorem, which exists under very general conditions for dissipations in the dynamics of the system, and the noise and fluctuations in the environment, can be traced to the formal mathematical relation between the dissipation and noise kernels of the influence functional depicting the open system, and is ultimately a consequence of the unitarity of the closed system. In particular, for semiclassical gravity, it embodies the back reaction effect of matter fields on the dynamics of spacetime. The back reaction equation derivable from the influence action is in the form of an Einstein-Langevin equation. It contains a dissipative term in the equation of motion for the dynamics of spacetime and a noise term related to the fluctuations of particle creation in the matter field. Using the well-studied model of a quantum scalar field in a Bianchi type-I universe we illustrate how this Langevin equation and the noise term are derived and show how the creation of particles and the dissipation of anisotropy during the expansion of the Universe can be understood as a manifestation of this fluctuation-dissipation relation.
122760989
Calculation of the trace anomaly of the conformal energy-momentum tensor in Kasner spacetime by adiabatic regularization
The anomalous trace of the energy-momentum tensor of a quantized massless conformal scalar field in a homogeneous anisotropic, spatially flat background is calculated by the method of adiabatic regularization. It yields the same results as derived by other methods, but has the advantage of simplicity in computation and clarity in physical interpretation. Explicit expressions are also obtained for the regularized energy desity and pressure, which are useful in formulating semiclassical theories of gravity and in calculating the back reaction of quantized fields in relativistic cosmology.
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.
16659491
Worldline Influence Functional: Abraham-Lorentz-Dirac-Langevin Equation from QED
We present a stochastic theory of charges moving in an electromagnetic field using nonequilibrium quantum field theory. We give a first principles' derivation of the Abraham-Lorentz-Dirac-Langevin equation which depicts the quantum expectation value for a particle's trajectory and its stochastic fluctuations by combining the worldline path integral quantization with the Feynman-Vernon influence functional or closed-time-path effective action methods. At lowest order, the equations of motion are approximated by a stochastic Lorentz-Dirac equation.
209934211
Anomalous dimensions of tensor operators in 4-epsilon dimensions
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.
119260706
Parametrized modified gravity constraints after Planck
We constrain $f(R)$ and chameleon-type modified gravity in the framework of the Berstchinger-Zukin parametrization using the recent released Planck data, including both CMB temperature power spectrum and lensing potential power spectrum. Some other external data sets are included, such as BAO measurements from the 6dFGS, SDSS DR7 and BOSS DR9 surveys, HST $H_0$ measurement and supernovae from Union2.1 compilation. We also use WMAP9yr data for consistency check and comparison. For $f(R)$ gravity, WMAP9yr results can only give quite a loose constraint on the modified gravity parameter $B_0$, which is related to the present value of the Compton wavelength of the extra scalar degree of freedom, $B_0<3.37$ at $95\% {\rm C.L.}$ We demonstrate that this constraint mainly comes from the late ISW effect. With only Planck CMB temperature power-spectrum data, we can improve the WMAP9yr result by a factor $3.7$ ($B_0<0.91$ at $95\% {\rm C.L.}$). If the Planck lensing potential power-spectrum data are also taken into account, the constraint can be further strenghtened by a factor $5.1$ ($B_0<0.18$ at $95\% {\rm C.L.}$). This major improvement mainly comes from the small-scale lensing signal. Furthermore, BAO, HST and supernovae data could slightly improve the $B_0$ bound ($B_0<0.12$ at $95\% {\rm C.L.}$).For the chameleon-type model, we find that the data set which we used cannot constrain the Compton wavelength $B_0$ and the potential index $s$ of chameleon field, but can give a tight constraint on the parameter $\beta_1=1.043^{+0.163}_{-0.104}$ at $95\% {\rm C.L.}$ ($\beta_1=1$ in general relativity), which accounts for the non-minimal coupling between the chameleon field and the matter component. In addition, we find that both modified gravity models we considered favor a relatively higher Hubble parameter than the concordance LCDM model in general relativity.
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.
118029650
Future CMB integrated-Sachs-Wolfe-lensing bispectrum constraints on modified gravity in the parametrized post-Friedmann formalism
We forecast the constraints on both Hu-Sawicki model and Bertschinger-Zukin model of modified gravity within the Parameterized Post-Friedmann (PPF) formalism for the Planck satellite experiment by performing the joint analysis of ISW-Lensing bispectrum and CMB power spectrum. We find that, even considering the temperature-temperature mode of CMB power spectrum only, Planck data are expected to reduce the error bars on the modified gravity parameter $B_0$ (related to the present value of Compton wavelength of the extra scalar degree of freedom) at least one order magnitude compared with WMAP. The spectrum-bispectrum joint analysis can further improve the results by a factor ranging from 1.14 to 5.32 depending on the specific modified gravity model. One of our main results is that the cross-correlation between ISW-Lensing bispectrum and power spectrum can be safely neglected when performing the joint analysis. For simplicity, we only investigate the likelihood of one parameter ({$B_0$}) and fix all other cosmological parameters to their best-fit values in WMAP7yr results.