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This is a sequel to a previous detailed study of quantum corrections to cosmological correlations. It was found there that except in special cases these corrections depend on the whole history of inflation, not just on the behavior of fields at horizon exit. It is shown here that at least in perturbation theory these corrections can nevertheless not be proportional to positive powers of the Robertson--Walker scale factor, but only at most to powers of its logarithm, and are therefore never large., Comment: 10 pages. Some explanations and references added. Paper now accepted for publication in Physical Review

We offer a method of calculating the source term in the line-of-sight integral for cosmic microwave background anisotropies without using a truncated partial-wave expansion in the Boltzmann hierarchy., 16 pages. Figure added, some typographical errors corrected

The electron is 100 years old this year. Of all the elementary particles, it is by far the most familiar, useful and venerable. But is it elementary? And what other particles are elementary?

The ``in-in'' formalism is reviewed and extended, and applied to the calculation of higher-order Gaussian and non-Gaussian correlations in cosmology. Previous calculations of these correlations amounted to the evaluation of tree graphs in the in-in formalism; here we also consider loop graphs. It turns out that for some though not all theories, the contributions of loop graphs as well as tree graphs depend only on the behavior of the inflaton potential near the time of horizon exit. A sample one-loop calculation is presented., Comment: 39 pages

In his later years, Einstein sought a unified theory that would extend general relativity and provide an alternative to quantum theory. There is now talk of a ‘theory of everything’ (although Einstein himself never used the phrase). Fifty years after his death, how close are we to such a theory?

Richard Rovetto has done a good job of assembling various arguments that are commonly advanced for a program of manned space flight. I will take them up one by one, and explain why I find them all unconvincing.

Even if non-adiabatic perturbations are generated in multi-field inflation, the perturbations will become adiabatic if the universe after inflation enters an era of local thermal equilibrium, with no non-zero conserved quantities, and will remain adiabatic as long as the wavelength is outside the horizon, even when local thermal equilibrium no longer applies. Small initial non-adiabatic perturbations associated with imperfect local thermal equilibrium remain small when baryons are created from out-of-equilibrium decay of massive particles, or when dark matter particles go out of local thermal equilibrium., 12 pages, typographical errors corrected, acknowledgment added. Article accepted for publication in Physical Review D

It is shown that non-adiabatic cosmological perturbations cannot arise during the period of reheating following inflation with a single scalar inflaton field., 7 pages, Latex, references added, discussion improved

An analytic formula is given for the traceless transverse part of the anisotropic stress tensor due to free streaming neutrinos, and used to derive an integro-differential equation for the propagation of cosmological gravitational waves. The solution shows that anisotropic stress reduces the squared amplitude by 35.6 % for wavelengths that enter the horizon during the radiation-dominated phase, independent of any cosmological parameters. This decreases the tensor temperature and polarization correlation functions for these wavelengths by the same amount. The effect is less for wavelengths that enter the horizon at later times. At the longest wavelengths the decrease in the tensor correlation functions due to neutrino free streaming ranges from 10.7% for $\Omega_Mh^2=0.1$ to 9.0% for $\Omega_Mh^2=0.15$. An Appendix gives a general proof that tensor as well as scalar modes satisfy a conservation law for perturbations outside the horizon, even when the anisotropic stress tensor is not negligible., Comment: 14 pages. The original version of this paper has been expanded to deal with perturbations of any wavelength. While for wavelengths short enough to enter the horizon during radiation dominance, temperature and polarization correlations are damped by 35.6%, at the longest wavelengths the damping is from 9.0% to 11%. An added Appendix gives a general proof that tensor as well as scalar modes satisfy a conservation law outside the horizon, even during neutrino decoupling. Some references are also added

We show that the field equations for cosmological perturbations in Newtonian gauge always have an adiabatic solution, for which a quantity ${\cal R}$ is non-zero and constant in all eras in the limit of large wavelength, so that it can be used to connect observed cosmological fluctuations in this mode with those at very early times. There is also a second adiabatic mode, for which ${\cal R}$ vanishes for large wavelength, and in general there may be non-adiabatic modes as well. These conclusions apply in all eras and whatever the constituents of the universe, under only a mild technical assumption about the wavelength dependence of the field equations for large wave length. In the absence of anisotropic inertia, the perturbations in the adiabatic modes are given for large wavelength by universal formulas in terms of the Robertson--Walker scale factor. We discuss an apparent discrepancy between these results and what appears to be a conservation law in all modes found for large wavelength in synchronous gauge: it turns out that, although equivalent, synchronous and Newtonian gauges suggest inequivalent assumptions about the behavior of the perturbations for large wavelength., Comment: 24 pages, Latex, no special macros

This paper presents a completely analytic treatment of cosmological fluctuations whose wavelength is small enough to come within the horizon well before the energy densities of matter and radiation become equal. This analysis yields a simple formula for the conventional transfer function T(k) at large wave number k, which agrees very well with computer calculations of T(k). It also yields an explicit formula for the microwave background multipole coefficient C_ell at very large ell., 15 pages, no figures

General asymptotic formulas are given for the coefficient $C_\ell$ of the term of multipole number $\ell$ in the temperature correlation function of the cosmic microwave background, in terms of scalar and dipole form factors introduced in a companion paper. The formulas apply in two overlapping limits: for $\ell\gg 1$ and for $\ell d/d_A\ll 1$ (where $d_A$ is the angular diameter distance of the surface of last scattering, and $d$ is a length, of the order of the acoustic horizon at the time of last scattering, that characterizes acoustic oscillations before this time.) The frequently used approximation that $C_\ell$ receives its main contribution from wave numbers of order $\ell/d_A$ is found to be less accurate for the contribution of the Doppler effect than for the Sachs--Wolfe effect and intrinsic temperature fluctuations. For $\ell d/d_A\ll 1$ and $\ell\geq 2$, the growth of $C_\ell$ with $\ell$ is shown to be affected by acoustic oscillation wave numbers of all scales. The asymptotic formulas are applied to a model of acoustic oscillations before the time of last scattering, with results in reasonable agreement with more elaborate computer calculations.

It is shown that the fluctuation in the temperature of the cosmic microwave background in any direction may be evaluated as an integral involving scalar and dipole form factors, which incorporate all relevant information about acoustic oscillations before the time of last scattering. A companion paper gives asymptotic expressions for the multipole coefficient $C_\ell$ in terms of these form factors. Explicit expressions are given here for the form factors in a simplified hydrodynamic model for the evolution of perturbations., 35 pages, no figures. Improved treatment of damping, including both Landau and Silk damping; inclusion of late-time effects; several references added; minor changes and corrections made. Accepted for publication in Phys. Rev. D15

This is the written version of the summary talk given at the 20th Texas Symposium on Relativistic Astrophysics in Austin, Texas, on December 15, 2000. After a brief summary of some of the highlights at the conference, comments are offered on three special topics: theories with large additional spatial dimensions, the cosmological constant problems, and the analysis of fluctuations in the cosmic microwave background.

The old cosmological constant problem is to understand why the vacuum energy is so small; the new problem is to understand why it is comparable to the present mass density. Several approaches to these problems are reviewed. Quintessence does not help with either; anthropic considerations offer a possibility of solving both. In theories with a scalar field that takes random initial values, the anthropic principle may apply to the cosmological constant, but probably to nothing else.

In calculations of the probability distribution for the cosmological constant, it has been previously assumed that the a priori probability distribution is essentially constant in the very narrow range that is anthropically allowed. This assumption has recently been challenged. Here we identify large classes of theories in which this assumption is justified., 15 pages, Latex

This volume deals with quantum field theories that are governed by supersymmetry, a symmetry that unites particles of integer and half-integer spin in common symmetry multiplets. These theories offer a possible way of solving the ‘hierarchy problem,’ the mystery of the enormous ratio of the Planck mass to the 300 GeV energy scale of electroweak symmetry breaking. Supersymmetry also has the quality of uniqueness that we search for in fundamental physical theories. There is an infinite number of Lie groups that can be used to combine particles of the same spin in ordinary symmetry multiplets, but there are only eight kinds of supersymmetry in four spacetime dimensions, of which only one, the simplest, could be directly relevant to observed particles. These are reasons enough to devote this third volume of The Quantum Theory of Fields to supersymmetry. In addition, the quantum field theories based on supersymmetry have remarkable properties that are not found among other field theories: some supersymmetric theories have couplings that are not renormalized in any order of perturbation theory; other theories are finite; and some even allow exact solutions. Indeed, much of the most interesting work in quantum field theory over the past decade has been in the context of supersymmetry.

The widely cited formula $\ell_1\simeq 200 \Omega_0^{-1/2}$ for the multipole number of the first Doppler peak is not even a crude approximation in the case of greatest current interest, in which the cosmic mass density is less than the vacuum energy density. For instance, with $\Omega_M$ fixed at 0.3, the position of any Doppler peak varies as $\Omega_0^{-1.58}$ near $\Omega_0=1$., Comment: 7 pages, Latex

Many have hypothesized that both chemical and mechanical material properties are important in the design of a small bore vascular graft. In an attempt to address both issues, a xenogeneic graft crosslinked by photo-oxidation and covalently modified with heparin was developed. The compliance, burst strength, and suture pull strength of photo-oxidized (PhotoFix®) and heparin-modified photo-oxidized ovine carotid tissue were tested in vitro. The heparin modification process was found to have no statistically significant effect on any of these properties. The shrink temperature of fresh, photo-oxidized, and heparin-modified photo-oxidized tissue was assessed using DSC. A small increase in the shrink temperature of the heparin-modified photo-oxidized tissue over the fresh tissue was found to be statistically significant (P < 0.05). In vivo assessment of unmodified, heparin-soaked, and heparin-modified PhotoFix ovine grafts indicated that covalent modification of the grafts was imperative for the graft’s success.

This is a talk presented at the conference ``Historical and Philosophical Reflections on the Foundations of Quantum Field Theory,'' at Boston University, March 1996. It will be published in the proceedings of this conference.

Household survey data consistently depict large variations in saving and wealth, even among households with similar socio-economic characteristics. Within the context of the life cycle hypothesis, families with identical lifetime resources might choose to accumulate different levels of wealth for a variety of reasons, including variation in time preference rates, risk tolerance, exposure to uncertainty, relative tastes for work and leisure at advanced ages, income replacement rates, and so forth. These factors can be divided into a small number of classes, each with a distinctive implication concerning the relation between accumulated wealth and the shape of the consumption profile. By examining this relation empirically, one can test for the presence or absence of particular factors. Using the Panel Study of Income Dynamics and the Consumer Expenditure Survey, we find very little support for life cycle models that rely on the above factors to explain wealth variation. The data are, however, consistent with "rule of thumb" or "mental accounting" theories of wealth accumulation.

September 1997 Household survey data consistently depict large variations in saving and wealth, even among households with similar socio-economic characteristics. Within the context of the life cycle hypothesis, families with identical lifetime resources might choose to accumulate different levels of wealth for a variety of reasons, including variation in time preference rates, risk tolerance, exposure to uncertainty, relative tastes for work and leisure at advanced ages, income replacement rates, and so forth. These factors can be divided into a small number of classes, each with a distinctive implication concerning the relation between accumulated wealth and the shape of the consumption profile. By examining this relation empirically, one can test for the presence or absence of particular factors. Using the Panel Study of Income Dynamics and the Consumer Expenditure Survey, we find very little support for life cycle models that rely on the above factors to explain wealth variation. The data are, however, consistent with “rule of thumb” or “mental accounting” theories of wealth accumulation.

In theories in which the cosmological constant Lambda takes a variety of values in different ``subuniverses,'' the probability distribution of its observed values is conditioned by the requirement that there must be someone to measure it. This probability is proportional to the fraction of matter which is destined to condense out of the background into mass concentrations large enough to form observers. We calculate this ``collapsed fraction'' by a simple, pressure-free, spherically symmetric, nonlinear model for the growth of density fluctuations in a flat universe with arbitrary value of the cosmological constant, applied in a statistical way to the observed spectrum of density fluctuations at recombination. From this, the probability distribution for the vacuum energy density rho_V=Lambda/8pi G for Gaussian random density fluctuations is derived analytically. It is shown that the results depend on only one quantity, sigma^3 RHO, where sigma^2 and RHO are the variance and mean value of the fluctuating matter density field at recombination, respectively. To calculate sigma, we adopt the flat CDM model with nonzero cosmological constant and fix the amplitude and shape of the primordial power spectrum in accordance with data on cosmic microwave background anisotropy from the COBE satellite DMR experiment. A comparison of the results of this calculation of the likely values of rho_V with present observational bounds on the cosmological constant indicates that the small, positive value of rho_V (up to 3 times greater than the present cosmic mass density) suggested recently by several lines of evidence is a reasonably likely value to observe, even if all values of rho_V are equally likely a priori., One single postscript file, gzip-ed, 603392 bytes (2303240 bytes when gunzip-ed)

This volume describes the advances in the quantum theory of fields that have led to an understanding of the electroweak and strong interactions of the elementary particles. These interactions have all turned out to be governed by principles of gauge invariance, so we start here in Chapters 15-17 with gauge theories, generalizing the familiar gauge invariance of electrodynamics to non-Abelian Lie groups. Some of the most dramatic aspects of gauge theories appear at high energy, and are best studied by the methods of the renormalization group. These methods are introduced in Chapter 18, and applied to quantum chromodynamics, the modern non-Abelian gauge theory of strong interactions, and also to critical phenomena in condensed matter physics. Chapter 19 deals with general spontaneously broken global symmetries, and their application to the broken approximate SU (2) × SU (2) and SU (3) × SU (3) symmetries of quantum chromodynamics. Both the renormalization group method and broken symmetries find some of their most interesting applications in the context of operator product expansions, discussed in Chapter 20. The key to the understanding of the electroweak interactions is the spontaneous breaking of gauge symmetries, which are explored in Chapter 21 and applied to superconductivity as well as to the electroweak interactions. Quite apart from spontaneous symmetry breaking is the possibility of symmetry breaking by quantum-mechanical effects known as anomalies. Anomalies and various of their physical implications are presented in Chapter 22.

In this third volume of The Quantum Theory of Fields, available for the first time in paperback, Nobel Laureate Steven Weinberg continues his masterly exposition of quantum field theory. This volume presents a self-contained, up-to-date and comprehensive introduction to supersymmetry, a highly active area of theoretical physics. The text introduces and explains a broad range of topics, including supersymmetric algebras, supersymmetric field theories, extended supersymmetry, supergraphs, non-perturbative results, theories of supersymmetry in higher dimensions, and supergravity. A thorough review is given of the phenomenological implications of supersymmetry, including theories of both gauge and gravitationally-mediated supersymmetry breaking. Also provided is an introduction to mathematical techniques, based on holomorphy and duality, that have proved so fruitful in recent developments. This book contains much material not found in other books on supersymmetry, including previously unpublished results. Exercises are included.