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Bell's inequality was originally derived under the assumption that experimenters are free to select detector settings independently of any local "hidden variables" that might affect the outcomes of measurements on entangled particles. This assumption has come to be known as "measurement independence" (also referred to as "freedom of choice" or "settings independence"). For a two-setting, two-outcome Bell test, we derive modified Bell inequalities that relax measurement independence, for either or both observers, while remaining locally causal. We describe the loss of measurement independence for each observer using the parameters $M_1$ and $M_2$, as defined by Hall in 2010, and also by a more complete description that adds two new parameters, which we call $\hat{M}_1$ and $\hat{M}_2$, deriving a modified Bell inequality for each description. These "relaxed" inequalities subsume those considered in previous work as special cases, and quantify how much the assumption of measurement independence needs to be relaxed in order for a locally causal model to produce a given violation of the standard Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality. We show that both relaxed Bell inequalities are tight bounds on the CHSH parameter by constructing locally causal models that saturate them. For any given Bell inequality violation, the new two-parameter and four-parameter models each require significantly less mutual information between the hidden variables and measurement settings than previous models. We conjecture that the new models, with optimal parameters, require the minimum possible mutual information for a given Bell violation. We further argue that, contrary to various claims in the literature, relaxing freedom of choice need not imply superdeterminism., 26pp, 7 figures. Minor edits to match published version more...

In this Letter, we present a cosmic Bell experiment with polarization-entangled photons, in which measurement settings were determined based on real-time measurements of the wavelength of photons from high-redshift quasars, whose light was emitted billions of years ago, the experiment simultaneously ensures locality. Assuming fair sampling for all detected photons and that the wavelength of the quasar photons had not been selectively altered or previewed between emission and detection, we observe statistically significant violation of Bell's inequality by $9.3$ standard deviations, corresponding to an estimated $p$ value of $\lesssim 7.4 \times 10^{-21}$. This experiment pushes back to at least $\sim 7.8$ Gyr ago the most recent time by which any local-realist influences could have exploited the "freedom-of-choice" loophole to engineer the observed Bell violation, excluding any such mechanism from $96\%$ of the space-time volume of the past light cone of our experiment, extending from the big bang to today., 9 pages, 4 figures, plus Supplemental Material (16 pages, 8 figures). Matches version to be published in Physical Review Letters more...

We show that the upper bound of the classical QCD axion window can be significantly relaxed for low-scale inflation. If the Gibbons-Hawking temperature during inflation is lower than the QCD scale, the initial QCD axion misalignment angle follows the Bunch-Davies distribution. The distribution is peaked at the strong CP conserving minimum if there is no other light degree of freedom contributing to the strong CP phase. As a result, the axion overproduction problem is significantly relaxed even for an axion decay constant larger than $10^{12}$GeV. We also provide concrete hilltop inflation models where the Hubble parameter during inflation is comparable to or much smaller than the QCD scale, with successful reheating taking place via perturbative decays or dissipation processes., 14 pages, 3 figures; v3:a version to appear in PRD more...

In this paper we develop a formalism for studying the nonrelativistic limit of relativistic field theories in a systematic way. By introducing a simple, nonlocal field redefinition, we transform a given relativistic theory, describing a real, self-interacting scalar field, into an equivalent theory, describing a complex scalar field that encodes at each time both the original field and its conjugate momentum. Our low-energy effective theory incorporates relativistic corrections to the kinetic energy as well as the backreaction of fast-oscillating terms on the behavior of the dominant, slowly varying component of the field. Possible applications of our new approach include axion dark matter, though the methods developed here should be applicable to the low-energy limits of other field theories as well., 31pp. References added, and 3 appendices added, showing (a) how to implement the field redefinition as a canonical transformation, (b) how to develop the effective field theory using a local field redefinition, and (c) how to use a further field redefinition to compare our results with those of Mukaida, Takimoto, and Yamada more...

The origins of space and time are among the most mysterious and contentious topics in science. Our February 2017 article “Pop Goes the Universe” argues against the dominant idea that the early cosmos underwent an extremely rapid expansion called inflation. Its authors instead advocate for another scenario—that our universe began not with a bang but with a bounce from a previously contracting cosmos. In the letter below, a group of 33 physicists who study inflationary cosmology respond to that article. It is followed by a reply from the authors. In “Pop Goes the Universe,” by Anna Ijjas, Paul J. Steinhardt and Abraham Loeb, the authors (hereafter “IS&L”) make the case for a bouncing cosmology, as was proposed by Steinhardt and others in 2001. They close by making the extraordinary claim that inflationary cosmology “cannot be evaluated using the scientific method” and go on to assert that some scientists who accept inflation have proposed “discarding one of [science's] defining properties: empirical testability,” thereby “promoting the idea of some kind of nonempirical science.” We have no idea what scientists they are referring to. We disagree with a number of statements in their article, but in this letter, we will focus on our categorical disagreement with these statements about the testability of inflation. more...

Models of cosmic inflation posit an early phase of accelerated expansion of the universe, driven by the dynamics of one or more scalar fields in curved spacetime. Though detailed assumptions about fields and couplings vary across models, inflation makes specific, quantitative predictions for several observable quantities, such as the flatness parameter ($\Omega_k = 1 - \Omega$) and the spectral tilt of primordial curvature perturbations ($n_s - 1 = d \ln {\cal P}_{\cal R} / d \ln k$), among others---predictions that match the latest observations from the {\it Planck} satellite to very good precision. In the light of data from {\it Planck} as well as recent theoretical developments in the study of eternal inflation and the multiverse, we address recent criticisms of inflation by Ijjas, Steinhardt, and Loeb. We argue that their conclusions rest on several problematic assumptions, and we conclude that cosmic inflation is on a stronger footing than ever before., Comment: 11 pages, no figures; added references, and brief additions to Footnote 1, Section VI, and the Acknowledgments more...

Bell’s theorem states that some predictions of quantum mechanics cannot be reproduced by a local-realist theory. That conflict is expressed by Bell’s inequality, which is usually derived under the assumption that there are no statistical correlations between the choices of measurement settings and anything else that can causally affect the measurement outcomes. In previous experiments, this “freedom of choice” was addressed by ensuring that selection of measurement settings via conventional “quantum random number generators” was spacelike separated from the entangled particle creation. This, however, left open the possibility that an unknown cause affected both the setting choices and measurement outcomes as recently as mere microseconds before each experimental trial. Here we report on a new experimental test of Bell’s inequality that, for the first time, uses distant astronomical sources as “cosmic setting generators.” In our tests with polarization-entangled photons, measurement settings were chosen using real-time observations of Milky Way stars while simultaneously ensuring locality. Assuming fair sampling for all detected photons, and that each stellar photon’s color was set at emission, we observe statistically significant ≳7.31σ and ≳11.93σ violations of Bell’s inequality with estimated p values of ≲1.8×10[superscript -13] and ≲4.0×10[superscript -33], respectively, thereby pushing back by ∼600 years the most recent time by which any local-realist influences could have engineered the observed Bell violation., Austrian Academy of Sciences, Austrian Science Fund (Projects SFB F40 (FOQUS) and CoQuS W1210-N16), Austria. Federal Ministry of Science, Research, and Economy, National Science Foundation (U.S.) (INSPIRE Grant PHY-1541160 and SES-1056580), Massachusetts Institute of Technology. Undergraduate Research Opportunities Program more...

The basic workings of inflationary models are summarized, along with the arguments that strongly suggest that our universe is the product of inflation. It is argued that essentially all inflationary models lead to (future-)eternal inflation, which implies that an infinite number of pocket universes are produced. Although the other pocket universes are unobservable, their existence nonetheless has consequences for the way that we evaluate theories and extract consequences from them. The question of whether the universe had a beginning is discussed but not definitively answered. It appears likely, however, that eternally inflating universes do require a beginning., Comment: 15 pages, including 2 figures, LaTeX 2.09. Review talk given at the conference on ``Cosmic Questions,'' April 14-16, 1999, Washington, D.C., organized by the Dialogue on Science, Ethics, and Religion of the American Association for the Advancement of Science. To be published in the proceedings, The New York Academy of Sciences Press more...

Recently there has been significant interest in the claim that dark matter axions gravitationally thermalize and form a Bose-Einstein condensate with cosmologically long-range correlation. This has potential consequences for galactic scale observations. Here we critically examine this claim. We point out that there is an essential difference between the thermalization and formation of a condensate due to repulsive interactions, which can indeed drive long-range order, and that due to attractive interactions, which can lead to localized Bose clumps (stars or solitons) that only exhibit short range correlation. While the difference between repulsion and attraction is not present in the standard collisional Boltzmann equation, we argue that it is essential to the field theory dynamics, and we explain why the latter analysis is appropriate for a condensate. Since the axion is primarily governed by attractive interactions -- gravitation and scalar-scalar contact interactions -- we conclude that while a Bose-Einstein condensate is formed, the claim of long-range correlation is unjustified., Comment: New version matches the version to be published in Physical Review D and includes a clarification about the non-relativistic limit more...

The eternally inflating multiverse provides a consistent framework to understand coincidences and fine-tuning in the universe. As such, it provides the possibility of finding another coincidence: if the amount of slow-roll inflation was only slightly more than the anthropic threshold, then spatial curvature might be measurable. We study this issue in detail, particularly focusing on the question: "If future observations reveal nonzero curvature, what can we conclude?" We find that whether an observable signal arises or not depends crucially on three issues: the cosmic history just before the observable inflation, the measure adopted to define probabilities, and the nature of the correlation between the tunneling and slow-roll parts of the potential. We find that if future measurements find positive curvature at \Omega_k < -10^-4, then the framework of the eternally inflating multiverse is excluded with high significance. If the measurements instead reveal negative curvature at \Omega_k > 10^-4, then we can conclude (1) diffusive (new or chaotic) eternal inflation did not occur in our immediate past; (2) our universe was born by a bubble nucleation; (3) the probability measure does not reward volume increase; and (4) the origin of the observed slow-roll inflation is an accidental feature of the potential, not due to a theoretical mechanism. Discovery of \Omega_k > 10^-4 would also give us nontrivial information about the correlation between tunneling and slow-roll; e.g. a strong correlation favoring large N would be excluded in certain measures. We also ask whether the current constraint on \Omega_k is consistent with multiverse expectations, finding that the answer is yes, except for certain cases. In the course of this work we were led to consider vacuum decay branching ratios, and found that it is more likely than one might guess that the decays are dominated by a single channel., Comment: 46 pages, 5 figures; reference updates and typo corrections arising from final Phys. Rev. D copy editing more...

To make predictions for an eternally inflating "multiverse", one must adopt a procedure for regulating its divergent spacetime volume. Recently, a new test of such spacetime measures has emerged: normal observers - who evolve in pocket universes cooling from hot big bang conditions - must not be vastly outnumbered by "Boltzmann brains" - freak observers that pop in and out of existence as a result of rare quantum fluctuations. If the Boltzmann brains prevail, then a randomly chosen observer would be overwhelmingly likely to be surrounded by an empty world, where all but vacuum energy has redshifted away, rather than the rich structure that we observe. Using the scale-factor cutoff measure, we calculate the ratio of Boltzmann brains to normal observers. We find the ratio to be finite, and give an expression for it in terms of Boltzmann brain nucleation rates and vacuum decay rates. We discuss the conditions that these rates must obey for the ratio to be acceptable, and we discuss estimates of the rates under a variety of assumptions., 32 pp, 2 figs. Modified to conform to the version accepted by Phys. Rev. D. The last paragraph of Sec. V-A, about Boltzmann brains in Minkowski space, has been significantly enlarged. Two sentences were added to the introduction concerning the classical approximation and the hope of finding a motivating principle for the measure. Several references were added more...

Gott has shown that a spacetime with two infinite parallel cosmic strings passing each other with sufficient velocity contains closed timelike curves. We discuss an attempt to build such a time machine. Using the energy-momentum conservation laws in the equivalent (2+1)-dimensional theory, we explicitly construct the spacetime representing the decay of one gravitating particle into two. We find that there is never enough mass in an open universe to build the time machine from the products of decays of stationary particles. More generally, the Gott time machine cannot exist in any open (2+1)-dimensional universe for which the total momentum is timelike. more...

We estimate the density perturbation spectrum {delta}{rho}/{rho} in the extended inflationary model, in which the scalar curvature is coupled to a Brans-Dicke field. Through a conformal transformation and a redefinition of the Brans-Dicke field, the action of the theory is cast into a form with no coupling to the scalar curvature and a canonical kinetic term for the redefined field. Following Kolb, Salopek, and Turner, we calculate {delta}{rho}/{rho} using the transformed action and the standard recipe developed for conventional inflation. This recipe is expected to give a valid order-of-magnitude estimate, but a precise calculation would require a more careful treatment of several aspects of the problem. The spectrum behaves as a positive power of the wavelength, a feature that might be useful in building models to account for the observed large-scale structure of the universe. Our result for the overall amplitude of density perturbations differs slightly from that of the previous authors, and the reasons for these differences are discussed. We also point out that the conformal transformation method can be applied to a wider class of generalized gravity theories. more...

Circular loops of string and spherical domain-wall bubbles of radius equal to the horizon can spontaneously nucleate in de Sitter space. These objects are expanded by the subsequent inflation, and by the end of the inflationary era they have a spectrum of sizes extending well beyond the present Hubble length. Monopole-antimonopole pairs with an initial separation equal to the horizon can also be produced. The cosmological implications of these effects are briefly discussed. more...

Essentially all modern particle theories suggest the possible existence of a false vacuum state – a metastable state with an energy density that cannot be lowered except by means of a very slow phase transition. Inflationary cosmology makes use of such a state to drive the expansion of the big bang, allowing the entire observed universe to evolve from a very small initial mass. A sphere of false vacuum in our present universe, if larger than a certain critical mass, could inflate to form a new universe which would rapidly detach from its parent. A false vacuum bubble of this size, however, cannot be produced classsically unless an initial singularity is present from the outset. We therefore explore the possibility that a bubble of subcritical size, which classically would evolve to a maximum size and collapse, might instead tunnel through a barrier to produce a new universe. We estimate the tunneling rate using semiclassical quantum gravity, and discover some interesting ambiguities in the formalism. more...

It is well known that anthropic selection from a landscape with a flat prior distribution of cosmological constant Lambda gives a reasonable fit to observation. However, a realistic model of the multiverse has a physical volume that diverges with time, and the predicted distribution of Lambda depends on how the spacetime volume is regulated. We study a simple model of the multiverse with probabilities regulated by a scale-factor cutoff, and calculate the resulting distribution, considering both positive and negative values of Lambda. The results are in good agreement with observation. In particular, the scale-factor cutoff strongly suppresses the probability for values of Lambda that are more than about ten times the observed value. We also discuss several qualitative features of the scale-factor cutoff, including aspects of the distributions of the curvature parameter Omega and the primordial density contrast Q., 16 pages, 6 figures, 2 appendices more...

The dynamics of a localized, O(3)-symmetric region of false vacuum, separated from an infinite region of true vacuum by a domain wall of non-negligible width, is studied through numerical general relativity. The spacetime trajectories of the thick'' domain-wall solutions are compared with the predictions of a thin-wall approximation for bubbles larger than the Schwarzschild radius, and found to be in good agreement over the time intervals studied. more...

We explore the possibility that a new universe can be created by producing a small bubble of false vacuum. The initial bubble is small enough to be produced without an initial singularity, but classically it could not become a universe — instead it would reach a maximum radius and then collapse. We investigate the possibility that quantum effects allow the bubble to tunnel into a larger bubble, of the same mass, which would then classically evolve to become a new universe. The calculation of the tunneling amplitude is attempted, in lowest order semiclassical approximation (in the thin-wall limit), using both a canonical and a functional integral approach. The canonical approach is found to have flaws, attributable to our method of space-time slicing. The functional integral approach leads to a euclidean interpolating solution that is not a manifold. To describe it, we define an object which we call a “pseudomanifold”, and give a prescription to define its action. We conjecture that the tunneling probability to produce a new universe can be approximated using this action, and we show that this leads to a plausible result. more...

It is well-entrenched folklore that torsion gravity theories predict observationally negligible torsion in the solar system, since torsion (if it exists) couples only to the intrinsic spin of elementary particles, not to rotational angular momentum. We argue that this assumption has a logical loophole which can and should be tested experimentally. In the spirit of action=reaction, if a rotating mass like a planet can generate torsion, then a gyroscope should also feel torsion. Using symmetry arguments, we show that to lowest order, the torsion field around a uniformly rotating spherical mass is determined by seven dimensionless parameters. These parameters effectively generalize the PPN formalism and provide a concrete framework for further testing GR. We construct a parametrized Lagrangian that includes both standard torsion-free GR and Hayashi- Shirafuji maximal torsion gravity as special cases. We demonstrate that classic solar system tests rule out the latter and constrain two observable parameters. We show that Gravity Probe B (GPB) is an ideal experiment for further constraining torsion theories, and work out the most general torsion-induced precession of its gyroscope in terms of our torsion parameters, Comment: "Director's cut" edition of accepted PRD version, including additional explanatory material more...

I summarize the arguments that strongly suggest that our universe is the product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are described. Although the infinity of pocket universes produced by eternal inflation are unobservable, it is argued that eternal inflation has real consequences in terms of the way that predictions are extracted from theoretical models. The ambiguities in defining probabilities in eternally inflating spacetimes are reviewed, with emphasis on the youngness paradox that results from a synchronous gauge regularization technique. Although inflation is generically eternal into the future, it is not eternal into the past: it can be proven under reasonable assumptions that the inflating region must be incomplete in past directions, so some physics other than inflation is needed to describe the past boundary of the inflating region., 21 pages, 5 figures. Talk presented at the "2nd International Conference on Quantum Theories and Renormalization Group in Gravity and Cosmology (IRGAC 2006)," Barcelona, Spain, 11-15 July 2006, to be published in J. Phys. A more...

A ``bubble universe'' nucleating in an eternally inflating false vacuum will experience, in the course of its expansion, collisions with an infinite number of other bubbles. In an idealized model, we calculate the rate of collisions around an observer inside a given reference bubble. We show that the collision rate violates both the homogeneity and the isotropy of the bubble universe. Each bubble has a center which can be related to ``the beginning of inflation'' in the parent false vacuum, and any observer not at the center will see an anisotropic bubble collision rate that peaks in the outward direction. Surprisingly, this memory of the onset of inflation persists no matter how much time elapses before the nucleation of the reference bubble., 27 pages, 3 figures more...

We consider a (1+1) dimensional scalar field theory that supports oscillons, which are localized, oscillatory, stable solutions to nonlinear equations of motion. We study this theory in an expanding background and show that oscillons now lose energy, but at a rate that is exponentially small when the expansion rate is slow. We also show numerically that a universe that starts with (almost) thermal initial conditions will cool to a final state where a significant fraction of the energy of the universe -- on the order of 50% -- is stored in oscillons. If this phenomenon persists in realistic models, oscillons may have cosmological consequences., Comment: 13 pages, 4 .eps figures, uses RevTeX4; v2: clarified details of expansion, added references more...

Understanding the behavior of the universe at large depends critically on insights about the smallest units of matter and their fundamental interactions. Inflationary cosmology is a highly successful framework for exploring these interconnections between particle physics and gravitation. Inflation makes several predictions about the present state of the universe -- such as its overall shape, large-scale smoothness, and smaller-scale structure -- which are being tested to unprecedented accuracy by a new generation of astronomical measurements. The agreement between these predictions and the latest observations is extremely promising. Meanwhile, physicists are busy trying to understand inflation's ultimate implications for the nature of matter, energy, and spacetime., 16 pages, 4 figures, written for "Einstein's Legacy" issue of Science magazine more...

The basic workings of inflationary models are summarized, along with the arguments that strongly suggest that our universe is the product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are described. Although the infinity of pocket universes produced by eternal inflation are unobservable, it is argued that eternal inflation has real consequences in terms of the way that predictions are extracted from theoretical models. The ambiguities in defining probabilities in eternally inflating spacetimes are reviewed, with emphasis on the youngness paradox that results from a synchronous gauge regularization technique. Vilenkin's proposal for avoiding these problems is also discussed., Comment: 27 pages, including 5 figures, LaTeX (elsart macros for Physics Reports, included). To be published in the David Schramm Memorial Volume of Physics Reports more...

It has been stated in the literature that the case of maximal mixing angle for \nu_e leads to no day-night effect for solar neutrinos and an energy independent flux suppression of 1/2. While the case of maximal mixing angle and \Delta m^2 in the MSW range does lead to suppression of the electron neutrinos reaching the earth from the sun by P_S=1/2, the situation is different for neutrinos that have passed through the earth. We make the pedagogical point that, just as with smaller mixing angles, the earth regenerates the |\nu_1> state from the predominantly |\nu_2 > state reaching the earth, leading to coherent interference effects. This regeneration can lead to a day-night effect and an energy dependence of the suppression of solar electron neutrinos, even for the case of maximal mixing. For large mixing angles, the energy dependence of the day-night asymmetry depends heavily on Delta m^2. With a sufficiently sensitive measurement of the day-night effect, this energy dependence could be used to distinguish among the large mixing angle solutions of the solar neutrino problem., Comment: JHEP style, 22 pages, 7 figures. References added, and minor rewording more...

Most models of inflation have small parameters, either to guarantee sufficient inflation or the correct magnitude of the density perturbations. In this paper we show that, in supersymmetric theories with weak scale supersymmetry breaking, one can construct viable inflationary models in which the requisite parameters appear naturally in the form of the ratio of mass scales that are already present in the theory. Successful inflationary models can be constructed from the flat-direction fields of a renormalizable supersymmetric potential, and such models can be realized even in the context of a simple GUT extension of the MSSM. We evade naive ``naturalness" arguments by allowing for more than one field to be relevant to inflation, as in ``hybrid inflation" models, and we argue that this is the most natural possibility if inflaton fields are to be associated with flat direction fields of a supersymmetric theory. Such models predict a very low Hubble constant during inflation, of order $10^3$-$10^4$ GeV, a scalar density perturbation index $n$ which is very close to or greater than unity, and negligible tensor perturbations. In addition, these models lead to a large spike in the density perturbation spectrum at short wavelengths., Comment: 27 pages, 4 figures, revtex, epsf, Figure 3 replaced with correct figure and minor changes to paper and references more...

The discovery by Gott of a remarkably simple spacetime with closed timelike curves (CTC's) provides a tool for investigating how the creation of time machines is prevented in classical general relativity. The Gott spacetime contains two infinitely long, parallel cosmic strings, which can equivalently be viewed as point masses in (2+1)-dimensional gravity. We examine the possibility of building such a time machine in an open universe. Specifically, we consider initial data specified on an edgeless, noncompact, spacelike hypersurface, for which the total momentum is timelike (i.e., not the momentum of a Gott spacetime). In contrast to the case of a closed universe (in which Gott pairs, although not CTC's, can be produced from the decay of stationary particles), we find that there is never enough energy for a Gott-like time machine to evolve from the specified data; it is impossible to accelerate two particles to sufficiently high velocity. Thus, the no-CTC theorems of Tipler and Hawking are enforced in an open (2+1)-dimensional universe by a mechanism different from that which operates in a closed universe. In proving our result, we develop a simple method to understand the inequalities that restrict the result of combining momenta in (2+1)-dimensional gravity., Comment: Plain TeX, 41 pages incl. 9 figures. MIT-CTP #2252 more...

The number of parameters entering a Euclidean Yang-Mills solution with topological charge $k$ is determined for a theory constructed from an arbitrary Lie group $G$. It is shown that this number is precisely that required to specify the position, scale, and relative group orientation of $k$ independent solutions each with minimum topological charge 1. Such minimal single-pseudoparticle solutions can be obtained by embedding the familiar ${\mathrm{SU}}_{2}$ pseudoparticle of Belavin et al. into the general Lie group. more...

Essentially all modern particle theories suggest the possible existence of a false vacuum state — a metastable state with an energy density that cannot be lowered except by means of a very slow phase transition. Inflationary cosmology makes use of such a state to drive the expansion of the big bang, allowing the entire observed universe to evolve from a very small initial mass. A sphere of false vacuum in our present universe, if larger than a certain critical mass, could inflate to form a new universe which would rapidly detach from its parent. A false vacuum bubble of this size, however, cannot be produced classically unless an initial singularity is present from the outset. E. Farhi, J. Guven, and I have therefore explored the possibility that a bubble of subcritical size, which classically would evolve to a maximum size and collapse, might instead tunnel through a barrier to produce a new universe. We estimated the tunneling rate using semiclassical quantum gravity, and discovered some interesting ambiguities in the formalism. more...

In this paper, we quantify the degree of fine tuning required for successful inflationary scenarios. We define a "fine-tuning" parameter $\ensuremath{\lambda}$ to be the ratio of the change in the potential $\ensuremath{\Delta}V$ to the change in the scalar field ${(\ensuremath{\Delta}\ensuremath{\psi})}^{4}$; i.e., $\ensuremath{\lambda}$ measures the required degree of flatness in the potential. For a quartic polynomial potential, the quartic coupling constant ${\ensuremath{\lambda}}_{q}$ is bounded by $|{\ensuremath{\lambda}}_{q}|\ensuremath{\le}36\ensuremath{\lambda}$. For a general class of inflationary models involving a slowly rolling field, we find that the potential must be very flat, with a fine-tuning parameter $\ensuremath{\lambda}\ensuremath{\lesssim}{10}^{\ensuremath{-}6}\ensuremath{-}{10}^{\ensuremath{-}8}$. The recently proposed "extended" inflationary scenario is even more tightly constrained, with $\ensuremath{\lambda}\ensuremath{\lesssim}{10}^{\ensuremath{-}15}$. more...

The mechanism of inflation is described, and the fundamental arguments in favor of inflation are summarized. It is claimed that the inflationary model provides a very plausible explanation for (1) the large number of particles in the universe, (2) the Hubble expansion, (3) the large-scale uniformity of the universe, (4) the nearness of the universe to a critical density, and (5) the absence of magnetic monopoles. more...

Ende der 70er Jahre schlos ich mich einem kleinen Gruppchen von Teilchenphysikern an, die damit begannen, sich mit der Fruhphase des Weltalls zu beschaftigen. Unser Interesse war zum Teil durch die der Kosmologie eigenen Faszination geweckt worden, aber auch durch neue Entwicklungen in der Elementarteilchenphysik selbst. more...

The 't Hooft disorder parameters are constructed within the framework of $\mathrm{SU}(N)$ lattice gauge theories in three or four dimensions. It is found that these operators arise naturally from a duality transformation which is similar to the standard transformation for $Z(N)$ gauge theories. To illustrate the behavior of dual variables in a simpler context, we study the Villain form of the $Z(N)$ gauge system in three and four dimensions. The techniques include duality, strong-coupling expansions, and the electrodynamic representation. In four dimensions it is found that for $Ng{N}_{c}\ensuremath{\approx}4$, the system possesses at least three phases: a strong-coupling phase with electric confinement, a weak-coupling phase with magnetic confinement, and an intermediate phase which resembles QED, with a massless photon and no confinement. We also study an $\mathrm{SU}(N)$-Higgs system, which interpolates between the $Z(N)$ and $\mathrm{SU}(N)$ systems. more...