David Kaiser

The power of a good idea: Quantitative modeling of the spread of ideas from epidemiological models

The population dynamics underlying the diffusion of ideas hold many qualitative similarities to those involved in the spread of infections. In spite of much suggestive evidence this analogy is hardly ever quantified in useful ways. The standard benefit of modeling epidemics is the ability to estimate quantitatively population average parameters, such as interpersonal contact rates, incubation times, duration of infectious periods, etc. In most cases such quantities generalize naturally to the spread of ideas and provide a simple means of quantifying sociological and behavioral patterns. Here we apply several paradigmatic models of epidemics to empirical data on the advent and spread of Feynman diagrams through the theoretical physics communities of the USA, Japan, and the USSR in the period immediately after World War II. This test case has the advantage of having been studied historically in great detail, which allows validation of our results. We estimate the effectiveness of adoption of the idea in the three communities and find values for parameters reflecting both intentional social organization and long lifetimes for the idea. These features are probably general characteristics of the spread of ideas, but not of common epidemics.

Nonperturbative Dynamics Of Reheating After Inflation: A Review

Our understanding of the state of the universe between the end of inflation and big bang nucleosynthesis (BBN) is incomplete. The dynamics at the end of inflation are rich and a potential source of observational signatures. Reheating, the energy transfer between the inflaton and Standard Model fields (possibly through intermediaries) and their subsequent thermalization, can provide clues to how inflation fits in with known high-energy physics. We provide an overview of our current understanding of the nonperturbative, nonlinear dynamics at the end of inflation, some salient features of realistic particle physics models of reheating, and how the universe reaches a thermal state before BBN. In addition, we review the analytical and numerical tools available in the literature to study preheating and reheating and discuss potential observational signatures from this fascinating era.

Population modeling of the emergence and development of scientific fields

We analyze the temporal evolution of emerging fields within several scientific disciplines in terms of numbers of authors and publications. From bibliographic searches we construct databases of authors, papers, and their dates of publication. We show that the temporal development of each field, while different in detail, is well described by population contagion models, suitably adapted from epidemiology to reflect the dynamics of scientific interaction. Dynamical parameters are estimated and discussed to reflect fundamental characteristics of the field, such as time of apprenticeship and recruitment rate. We also show that fields are characterized by simple scaling laws relating numbers of new publications to new authors, with exponents that reflect increasing or decreasing returns in scientific productivity.

Inflationary paradigm after Planck 2013

Abstract 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 ( Ω k = 1 − Ω ) and the spectral tilt of primordial curvature perturbations ( n s − 1 = d ln ⁡ P R / d ln ⁡ k ), among others—predictions that match the latest observations from the Planck satellite to very good precision. In the light of data from 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.

Multifield Inflation after Planck: The Case for Nonminimal Couplings

Multifield models of inflation with nonminimal couplings are in excellent agreement with the recent results from Planck. Across a broad range of couplings and initial conditions, such models evolve along an effectively single-field attractor solution and predict values of the primordial spectral index and its running, the tensor-to-scalar ratio, and non-Gaussianities squarely in the observationally most-favored region. Such models can also amplify isocurvature perturbations, which could account for the low power recently observed in the cosmic microwave background power spectrum at low multipoles. Future measurements of primordial isocurvature perturbations could distinguish between the currently viable possibilities.

Conformal Transformations with Multiple Scalar Fields

Center for Theoretical Physics and Department of Physics,Massachusetts Institute of Technology,Cambridge, Massachusetts 02139 USA(Dated: April 26, 2010)Many interesting models incorporate scalar fields with non-minimal couplings tothe spacetime Ricci curvature scalar. As is well known, if only one scalar field isnon-minimally coupled, then one may perform a conformal transformation to a newframe in which both the gravitational portion of the Lagrangian and the kinetic termfor the (rescaled) field assume canonical form. We examine under what conditionsthe gravitational and kinetic terms in the Lagrangian may be brought into canonicalform when more than one scalar field has non-minimal coupling. A particular classof two-field models admits such a transformation, but models with more than twonon-minimally coupled fields in general do not.

Inflationary cosmology: exploring the universe from the smallest to the largest scales.

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 inflations ultimate implications for the nature of matter, energy, and spacetime.

Scientific discovery and topological transitions in collaboration networks

We analyze the advent and development of eight scientific fields from their inception to maturity and map the evolution of their networks of collaboration over time, measured in terms of co-authorship of scientific papers. We show that as a field develops it undergoes a topological transition in its collaboration structure between a small disconnected graph to a much larger network where a giant connected component of collaboration appears. As a result, the number of edges and nodes in the largest component undergoes a transition between a small fraction of the total to a majority of all occurrences. These results relate to many qualitative observations of the evolution of technology and discussions of the “structure of scientific revolutions”. We analyze this qualitative change in network topology in terms of several quantitative graph theoretical measures, such as density, diameter, and relative size of the networks largest component.

General relativistic effects in preheating

General relativistic effects in the form of metric perturbations are usually neglected in the preheating era that follows inflation. We argue that in realistic multi-field models these effects are in fact crucial, and the fully coupled system of metric and quantum field fluctuations needs to be considered. Metric perturbations are resonantly amplified, breaking the scale-invariance of the primordial spectrum, and in turn stimulate scalar field resonances via gravitational rescattering. This non-gravitationally dominated nonlinear growth of gravitational fluctuations may have significant effects on the Doppler peaks in the cosmic background radiation, primordial black hole formation, gravitational waves and nonthermal symmetry restoration.

Metric preheating and limitations of linearized gravity

Abstract During the preheating era after inflation, resonant amplification of quantum field fluctuations takes place. Recently it has become clear that this must be accompanied by resonant amplification of scalar metric fluctuations, since the two are united by Einsteins equations. Furthermore, this “metric preheating” enhances particle production, and leads to gravitational rescattering effects even at linear order . In multi-field models with strong preheating ( q ≫1), metric perturbations are driven non-linear, with the strongest amplification typically on super-Hubble scales ( k →0). This amplification is causal, being due to the super-Hubble coherence of the inflaton condensate, and is accompanied by resonant growth of entropy perturbations. The amplification invalidates the use of the linearized Einstein field equations, irrespective of the amount of fine-tuning of the initial conditions. This has serious implications on all scales – from large-angle cosmic microwave background (CMB) anisotropies to primordial black holes. We investigate the ( q , k ) parameter space in a two-field model, and introduce the time to non-linearity, t nl , as the timescale for the breakdown of the linearized Einstein equations. t nl is a robust indicator of resonance behavior, showing the fine structure in q and k that one expects from a quasi-Floquet system, and we argue that t nl is a suitable generalization of the static Floquet index in an expanding universe. Backreaction effects are expected to shut down the linear resonances, but cannot remove the existing amplification, which threatens the viability of strong preheating when confronted with the CMB. Mode–mode coupling and turbulence tend to re-establish scale invariance, but this process is limited by causality and for small k the primordial scale invariance of the spectrum may be destroyed. We discuss ways to escape the above conclusions, including secondary phases of inflation and preheating solely to fermions. The exclusion principle constrains the amplification of metric perturbations significantly. Finally we rank known classes of inflation from strongest (chaotic and strongly coupled hybrid inflation) to weakest (hidden sector, warm inflation), in terms of the distortion of the primordial spectrum due to these resonances in preheating.