5,319 research outputs found

### Scalar Field Equations from Quantum Gravity during Inflation

We exploit a previous computation of the self-mass-squared from quantum
gravity to include quantum corrections to the scalar evolution equation. The
plane wave mode functions are shown to receive no significant one loop
corrections at late times. This result probably applies as well to the inflaton
of scalar-driven inflation. If so, there is no significant correction to the
$\phi \phi$ correlator that plays a crucial role in computations of the power
spectrum.Comment: 19 pages, 5 table

### One Loop Corrected Mode Functions for SQED during Inflation

We solve the one loop effective scalar field equations for spatial plane
waves in massless, minimally coupled scalar quantum electrodynamics on a
locally de Sitter background. The computation is done in two different gauges:
a non-de Sitter invariant analogue of Feynman gauge, and in the de Sitter
invariant, Lorentz gauge. In each case our result is that the finite part of
the conformal counterterm can be chosen so that the mode functions experience
no significant one loop corrections at late times. This is in perfect agreement
with a recent, all orders stochastic prediction.Comment: 26 pages, uses LaTeX 2 epsilon, no figures, version 2 has an updated
reference lis

### A circuit topology approach to categorizing changes in biomolecular structure

The biological world is composed of folded linear molecules of bewildering topological complexity and diversity. The topology of folded biomolecules such as proteins and ribonucleic acids is often subject to change during biological processes. Despite intense research, we lack a solid mathematical framework that summarizes these operations in a principled manner. Circuit topology, which formalizes the arrangements of intramolecular contacts, serves as a general mathematical framework to analyze the topological characteristics of folded linear molecules. In this work, we translate familiar molecular operations in biology, such as duplication, permutation, and elimination of contacts, into the language of circuit topology. We show that for such operations there are corresponding matrix representations as well as basic rules that serve as a foundation for understanding these operations within the context of a coherent algebraic framework. We present several biological examples and provide a simple computational framework for creating and analyzing the circuit diagrams of proteins and nucleic acids. We expect our study and future developments in this direction to facilitate a deeper understanding of natural molecular processes and to provide guidance to engineers for generating complex polymeric materials

### Leading Log Solution for Inflationary Yukawa

We generalize Starobinskii's stochastic technique to the theory of a
massless, minimally coupled scalar interacting with a massless fermion in a
locally de Sitter geometry. The scalar is an ``active'' field that can engender
infrared logarithms. The fermion is a ``passive'' field that cannot cause
infrared logarithms but which can carry them, and which can also induce new
interactions between the active fields. The procedure for dealing with passive
fields is to integrate them out, then stochastically simplify the resulting
effective action following Starobinski\u{\i}. Because Yukawa theory is
quadratic in the fermion this can be done explicitly using the classic solution
of Candelas and Raine. We check the resulting stochastic formulation against an
explicit two loop computation. We also derive a nonperturbative, leading log
result for the stress tensor. Because the scalar effective potential induced by
fermions is unbounded below, back-reaction from this model might dynamically
cancel an arbitrarily large cosmological constant.Comment: 35 pages, LaTeX 2epsilon, 4 figures (using axodraw), version 2 has an
updated reference lis

### Two Loop Scalar Bilinears for Inflationary SQED

We evaluate the one and two loop contributions to the expectation values of
two coincident and gauge invariant scalar bilinears in the theory of massless,
minimally coupled scalar quantum electrodynamics on a locally de Sitter
background. One of these bilinears is the product of two covariantly
differentiated scalars, the other is the product of two undifferentiated
scalars. The computations are done using dimensional regularization and the
Schwinger-Keldysh formalism. Our results are in perfect agreement with the
stochastic predictions at this order.Comment: 43 pages, LaTeX 2epsilon, 5 figures (using axodraw.sty) Version 2 has
updated references and important corrections to Tables 3-5 and to eqns
(139-141), (145-146), (153-155), (158) and (160

### Quantum Gravity Corrections to the One Loop Scalar Self-Mass during Inflation

We compute the one loop corrections from quantum gravity to the
self-mass-squared of a massless, minimally coupled scalar on a locally de
Sitter background. The calculation was done using dimensional regularization
and renormalized by subtracting fourth order BPHZ counterterms. Our result
should determine whether quantum gravitational loop corrections can
significantly alter the dynamics of a scalar inflaton.Comment: 47 pages, 3 figures, 20 tables, uses LaTeX 2 epsilon, version 2
revised for publication in Physical Review

### Charged Scalar Self-Mass during Inflation

We compute the one loop self-mass of a charged massless, minimally coupled
scalar in a locally de Sitter background geometry. The computation is done in
two different gauges: the noninvariant generalization of Feynman gauge which
gives the simplest expression for the photon propagator and the de Sitter
invariant gauge of Allen and Jacobson. In each case dimensional regularization
is employed and fully renormalized results are obtained. By using our result in
the linearized, effective field equations one can infer how the scalar responds
to the dielectric medium produced by inflationary particle production. We also
work out the result for a conformally coupled scalar. Although the conformally
coupled case is of no great physical interest the fact that we obtain a
manifestly de Sitter invariant form for its self-mass-squared establishes that
our noninvariant gauge introduces no physical breaking of de Sitter invariance
at one loop order.Comment: 41 pages, LaTeX 2epsilon, 3 figures, uses axodra

### Primordial Density Perturbations and Reheating from Gravity

We consider the presence and evolution of primordial density perturbations in
a cosmological model based on a simple ansatz which captures -- by providing a
set of effective gravitational field equations -- the strength of the enhanced
quantum loop effects that can arise during inflation. After deriving the
general equations that perturbations obey, we concentrate on scalar
perturbations and show that their evolution is quite different than that of
conventional inflationary models but still phenomenologically acceptable. The
main reason for this novel evolution is the presence of an oscillating regime
after the end of inflation which makes all super-horizon scalar modes
oscillate. The same reason allows for a natural and very fast reheating
mechanism for the universe.Comment: 37 pages, 2 figures, uses LaTeX2

### Reply to `Can infrared gravitons screen $\Lambda$?'

We reply to the recent criticism by Garriga and Tanaka of our proposal that
quantum gravitational loop corrections may lead to a secular screening of the
effective cosmological constant. Their argument rests upon a renormalization
scheme in which the composite operator $(R \sqrt{-g} - 4 \Lambda \sqrt{-g}
)_{\rm ren}$ is defined to be the trace of the renormalized field equations.
Although this is a peculiar prescription, we show that it {\it does not
preclude secular screening}. Moreover, we show that a constant Ricci scalar
{\it does not even classically} imply a constant expansion rate. Other
important points are: (1) the quantity $R_{\rm ren}$ of Garriga and Tanaka is
neither a properly defined composite operator, nor is it constant; (2) gauge
dependence does not render a Green's function devoid of physical content; (3)
scalar models on a non-dynamical de Sitter background (for which there is no
gauge issue) can induce arbitrarily large secular contributions to the stress
tensor; (4) the same secular corrections appear in observable quantities in
quantum gravity; and (5) the prospects seem good for deriving a simple
stochastic formulation of quantum gravity in which the leading secular effects
can be summed and for which the expectation values of even complicated, gauge
invariant operators can be computed at leading order.Comment: 17 pages, no figures, uses LaTeX 2epsilon. Version 2 adds important
points about R_ren being neither finite nor constant, and that a constant
Ricci scalar is not even classically an indicator of de Sitter expansion.
Version 3 corrects some typoes and updates the reference

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