Leading slow roll corrections to the volume of the universe and the entropy bound

We make an extension to recent calculations of the probability density \rho(V) for the volume of the universe after inflation. Previous results have been accurate to leading order in the slow roll parameters \epsilon=\dot{H}/H^2 and \eta=\ddot{\phi}/(\dot{\phi} H), and 1/N_c, where H is the Hubble parameter and N_c is the classical number of e-foldings. Here, we present a modification which captures effects of order \epsilon N_c, which amounts to letting the parameters of inflation H and \dot{\phi} depend on the value of the inflaton \phi. The phase of slow roll eternal inflation can be defined as when the probability to have an infinite volume is greater than zero. Using this definition, we study the Laplace transform of \rho(V) numerically to determine the condition that triggers the transition to eternal inflation. We also study the average volume analytically and show that it satisfies the universal volume bound. This bound states that, in any realization of inflation which ends with a finite volume, an initial volume must grow by less than a factor of exp(S_{dS}/2), where S_{dS} is the de Sitter (dS) entropy.Comment: 18 pages, 3 figure

Direct signatures of the formation time of galaxies

We show that it is possible to directly measure the formation time of galaxies using large-scale structure. In particular, we show that the large-scale distribution of galaxies is sensitive to whether galaxies form over a narrow period of time before their observed times, or are formed over a time scale on the order of the age of the Universe. Along the way, we derive simple recursion relations for the perturbative terms of the most general bias expansion for the galaxy density, thus fully extending the famous dark-matter recursion relations to generic tracers.Comment: 6+2 pages, 1 figure, ancillary file include

Tensors Mesons in AdS/QCD

We explore tensor mesons in AdS/QCD focusing on f2 (1270), the lightest spin-two resonance in QCD. We find that the f2 mass and the partial width for f2 -> gamma gamma are in very good agreement with data. In fact, the dimensionless ratio of these two quantities comes out within the current experimental bound. The result for this ratio depends only on Nc and Nf, and the quark and glueball content of the operator responsible for the f2; more importantly, it does not depend on chiral symmetry breaking and so is both independent of much of the arbitrariness of AdS/QCD and completely out of reach of chiral perturbation theory. For comparison, we also explore f2 -> pi pi, which because of its sensitivity to the UV corrections has much more uncertainty. We also calculate the masses of the higher spin resonances on the Regge trajectory of the f2, and find they compare favorably with experiment.Comment: 21 pages, 1 figure; Li's correcte

Double-copy towards supergravity inflation with α\alpha-attractor models

Key to the simplicity of supergravity alpha-attractor models of inflation are Volkov-Akulov fermions, often in the form of nilpotent superfields. Here we explore the possibility of using the double-copy to construct theories of Dirac-Born-Infeld-Volkov-Akulov (DBIVA) coupled to supergravity. A color-dual bootstrap admits scattering amplitudes involving pions and vectors through five-point tree-level order by order in mass-dimension, but requires the introduction of a tr(F^3) operator. Gauge theories with this operator were recently found to require a tower of higher-derivative operators to be compatible with the duality between color and kinematics. Adjoint-type double-copy construction at its most conservative seems to require the UV completion of DBVIA + pure Poincare supergravity scattering amplitudes to a family of theories involving DBVIA-like particles coupled to Weyl-Einstein supergravity. We also point out an alternative solution to color-dual gauged pions that allows adjoint double-copy without a tower of higher derivative corrections but at the cost of exchange symmetry between scalars.Comment: 40 pages, 3 figures, 4 tables, ancillary data available at this url: https://github.com/drjjmc/colorDualPion

The one-loop bispectrum of galaxies in redshift space from the Effective Field Theory of Large-Scale Structure

We derive the kernels and the Effective Field Theory of Large-Scale Structure counterterms for the one-loop bispectrum of dark matter and of biased tracers in real and redshift space. This requires the expansion of biased tracers up to fourth order in fluctuations. In the process, we encounter several subtleties related to renormalization. One is the fact that, in renormalizing the momentum, a local counterterm contributes non-locally. A second subtlety is related to the renormalization of local products of the velocity fields, which need to be expressed in terms of the renormalized velocity in order to preserve Galilean symmetry. We check that the counterterms we identify are necessary and sufficient to renormalize the one-loop bispectrum at leading and subleading order in the derivative expansion. The kernels that we originally present here have already been used for the first analyses of the one-loop bispectrum in BOSS data [1, 2].Comment: 39 + 28 pages, typos corrected, some expanded comments, ancillary Mathematica file in "Other formats

Unraveling the complexity of protein backbone dynamics with combined 13C and 15N solid-state NMR relaxation measurements

Typically, protein dynamics involve a complex hierarchy of motions occurring on different time scales between conformations separated by a range of different energy barriers. NMR relaxation can in principle provide a site-specific picture of both the time scales and amplitudes of these motions, but independent relaxation rates sensitive to fluctuations in different time scale ranges are required to obtain a faithful representation of the underlying dynamic complexity. This is especially pertinent for relaxation measurements in the solid state, which report on dynamics in a broader window of time scales by more than 3 orders of magnitudes compared to solution NMR relaxation. To aid in unraveling the intricacies of biomolecular dynamics we introduce 13C spin–lattice relaxation in the rotating frame (R1ρ) as a probe of backbone nanosecond-microsecond motions in proteins in the solid state. We present measurements of 13C′ R1ρ rates in fully protonated crystalline protein GB1 at 600 and 850 MHz 1H Larmor frequencies and compare them to 13C′ R1, 15N R1 and R1ρ measured under the same conditions. The addition of carbon relaxation data to the model free analysis of nitrogen relaxation data leads to greatly improved characterization of time scales of protein backbone motions, minimizing the occurrence of fitting artifacts that may be present when 15N data is used alone. We also discuss how internal motions characterized by different time scales contribute to 15N and 13C relaxation rates in the solid state and solution state, leading to fundamental differences between them, as well as phenomena such as underestimation of picosecond-range motions in the solid state and nanosecond-range motions in solution