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

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

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

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

Anomalous Dimensions and Non-Gaussianity

We analyze the signatures of inflationary models that are coupled to strongly interacting field theories, a basic class of multifield models also motivated by their role in providing dynamically small scales. Near the squeezed limit of the bispectrum, we find a simple scaling behavior determined by operator dimensions, which are constrained by the appropriate unitarity bounds. Specifically, we analyze two simple and calculable classes of examples: conformal field theories (CFTs), and large-N CFTs deformed by relevant time-dependent double-trace operators. Together these two classes of examples exhibit a wide range of scalings and shapes of the bispectrum, including nearly equilateral, orthogonal and local non-Gaussianity in different regimes. Along the way, we compare and contrast the shape and amplitude with previous results on weakly coupled fields coupled to inflation. This signature provides a precision test for strongly coupled sectors coupled to inflation via irrelevant operators suppressed by a high mass scale up to 1000 times the inflationary Hubble scale.Comment: 40 pages, 10 figure