Curvature perturbation in multi-field inflation with non-minimal coupling

In this paper we discuss a multi-field model of inflation in which generally all fields are non-minimally coupled to the Ricci scalar and have non-canonical kinetic terms. The background evolution and first-order perturbations for the model are evaluated in both the Jordan and Einstein frames, and the respective curvature perturbations compared. We confirm that they are indeed not the same - unlike in the single-field case - and also that the difference is a direct consequence of the isocurvature perturbations inherent to multi-field models. This result leads us to conclude that the notion of adiabaticity is not invariant under conformal transformations. Using a two-field example we show that even if in one frame the evolution is adiabatic, meaning that the curvature perturbation is conserved on super-horizon scales, in general in the other frame isocurvature perturbations continue to source the curvature perturbation. We also find that it is possible to realise a particular model in which curvature perturbations in both frames are conserved but with each being of different magnitude. These examples highlight that the curvature perturbation itself, despite being gauge-invariant, does not correspond directly to an observable. The non-equivalence of the two curvature perturbations would also be important when considering the addition of Standard Model matter into the system.Comment: 21 pages, 2 figures, references added, typos corrected, version to appear in JCA

In-hospital mortality of non-st segment elevation myocardial infarction in a Puerto Rican population

Introduction: Currently, there is limited published information on in-hospital mortality regarding ST segment elevation and non-ST segment elevation myocardial infarction. This information is even scarcer on the Hispanic population. We aim to study if there is a difference on in-hospital mortality between ST elevation myocardial infarction (STEMI) and non-ST elevation myocardial infarction (NSTEMI) in a mostly Hispanic population. Methods: A secondary data analysis of a non-concurrent prospective study was performed using the Puerto Rican Heart Attack study database. Dependent variable was in-hospital mortality and independent variable was type of myocardial infarction (STEMI or NSTEMI). We conducted, sequentially, a descriptive, bivariate and multivariate analysis. The chi-squared test was used to compare categorical variables and t-test for continuous variables. Finally, a logistic regression model was used to perform the multivariate analysis. Results: From the 838 Puerto Rican patients hospitalized with ST classification, 310 (37%) were diagnosed with STEMI. Patients with STEMI were younger (65 years vs 68 years; p=0.008), more likely to receive invasive treatment (47.9% vs 27.5%, p<0.001), and less likely to have a history of hypertension (72.5% vs 79.0%, p=0.033) compared to NSTEMI patients. For every 1- year increase in age, there is a 4% increase in in-hospital mortality. Patients with hyperlipidemia were approximately two times more likely to die in the hospital compared to patients without hyperlipidemia. In the unadjusted analysis, there was no significant association between STEMI and NSTEMI patients and in-hospital mortality. After adjusting for confounders, patients with STEMI had twice the risk of dying than those with NSTEMI. Conclusions: Findings from this study suggest that Puerto Ricans with STEMI have double the risk of in-hospital mortality than NSTEMI patients. Our findings were similar to those reported in the literature. A timely recognition of at-risk patients, especially among STEMI patients, may help reduce short-term morality among patients hospitalized with acute myocardial infarction in Puerto Rico

Heat flow and calculus on metric measure spaces with Ricci curvature bounded below - the compact case

We provide a quick overview of various calculus tools and of the main results concerning the heat flow on compact metric measure spaces, with applications to spaces with lower Ricci curvature bounds. Topics include the Hopf-Lax semigroup and the Hamilton-Jacobi equation in metric spaces, a new approach to differentiation and to the theory of Sobolev spaces over metric measure spaces, the equivalence of the L^2-gradient flow of a suitably defined "Dirichlet energy" and the Wasserstein gradient flow of the relative entropy functional, a metric version of Brenier's Theorem, and a new (stronger) definition of Ricci curvature bound from below for metric measure spaces. This new notion is stable w.r.t. measured Gromov-Hausdorff convergence and it is strictly connected with the linearity of the heat flow.Comment: To the memory of Enrico Magenes, whose exemplar life, research and teaching shaped generations of mathematician

Features of heavy physics in the CMB power spectrum

The computation of the primordial power spectrum in multi-field inflation models requires us to correctly account for all relevant interactions between adiabatic and non-adiabatic modes around and after horizon crossing. One specific complication arises from derivative interactions induced by the curvilinear trajectory of the inflaton in a multi-dimensional field space. In this work we compute the power spectrum in general multi-field models and show that certain inflaton trajectories may lead to observationally significant imprints of `heavy' physics in the primordial power spectrum if the inflaton trajectory turns, that is, traverses a bend, sufficiently fast (without interrupting slow roll), even in cases where the normal modes have masses approaching the cutoff of our theory. We emphasise that turning is defined with respect to the geodesics of the sigma model metric, irrespective of whether this is canonical or non-trivial. The imprints generically take the form of damped superimposed oscillations on the power spectrum. In the particular case of two-field models, if one of the fields is sufficiently massive compared to the scale of inflation, we are able to compute an effective low energy theory for the adiabatic mode encapsulating certain relevant operators of the full multi-field dynamics. As expected, a particular characteristic of this effective theory is a modified speed of sound for the adiabatic mode which is a functional of the background inflaton trajectory and the turns traversed during inflation. Hence in addition, we expect non-Gaussian signatures directly related to the features imprinted in the power spectrum.Comment: 41 pages, 6 figures, references updated, minor modifications. Version to appear in JCAP. v4: Equations (4.28) and (4.30) and Figures 5 and 6 correcte

A Statistical Approach to Multifield Inflation: Many-field Perturbations Beyond Slow Roll

We study multifield contributions to the scalar power spectrum in an ensemble of six-field inflationary models obtained in string theory. We identify examples in which inflation occurs by chance, near an approximate inflection point, and we compute the primordial perturbations numerically, both exactly and using an array of truncated models. The scalar mass spectrum and the number of fluctuating fields are accurately described by a simple random matrix model. During the approach to the inflection point, bending trajectories and violations of slow roll are commonplace, and 'many-field' effects, in which three or more fields influence the perturbations, are often important. However, in a large fraction of models consistent with constraints on the tilt the signatures of multifield evolution occur on unobservably large scales. Our scenario is a concrete microphysical realization of quasi-single-field inflation, with scalar masses of order $H$, but the cubic and quartic couplings are typically too small to produce detectable non-Gaussianity. We argue that our results are characteristic of a broader class of models arising from multifield potentials that are natural in the Wilsonian sense.Comment: 39 pages, 17 figures. References added. Matches version published in JCA

Biomarker-based asthma phenotypes of corticosteroid response

BackgroundAsthma is a heterogeneous disease with different phenotypes. Inhaled corticosteroid (ICS) therapy is a mainstay of treatment for asthma, but the clinical response to ICSs is variable.ObjectiveWe hypothesized that a panel of inflammatory biomarkers (ie, fraction of exhaled nitric oxide [Feno], sputum eosinophil count, and urinary bromotyrosine [BrTyr] level) might predict steroid responsiveness.MethodsThe original study from which this analysis originates comprised 2 phases: a steroid-naive phase 1 and a 28-day trial of ICSs (phase 2) during which Feno values, sputum eosinophil counts, and urinary BrTyr levels were measured. The response to ICSs was based on clinical improvements, including a 12% or greater increase in FEV1, a 0.5-point or greater decrease in Asthma Control Questionnaire score, and 2 doubling dose or greater increase in provocative concentration of adenosine 5′-monophosphate causing a 20% decrease in FEV1 (PC20AMP). Healthy control subjects were also evaluated in this study for comparison of biomarkers with those seen in asthmatic patients.ResultsAsthmatic patients had higher than normal Feno values, sputum eosinophil counts, and urinary BrTyr levels during the steroid-naive phase and after ICS therapy. After 28-day trial of ICSs, Feno values decreased in 82% of asthmatic patients, sputum eosinophil counts decreased in 60%, and urinary BrTyr levels decreased in 58%. Each of the biomarkers at the steroid-naive phase had utility for predicting steroid responsiveness, but the combination of high Feno values and high urinary BrTyr levels had the best power (13.3-fold, P < .01) to predict a favorable response to ICS therapy. However, the magnitude of the decrease in biomarker levels was unrelated to the magnitude of clinical response to ICS therapy.ConclusionA noninvasive panel of biomarkers in steroid-naive asthmatic patients predicts clinical responsiveness to ICS therapy

The inflationary bispectrum with curved field-space

We compute the covariant three-point function near horizon-crossing for a system of slowly-rolling scalar fields during an inflationary epoch, allowing for an arbitrary field-space metric. We show explicitly how to compute its subsequent evolution using a covariantized version of the separate universe or "delta-N" expansion, which must be augmented by terms measuring curvature of the field-space manifold, and give the nonlinear gauge transformation to the comoving curvature perturbation. Nonlinearities induced by the field-space curvature terms are a new and potentially significant source of non-Gaussianity. We show how inflationary models with non-minimal coupling to the spacetime Ricci scalar can be accommodated within this framework. This yields a simple toolkit allowing the bispectrum to be computed in models with non-negligible field-space curvature.Comment: 22 pages, plus appendix and reference