The Spectral Zeta Function for Laplace Operators on Warped Product Manifolds of the type I×fNI\times_{f} N

In this work we study the spectral zeta function associated with the Laplace operator acting on scalar functions defined on a warped product of manifolds of the type $I\times_{f} N$ where $I$ is an interval of the real line and $N$ is a compact, $d$-dimensional Riemannian manifold either with or without boundary. Starting from an integral representation of the spectral zeta function, we find its analytic continuation by exploiting the WKB asymptotic expansion of the eigenfunctions of the Laplace operator on $M$ for which a detailed analysis is presented. We apply the obtained results to the explicit computation of the zeta regularized functional determinant and the coefficients of the heat kernel asymptotic expansion.Comment: 29 pages, LaTe

One-Loop Renormalization of a Self-Interacting Scalar Field in Nonsimply Connected Spacetimes

Using the effective potential, we study the one-loop renormalization of a massive self-interacting scalar field at finite temperature in flat manifolds with one or more compactified spatial dimensions. We prove that, owing to the compactification and finite temperature, the renormalized physical parameters of the theory (mass and coupling constant) acquire thermal and topological contributions. In the case of one compactified spatial dimension at finite temperature, we find that the corrections to the mass are positive, but those to the coupling constant are negative. We discuss the possibility of triviality, i.e. that the renormalized coupling constant goes to zero at some temperature or at some radius of the compactified spatial dimension.Comment: 16 pages, plain LATE

Conformal Transformations in Cosmology of Modified Gravity: the Covariant Approach Perspective

The 1+3 covariant approach and the covariant gauge-invariant approach to perturbations are used to analyze in depth conformal transformations in cosmology. Such techniques allow us to obtain very interesting insights on the physical content of these transformations, when applied to non-standard gravity. The results obtained lead to a number of general conclusions on the change of some key quantities describing any two conformally related cosmological models. In particular, it is shown that the physics in the Einstein frame has characteristics which are completely different from those in the Jordan frame. Even if some of the geometrical properties of the cosmology are preserved (homogeneous and isotropic Universes are mapped into homogeneous and isotropic universes), it can happen that decelerating cosmologies are mapped into accelerated ones. Differences become even more pronounced when first-order perturbations are considered: from the 1+3 equations it is seen that first-order vector and tensor perturbations are left unchanged in their structure by the conformal transformation, but this cannot be said of the scalar perturbations, which include the matter density fluctuations. Behavior in the two frames of the growth rate, as well as other evolutionary features, like the presence or absence of oscillations, etc., appear to be different too. The results obtained are then explicitly interpreted and verified with the help of some clarifying examples based on $f(R)$-gravity cosmologies.Comment: 26 pages, 8 figure

Trace anomaly driven inflation

This paper investigates Starobinsky's model of inflation driven by the trace anomaly of conformally coupled matter fields. This model does not suffer from the problem of contrived initial conditions that occurs in most models of inflation driven by a scalar field. The universe can be nucleated semi-classically by a cosmological instanton that is much larger than the Planck scale provided there are sufficiently many matter fields. There are two cosmological instantons: the four sphere and a new ``double bubble'' solution. This paper considers a universe nucleated by the four sphere. The AdS/CFT correspondence is used to calculate the correlation function for scalar and tensor metric perturbations during the ensuing de Sitter phase. The analytic structure of the scalar and tensor propagators is discussed in detail. Observational constraints on the model are discussed. Quantum loops of matter fields are shown to strongly suppress short scale metric perturbations, which implies that short distance modifications of gravity would probably not be observable in the cosmic microwave background. This is probably true for any model of inflation provided there are sufficiently many matter fields. This point is illustrated by a comparison of anomaly driven inflation in four dimensions and in a Randall-Sundrum brane-world model.Comment: LaTeX, 42 pages, 5 .eps figures. v2: typos corrected, references added and 2 new paragraphs in conclusions section. v3: comments about strong coupling and unboundedness of action changed, other minor changes. v4: Comments about strong coupling changed again (2-point functions of metric perturbations do not depend on Yang-Mills coupling

The Causal Structure of QED in Curved Spacetime: Analyticity and the Refractive Index

The effect of vacuum polarization on the propagation of photons in curved spacetime is studied in scalar QED. A compact formula is given for the full frequency dependence of the refractive index for any background in terms of the Van Vleck-Morette matrix for its Penrose limit and it is shown how the superluminal propagation found in the low-energy effective action is reconciled with causality. The geometry of null geodesic congruences is found to imply a novel analytic structure for the refractive index and Green functions of QED in curved spacetime, which preserves their causal nature but violates familiar axioms of S-matrix theory and dispersion relations. The general formalism is illustrated in a number of examples, in some of which it is found that the refractive index develops a negative imaginary part, implying an amplification of photons as an electromagnetic wave propagates through curved spacetime.Comment: 54 pages, 19 figures, corrected some signs in formulae and graph

Procoagulant Adaptation of a Blood Coagulation Prothrombinase-like Enzyme Complex in Australian Elapid Venom

The macromolecular enzyme complex prothrombinase serves an indispensable role in blood coagulation as it catalyzes the conversion of prothrombin to thrombin, a key regulatory enzyme in the formation of a blood clot. Interestingly, a virtually identical enzyme complex is found in the venom of some Australian elapid snakes, which is composed of a cofactor factor Va-component and a serine protease factor Xa-like subunit. This review will provide an overview of the identification and characterization of the venom prothrombinase complex and will discuss the rationale for its powerful procoagulant nature responsible for the potent hemostatic toxicity of the elapid venom

Noise induced transitions in semiclassical cosmology

A semiclassical cosmological model is considered which consists of a closed Friedmann-Robertson-Walker in the presence of a cosmological constant, which mimics the effect of an inflaton field, and a massless, non-conformally coupled quantum scalar field. We show that the back-reaction of the quantum field, which consists basically of a non local term due to gravitational particle creation and a noise term induced by the quantum fluctuations of the field, are able to drive the cosmological scale factor over the barrier of the classical potential so that if the universe starts near zero scale factor (initial singularity) it can make the transition to an exponentially expanding de Sitter phase. We compute the probability of this transition and it turns out to be comparable with the probability that the universe tunnels from "nothing" into an inflationary stage in quantum cosmology. This suggests that in the presence of matter fields the back-reaction on the spacetime should not be neglected in quantum cosmology.Comment: LaTex, 33.tex pages, no figure

Black Hole Thermodynamics and Statistical Mechanics

We have known for more than thirty years that black holes behave as thermodynamic systems, radiating as black bodies with characteristic temperatures and entropies. This behavior is not only interesting in its own right; it could also, through a statistical mechanical description, cast light on some of the deep problems of quantizing gravity. In these lectures, I review what we currently know about black hole thermodynamics and statistical mechanics, suggest a rather speculative "universal" characterization of the underlying states, and describe some key open questions.Comment: 35 pages, Springer macros; for the Proceedings of the 4th Aegean Summer School on Black Hole

Extended Theories of Gravity and their Cosmological and Astrophysical Applications

We review Extended Theories of Gravity in metric and Palatini formalism pointing out their cosmological and astrophysical application. The aim is to propose an alternative approach to solve the puzzles connected to dark components.Comment: 44 pages, 11 figure

Long-term cardiovascular safety of febuxostat compared with allopurinol in patients with gout (FAST): a multicentre, prospective, randomised, open-label, non-inferiority trial

Background: Febuxostat and allopurinol are urate-lowering therapies used to treat patients with gout. Following concerns about the cardiovascular safety of febuxostat, the European Medicines Agency recommended a post-licensing study assessing the cardiovascular safety of febuxostat compared with allopurinol. Methods: We did a prospective, randomised, open-label, blinded-endpoint, non-inferiority trial of febuxostat versus allopurinol in patients with gout in the UK, Denmark, and Sweden. Eligible patients were 60 years or older, already receiving allopurinol, and had at least one additional cardiovascular risk factor. Those who had myocardial infarction or stroke in the previous 6 months or who had severe congestive heart failure or severe renal impairment were excluded. After a lead-in phase in which allopurinol dose was optimised towards achieving a serum urate concentration of less than 0·357 mmol/L (<6 mg/dL), patients were randomly assigned (1:1, with stratification according to previous cardiovascular events) to continue allopurinol (at the optimised dose) or start febuxostat at 80 mg/day, increasing to 120 mg/day if necessary to achieve the target serum urate concentration. The primary outcome was a composite of hospitalisation for non-fatal myocardial infarction or biomarker-positive acute coronary syndrome; non-fatal stroke; or cardiovascular death. The hazard ratio (HR) for febuxostat versus allopurinol in a Cox proportional hazards model (adjusted for the stratification variable and country) was assessed for non-inferiority (HR limit 1·3) in an on-treatment analysis. This study is registered with the EU Clinical Trials Register (EudraCT 2011-001883-23) and ISRCTN (ISRCTN72443728) and is now closed. Findings: From Dec 20, 2011, to Jan 26, 2018, 6128 patients (mean age 71·0 years [SD 6·4], 5225 [85·3%] men, 903 [14·7%] women, 2046 [33·4%] with previous cardiovascular disease) were enrolled and randomly allocated to receive allopurinol (n=3065) or febuxostat (n=3063). By the study end date (Dec 31, 2019), 189 (6·2%) patients in the febuxostat group and 169 (5·5%) in the allopurinol group withdrew from all follow-up. Median follow-up time was 1467 days (IQR 1029–2052) and median on-treatment follow-up was 1324 days (IQR 870–1919). For incidence of the primary endpoint, on-treatment, febuxostat (172 patients [1·72 events per 100 patient-years]) was non-inferior to allopurinol (241 patients [2·05 events per 100 patient-years]; adjusted HR 0·85 [95% CI 0·70–1·03], p<0·0001). In the febuxostat group, 222 (7·2%) of 3063 patients died and 1720 (57·3%) of 3001 in the safety analysis set had at least one serious adverse event (with 23 events in 19 [0·6%] patients related to treatment). In the allopurinol group, 263 (8·6%) of 3065 patients died and 1812 (59·4%) of 3050 had one or more serious adverse events (with five events in five [0·2%] patients related to treatment). Randomised therapy was discontinued in 973 (32·4%) patients in the febuxostat group and 503 (16·5%) patients in the allopurinol group. Interpretation: Febuxostat is non-inferior to allopurinol therapy with respect to the primary cardiovascular endpoint, and its long-term use is not associated with an increased risk of death or serious adverse events compared with allopurinol. Funding: Menarini, Ipsen, and Teijin Pharma Ltd