Fluctuating geometries, q-observables, and infrared growth in inflationary spacetimes

Infrared growth of geometrical fluctuations in inflationary spacetimes is investigated. The problem of gauge-invariant characterization of growth of perturbations, which is of interest also in other spacetimes such as black holes, is addressed by studying evolution of the lengths of curves in the geometry. These may either connect freely falling "satellites," or wrap non-trivial cycles of geometries like the torus, and are also used in diffeomorphism- invariant constructions of two-point functions of field operators. For spacelike separations significantly exceeding the Hubble scale, no spacetime geodesic connects two events, but one may find geodesics constrained to lie within constant-time spatial slices. In inflationary geometries, metric perturbations produce significant and growing corrections to the lengths of such geodesics, as we show in both quantization on an inflating torus and in standard slow-roll inflation. These become large, signaling breakdown of a perturbative description of the geometry via such observables, and consistent with perturbative instability of de Sitter space. In particular, we show that the geodesic distance on constant time slices during inflation becomes non-perturbative a few e-folds after a given scale has left the horizon, by distances \sim 1/H^3 \sim RS, obstructing use of such geodesics in constructing IR-safe observables based on the spatial geometry. We briefly discuss other possible measures of such geometrical fluctuations.Comment: 33 pages, 2 figures, latex; v2: typos corrected, references improve

On the divergences of inflationary superhorizon perturbations

We discuss the infrared divergences that appear to plague cosmological perturbation theory. We show that within the stochastic framework they are regulated by eternal inflation so that the theory predicts finite fluctuations. Using the $\Delta N$ formalism to one loop, we demonstrate that the infrared modes can be absorbed into additive constants and the coefficients of the diagrammatic expansion for the connected parts of two and three-point functions of the curvature perturbation. As a result, the use of any infrared cutoff below the scale of eternal inflation is permitted, provided that the background fields are appropriately redefined. The natural choice for the infrared cutoff would of course be the present horizon; other choices manifest themselves in the running of the correlators. We also demonstrate that it is possible to define observables that are renormalization group invariant. As an example, we derive a non-perturbative, infrared finite and renormalization point independent relation between the two-point correlators of the curvature perturbation for the case of the free single field.Comment: 12 page

Holographic bounds on the UV cutoff scale in inflationary cosmology

We discuss how holographic bounds can be applied to the quantum fluctuations of the inflaton. In general the holographic principle will lead to a bound on the UV cutoff scale of the effective theory of inflation, but it will depend on the coarse-graining prescription involved in calculating the entropy. We propose that the entanglement entropy is a natural measure of the entropy of the quantum perturbations, and show which kind of bound on the cutoff it leads to. Such bounds are related to whether the effects of new physics will show up in the CMB.Comment: 19 pages, 2 figures;(V3):Comments and references adde

Low-scale Quintessential Inflation

In quintessential inflationary model, the same master field that drives inflation becomes, later on, the dynamical source of the (present) accelerated expansion. Quintessential inflationary models require a curvature scale at the end of inflation around $10^{-6}M_{\rm P}$ in order to explain the large scale fluctuations observed in the microwave sky. If the curvature scale at the end of inflation is much smaller than $10^{-6}M_{\rm P}$, the large scale adiabatic mode may be produced thanks to the relaxation of a scalar degree of freedom, which will be generically denoted, according to the recent terminology, as the curvaton field. The production of the adiabatic mode is analysed in detail in the case of the minimal quintessential inflationary model originally proposed by Peebles and Vilenkin.Comment: 25 pages; 5 figure

Toxic elements and speciation in seafood samples from different contaminated sites in Europe

The presence of cadmium (Cd), lead (Pb), mercury (THg), methylmercury (MeHg), arsenic (TAs), inorganic arsenic (iAs), cobalt (Co), copper (Cu), zinc (Zn), nickel (Ni), chromium (Cr) and iron (Fe) was investigated in seafood collected from European marine ecosystems subjected to strong anthropogenic pressure, i.e. hotspot areas. Different species (Mytilus galloprovincialis, n=50; Chamelea gallina, n=50; Liza aurata, n=25; Platichthys flesus, n=25; Laminaria digitata, n=15; and Saccharina latissima, n=15) sampled in Tagus estuary, Po delta, Ebro delta, western Scheldt, and in the vicinities of a fish farm area (Solund, Norway), between September and December 2013, were selected to assess metal contamination and potential risks to seafood consumers, as well as to determine the suitability of ecologically distinct organisms as bioindicators in environmental monitoring studies. Species exhibited different elemental profiles, likely as a result of their ecological strategies, metabolism and levels in the environment (i.e. seawater and sediments). Higher levels of Cd (0.15–0.94 mg kg-1), Pb (0.37-0.89 mg kg-1), Co (0.48–1.1 mg kg-1), Cu (4.8–8.4 mg kg-1), Zn (75–153 mg kg-1), Cr (1.0–4.5 mg kg-1) and Fe (283–930 mg kg-1) were detected in bivalve species, particularly in M. galloprovincialis from Ebro and Po deltas, whereas the highest content of Hg was found in P. flesus (0.86 mg kg-1). In fish species, most Hg was organic (MeHg; from 69 to 79%), whereas lower proportions of MeHg were encountered in bivalve species (between 20 and 43%). The highest levels of As were found in macroalgae species L. digitata and S. latissima (41 mg kg-1 and 43 mg kg-1, respectively), with iAs accounting almost 50% of the total As content in L. digitata but not with S. latissima nor in the remaining seafood samples. This work highlights that the selection of the most appropriate bioindicator species is a fundamental step in environmental monitoring of each contaminant, especially in coastal areas. Furthermore, data clearly shows that the current risk assessment and legislation solely based on total As or Hg data is limiting, as elemental speciation greatly varies according to seafood species, thus playing a key role in human exposure assessment via food

Urinary tract infections and post-operative fever in percutaneous nephrolithotomy

To review the incidence of UTIs, post-operative fever, and risk factors for post-operative fever in PCNL patients. Between 2007 and 2009, consecutive PCNL patients were enrolled from 96 centers participating in the PCNL Global Study. Only data from patients with pre-operative urine samples and who received antibiotic prophylaxis were included. Pre-operative bladder urine culture and post-operative fever (>38.5°C) were assessed. Relationship between various patient and operative factors and occurrence of post-operative fever was assessed using logistic regression analyses. Eight hundred and sixty-five (16.2%) patients had a positive urine culture; Escherichia coli was the most common micro-organism found in urine of the 350 patients (6.5%). Of the patients with negative pre-operative urine cultures, 8.8% developed a fever post-PCNL, in contrast to 18.2% of patients with positive urine cultures. Fever developed more often among the patients whose urine cultures consisted of Gram-negative micro-organisms (19.4-23.8%) versus those with Gram-positive micro-organisms (9.7-14.5%). Multivariate analysis indicated that a positive urine culture (odds ratio [OR] = 2.12, CI [1.69-2.65]), staghorn calculus (OR = 1.59, CI [1.28-1.96]), pre-operative nephrostomy (OR = 1.61, CI [1.19-2.17]), lower patient age (OR for each year of 0.99, CI [0.99-1.00]), and diabetes (OR = 1.38, CI [1.05-1.81]) all increased the risk of post-operative fever. Limitations include the use of fever as a predictor of systemic infection. Approximately 10% of PCNL-treated patients developed fever in the post-operative period despite receiving antibiotic prophylaxis. Risk of post-operative fever increased in the presence of a positive urine bacterial culture, diabetes, staghorn calculi, and a pre-operative nephrostom

The Kramers-Moyal Equation of the Cosmological Comoving Curvature Perturbation

Fluctuations of the comoving curvature perturbation with wavelengths larger than the horizon length are governed by a Langevin equation whose stochastic noise arise from the quantum fluctuations that are assumed to become classical at horizon crossing. The infrared part of the curvature perturbation performs a random walk under the action of the stochastic noise and, at the same time, it suffers a classical force caused by its self-interaction. By a path-interal approach and, alternatively, by the standard procedure in random walk analysis of adiabatic elimination of fast variables, we derive the corresponding Kramers-Moyal equation which describes how the probability distribution of the comoving curvature perturbation at a given spatial point evolves in time and is a generalization of the Fokker-Planck equation. This approach offers an alternative way to study the late time behaviour of the correlators of the curvature perturbation from infrared effects.Comment: 27 page

The inflationary trispectrum

We calculate the trispectrum of the primordial curvature perturbation generated by an epoch of slow-roll inflation in the early universe, and demonstrate that the non-gaussian signature imprinted at horizon crossing is unobservably small, of order tau_NL < r/50, where r < 1 is the tensor-to-scalar ratio. Therefore any primordial non-gaussianity observed in future microwave background experiments is likely to have been synthesized by gravitational effects on superhorizon scales. We discuss the application of Maldacena's consistency condition to the trispectrum.Comment: 23 pages, 2 diagrams drawn with feynmp.sty, uses iopart.cls. v2, replaced with version accepted by JCAP. Estimate of maximal tau_NL refined in Section 5, resulting in smaller numerical value. Sign errors in Eq. (44) and Eq. (48) corrected. Some minor notational change

Non-gaussianity from the inflationary trispectrum

We present an estimate for the non-linear parameter \tau_NL, which measures the non-gaussianity imprinted in the trispectrum of the comoving curvature perturbation, \zeta. Our estimate is valid throughout the inflationary era, until the slow-roll approximation breaks down, and takes into account the evolution of perturbations on superhorizon scales. We find that the non-gaussianity is always small if the field values at the end of inflation are negligible when compared to their values at horizon crossing. Under the same assumption, we show that in Nflation-type scenarios, where the potential is a sum of monomials, the non-gaussianity measured by \tau_NL is independent of the couplings and initial conditions.Comment: 15 pages, uses iopart.sty. Replaced with version accepted by JCAP; journal reference adde