Noise Kernel in Stochastic Gravity and Stress Energy Bi-Tensor of Quantum Fields in Curved Spacetimes

The noise kernel is the vacuum expectation value of the (operator-valued) stress-energy bi-tensor which describes the fluctuations of a quantum field in curved spacetimes. It plays the role in stochastic semiclassical gravity based on the Einstein-Langevin equation similar to the expectation value of the stress-energy tensor in semiclassical gravity based on the semiclassical Einstein equation. According to the stochastic gravity program, this two point function (and by extension the higher order correlations in a hierarchy) of the stress energy tensor possesses precious statistical mechanical information of quantum fields in curved spacetime and, by the self-consistency required of Einstein's equation, provides a probe into the coherence properties of the gravity sector (as measured by the higher order correlation functions of gravitons) and the quantum nature of spacetime. It reflects the low and medium energy (referring to Planck energy as high energy) behavior of any viable theory of quantum gravity, including string theory. It is also useful for calculating quantum fluctuations of fields in modern theories of structure formation and for backreaction problems in cosmological and black holes spacetimes. We discuss the properties of this bi-tensor with the method of point-separation, and derive a regularized expression of the noise-kernel for a scalar field in general curved spacetimes. One collorary of our finding is that for a massless conformal field the trace of the noise kernel identically vanishes. We outline how the general framework and results derived here can be used for the calculation of noise kernels for Robertson-Walker and Schwarzschild spacetimes.Comment: 22 Pages, RevTeX; version accepted for publication in PR

Otimização de protocolos de extração de RNA em diferentes tecidos de milho.

Neste trabalho, foram testados cinco métodos de extração de RNA (CTAB microextração, Concert? Invitrogen, Concert? Adaptado, TRI Reagente® Sigma e TRI Reagente® Adaptado), em dois diferentes tecidos de milho (mesocótilo e raiz), com o objetivo de estabelecer um método eficiente de extração de RNA, visando posteriormente estudos de expressão gênica. Observou-se que o método Concert,utilizando o protocolo adaptado, foi o mais eficiente para a extração de RNA de ambos os tecidos de plântulas de milho, originando 2351,35 ?g por 100 mg de tecido para mesocótilo e 893,75 ?g por 100 mg de tecido para raiz, considerando tanto a quantidade como a qualidade das amostras, podendo ser submetidas às etapas posteriores de tratamento com DNAse e construção de cDNA para estudos de expressão gênica. Pôde-se observar que pequenas modificações nos protocolos, como, por exemplo, mudança no tempo e na posição dos tubos durante a incubação e o incremento de duas lavagens com clorofórmio, podem melhorar muito tanto a qualidade quanto a quantidade do RNA extraído

Vacuum Energy Density Fluctuations in Minkowski and Casimir States via Smeared Quantum Fields and Point Separation

We present calculations of the variance of fluctuations and of the mean of the energy momentum tensor of a massless scalar field for the Minkowski and Casimir vacua as a function of an intrinsic scale defined by a smeared field or by point separation. We point out that contrary to prior claims, the ratio of variance to mean-squared being of the order unity is not necessarily a good criterion for measuring the invalidity of semiclassical gravity. For the Casimir topology we obtain expressions for the variance to mean-squared ratio as a function of the intrinsic scale (defined by a smeared field) compared to the extrinsic scale (defined by the separation of the plates, or the periodicity of space). Our results make it possible to identify the spatial extent where negative energy density prevails which could be useful for studying quantum field effects in worm holes and baby universe, and for examining the design feasibility of real-life `time-machines'. For the Minkowski vacuum we find that the ratio of the variance to the mean-squared, calculated from the coincidence limit, is identical to the value of the Casimir case at the same limit for spatial point separation while identical to the value of a hot flat space result with a temporal point-separation. We analyze the origin of divergences in the fluctuations of the energy density and discuss choices in formulating a procedure for their removal, thus raising new questions into the uniqueness and even the very meaning of regularization of the energy momentum tensor for quantum fields in curved or even flat spacetimes when spacetime is viewed as having an extended structure.Comment: 41 pages, 2 figure

Stochastic semiclassical fluctuations in Minkowski spacetime

The semiclassical Einstein-Langevin equations which describe the dynamics of stochastic perturbations of the metric induced by quantum stress-energy fluctuations of matter fields in a given state are considered on the background of the ground state of semiclassical gravity, namely, Minkowski spacetime and a scalar field in its vacuum state. The relevant equations are explicitly derived for massless and massive fields arbitrarily coupled to the curvature. In doing so, some semiclassical results, such as the expectation value of the stress-energy tensor to linear order in the metric perturbations and particle creation effects, are obtained. We then solve the equations and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. In the conformal field case, explicit results are obtained. These results hint that gravitational fluctuations in stochastic semiclassical gravity have a ``non-perturbative'' behavior in some characteristic correlation lengths.Comment: 28 pages, RevTeX, no figure

Critical phenomena of thick branes in warped spacetimes

We have investigated the effects of a generic bulk first-order phase transition on thick Minkowski branes in warped geometries. As occurs in Euclidean space, when the system is brought near the phase transition an interface separating two ordered phases splits into two interfaces with a disordered phase in between. A remarkable and distinctive feature is that the critical temperature of the phase transition is lowered due to pure geometrical effects. We have studied a variety of critical exponents and the evolution of the transverse-traceless sector of the metric fluctuations.Comment: revtex4, 4 pages, 4 figures, some comments added, typos corrected, published in PR

Anisotropic brane cosmologies with exponential potentials

We study Bianchi I type brane cosmologies with scalar matter self-interacting through combinations of exponential potentials. Such models correspond in some cases to inflationary universes. We discuss the conditions for accelerated expansion to occur, and pay particular attention to the influence of extra dimensions and anisotropy. Our results show that the associated effects evolve in such a way that they become negligible in the late time limit, those related to the anisotropy disappearing earlier. This study focuses mainly on single field models, but we also consider a generalization yielding models with multiple non-interacting fields and examine its features briefly. We conclude that in the brane scenario, as happens in general relativity, an increase in the number of fields assists inflation.Comment: 11 pages, 1 figur

Galaxy number counts- IV. surveying the Herschel deep field in the near-infrared

(abridged) We present results from two new near-infrared imaging surveys. One covers 47.2 arcmin^2 to K(3\sigma)<20 whilst a second, deeper survey covers a sub-area of 1.8 arcmin^2 to K(3\sigma)<22.75. Over the entire area we have extremely deep UBRI photometry. Our K- counts are consistent with the predictions of non-evolving models with 0 < q0 <0.5. The K-selected (B-K) galaxy colour distributions move sharply bluewards fainter than K~20 and at at brighter magnitudes (K<20) our observed colour distributions indicate a deficiency of red, early-type galaxies at z~1 in comparison with passively evolving models. This implies either a pure luminosity evolution (PLE) model with a low level of continuing star-formation following an an initial burst, or dynamical merging. At fainter magnitudes, the continuing bluewards trend observed in (B-K) can be explained purely in terms of passively evolving PLE models. Our observed numbers of (I-K)>4 galaxies at K<20 exhibit the same deficiency, suggesting that at least part of the larger deficit observed in (B-K) at K<20 may be due to star-formation rather than dynamical merging. Finally, as we and others have noted, the number-redshift distribution at 18<K<19 of recent, deep K- selected redshift surveys is well fitted by non-evolving models; passively evolving models with a Salpeter or Scalo initial mass functions overpredict the numbers of galaxies with z>1. Dynamical merging is one possible solution to reduce the numbers of these galaxies but a dwarf-dominated IMF for early-type galaxies could offer an alternative explanation; we show that this model reproduces both the optical-infrared colour distributions and the K- band galaxy counts.Comment: 15 pages, 9 figures, revised version, requires astrobib.sty, mn-abs.sty, submitted to MNRA

Stochastic semiclassical cosmological models

We consider the classical stochastic fluctuations of spacetime geometry induced by quantum fluctuations of massless non-conformal matter fields in the Early Universe. To this end, we supplement the stress-energy tensor of these fields with a stochastic part, which is computed along the lines of the Feynman-Vernon and Schwinger-Keldysh techniques; the Einstein equation is therefore upgraded to a so called Einstein-Langevin equation. We consider in some detail the conformal fluctuations of flat spacetime and the fluctuations of the scale factor in a simple cosmological modelintroduced by Hartle, which consists of a spatially flat isotropic cosmology driven by radiation and dust.Comment: 29 pages, no figures, ReVTeX fil

Wrapped fivebranes and N=2 super Yang-Mills theory

We construct D=10 supergravity solutions corresponding to type IIB fivebranes wrapping a two-sphere in a Calabi-Yau two-fold. These are related in the IR to the large N limit of pure N=2 SU(N) super Yang-Mills theory. We show that the singularities in the IR correspond to the wrapped branes being distributed on a ring. We analyse the dynamics of a probe fivebrane and show that it incorporates the full perturbative structure of the gauge theory. For a class of solutions the two-dimensional moduli space is non-singular and we match the result for the corresponding slice of the Coulomb branch of the gauge theory.Comment: 24 Latex pages, two figures;v2 typos corrected, references adde