Cosmological Models and Renormalization Group Flow

We study cosmological solutions of Einstein gravity with a positive cosmological constant in diverse dimensions. These include big-bang models that re-collapse, big-bang models that approach de Sitter acceleration at late times, and bounce models that are both past and future asymptotically de Sitter. The re-collapsing and the bounce geometries are all tall in the sense that entire spatial slices become visible to a comoving observer before the end of conformal time, while the accelerating big-bang geometries can be either short or tall. We consider the interpretation of these cosmological solutions as renormalization group flows in a dual field theory and give a geometric interpretation of the associated c-function as the area of the apparent cosmological horizon in Planck units. The covariant entropy bound requires quantum effects to modify the early causal structure of some of our big-bang solutions.Comment: 26 pages, 11 figures, v2: improved discussion of entropy bounds, references added, v3: minor changes, reference adde

Duality for symmetric second rank tensors. II. The linearized gravitational field

The construction of dual theories for linearized gravity in four dimensions is considered. Our approach is based on the parent Lagrangian method previously developed for the massive spin-two case, but now considered for the zero mass case. This leads to a dual theory described in terms of a rank two symmetric tensor, analogous to the usual gravitational field, and an auxiliary antisymmetric field. This theory has an enlarged gauge symmetry, but with an adequate partial gauge fixing it can be reduced to a gauge symmetry similar to the standard one of linearized gravitation. We present examples illustrating the general procedure and the physical interpretation of the dual fields. The zero mass case of the massive theory dual to the massive spin-two theory is also examined, but we show that it only contains a spin-zero excitation.Comment: 20 pages, no figure

Oxidised cosmic acceleration

We give detailed proofs of several new no-go theorems for constructing flat four-dimensional accelerating universes from warped dimensional reduction. These new theorems improve upon previous ones by weakening the energy conditions, by including time-dependent compactifications, and by treating accelerated expansion that is not precisely de Sitter. We show that de Sitter expansion violates the higher-dimensional null energy condition (NEC) if the compactification manifold M is one-dimensional, if its intrinsic Ricci scalar R vanishes everywhere, or if R and the warp function satisfy a simple limit condition. If expansion is not de Sitter, we establish threshold equation-of-state parameters w below which accelerated expansion must be transient. Below the threshold w there are bounds on the number of e-foldings of expansion. If M is one-dimensional or R everywhere vanishing, exceeding the bound implies the NEC is violated. If R does not vanish everywhere on M, exceeding the bound implies the strong energy condition (SEC) is violated. Observationally, the w thresholds indicate that experiments with finite resolution in w can cleanly discriminate between different models which satisfy or violate the relevant energy conditions.Comment: v2: corrections, references adde

T-Duality and Penrose limits of spatially homogeneous and inhomogeneous cosmologies

Penrose limits of inhomogeneous cosmologies admitting two abelian Killing vectors and their abelian T-duals are found in general. The wave profiles of the resulting plane waves are given for particular solutions. Abelian and non-abelian T-duality are used as solution generating techniques. Furthermore, it is found that unlike in the case of abelian T-duality, non-abelian T-duality and taking the Penrose limit are not commutative procedures.Comment: 16 pages, 4 figures. Discussion on non-abelian T-duality expande

On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence principle (Part One)

In October 1924, the Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Van Vleck combined advanced techniques of classical mechanics with Bohr's correspondence principle and Einstein's quantum theory of radiation to find quantum analogues of classical expressions for the emission, absorption, and dispersion of radiation. For modern readers Van Vleck's paper is much easier to follow than the famous paper by Kramers and Heisenberg on dispersion theory, which covers similar terrain and is widely credited to have led directly to Heisenberg's "Umdeutung" paper. This makes Van Vleck's paper extremely valuable for the reconstruction of the genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did not take the next step and develop matrix mechanics himself.Comment: 82 page

A robust spectral method for solving Heston’s model

In this paper, we consider the Heston’s volatility model (Heston in Rev. Financ. Stud. 6: 327–343, 1993]. We simulate this model using a combination of the spectral collocation method and the Laplace transforms method. To approximate the two dimensional PDE, we construct a grid which is the tensor product of the two grids, each of which is based on the Chebyshev points in the two spacial directions. The resulting semi-discrete problem is then solved by applying the Laplace transform method based on Talbot’s idea of deformation of the contour integral (Talbot in IMA J. Appl. Math. 23(1): 97–120, 1979)

Hidden Voices of Black Men

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66982/2/10.1177_002193479402500102.pd

Hepatitis B care cascade among people with HIV/HBV coinfection in the North American AIDS Cohort Collaboration on Research and Design, 2012-2016

A care cascade is a critical tool for evaluating delivery of care for chronic infections across sequential stages, starting with diagnosis and ending with viral suppression. However, there have been few data describing the hepatitis B virus (HBV) care cascade among people living with HIV infection who have HBV coinfection. We conducted a cross-sectional study among people living with HIV and HBV coinfection receiving care between January 1, 2012 and December 31, 2016 within 13 United States and Canadian clinical cohorts contributing data to the North American AIDS Cohort Collaboration on Research and Design (NA-ACCORD). We evaluated each of the steps in this cascade, including: 1) laboratory-confirmed HBV infection, 2) tenofovir-based or entecavir-based HBV therapy prescribed, 3) HBV DNA measured during treatment, and 4) viral suppression achieved via undetectable HBV DNA. Among 3,953 persons with laboratory-confirmed HBV (median age, 50 years; 6.5% female; 43.8% were Black; 7.1% were Hispanic), 3,592 (90.9%; 95% confidence interval, 90.0-91.8%) were prescribed tenofovir-based antiretroviral therapy or entecavir along with their antiretroviral therapy regimen, 2,281 (57.7%; 95% confidence interval, 56.2-59.2%) had HBV DNA measured while on therapy, and 1,624 (41.1%; 95% confidence interval, 39.5-42.6) achieved an undetectable HBV DNA during HBV treatment. Our study identified significant gaps in measurement of HBV DNA and suppression of HBV viremia among people living with HIV and HBV coinfection in the United States and Canada. Periodic evaluation of the HBV care cascade among persons with HIV/HBV will be critical to monitoring success in completion of each step