Remarks on the Formulation of the Cosmological Constant/Dark Energy Problems

Associated with the cosmic acceleration are the old and new cosmological constant problems, recently put into the more general context of the dark energy problem. In broad terms, the old problem is related to an unexpected order of magnitude of this component while the new problem is related to this magnitude being of the same order of the matter energy density during the present epoch of cosmic evolution. Current plans to measure the equation of state or density parameters certainly constitute an important approach; however, as we discuss, this approach is faced with serious feasibility challenges and is limited in the type of conclusive answers it could provide. Therefore, is it really too early to seek actively for new tests and approaches to these problems? In view of the difficulty of this endeavor, we argue in this work that a good place to start is by questioning some of the assumptions underlying the formulation of these problems and finding new ways to put this questioning to the test. First, we calculate how much fine tuning the cosmic coincidence problem represents. Next, we discuss the potential of some cosmological probes such as weak gravitational lensing to identify novel tests to probe dark energy questions and assumptions and provide an example of consistency tests. Then, motivated by some theorems in General Relativity, we discuss if the full identification of the cosmological constant with vacuum energy is unquestionable. We discuss some implications of the simplest solution for the principles of General Relativity. Also, we point out the relevance of experiments at the interface of astrophysics and quantum field theory, such as the Casimir effect in gravitational and cosmological contexts. We conclude that challenging some of the assumptions underlying the cosmological constant problems and putting them to the test may prove useful and necessary to make progress on these questions.     

Nonlocal properties of entangled two-photon generalized binomial states in two separate cavities

Entangled two-photon generalized binomial states of the electromagnetic field in two separate cavities are considered. The nonlocal properties of this entangled field state are analyzed by studying the electric field correlations between the two cavities. A Bell’s inequality violation is obtained using an appropriate dichotomic cavity operator that is, in principle, measurable. The text was submitted by the authors in English.     

On the BKP Hierarchy: Additional Symmetries,Fay Identity and Adler–Shiota–van Moerbeke Formula

We give an alternative proof of the Adler–Shiota–van Moerbeke formula for the BKP hierarchy. The proof is based on a simple expression for the generator of additional symmetries and the Fay identity of the BKP hierarchy.      

Particle Propagation in Cosmological Backgrounds

We analyse the quantum propagation of interacting particles in cosmological backgrounds. The model we use consists of a doublet of massive scalar fields propagating in an expanding universe filled with massless radiation. The masses are much larger than the Hubble expansion rate, so that the number of massive particles is preserved and the fields adequately described within the adiabatic approximation. We focus on the dissipative effects related to the expansion rate by computing the imaginary part of the self-energy. In the quasi static approximation, we recover the expected result that instantaneous decay rate is governed by the local temperature. We then analyse the long time behavior of the propagator to unravel the secular effects induced by the self-energy. We show that these effects can be expressed in terms of integrals of local quantities. Applications to the trans-Planckian question are briefly discussed.     

Marginal Distributions of Wigner Function in a Mesoscopic L-C Circuit at Finite Temperature and Thermal Wigner Operator

Wigner function in phase space has its physical meaning as marginal probability distribution in coordinate space and momentum space respectively, here we endow the Wigner function with a new physical meaning, i.e., its marginal distributions’ statistical average for q ²/(2C) and p ²/(2L) are the energy stored in capacity and in inductance of a mesoscopic L-C circuit at finite temperature, respectively. PACS numbers: 03.65.-w, 73.21.-b     

Symmetries,Conservation Laws and Multipliers via Partial Lagrangians and Noether’s Theorem for Classically Non-Variational Problems

We show how one can construct conservation laws of equations that are not variational but are Euler–Lagrange in part using Noether-type symmetries associated with partial Lagrangians. These Noether-type symmetries are, usually, not symmetries of the system. The resultant construction of the conservation law resorts to a formula equivalent to Noether’s theorem. A variety of examples are given.     

Improvement of a low pH antigen-antibody dissociation procedure for ELISA measurement of circulating anti-Aβ antibodies

Background  

Prior work from our group found that acid dissociation (pH 2.5 incubation) of serum from APP transgenic mice vaccinated against Aβ increased the apparent anti-Aβ titers, suggesting antibody masking by antigen in the ELISA assay. Subsequently, we found that pH 2.5 incubation of serum from unvaccinated non-transgenic mice showed antibody binding to Aβ1–42, but no increase when other proteins, including shorter Aβ peptides, coated the ELISA plate. To investigate further the effects of low pH incubation on apparent anti-Aβ1–42 signals, we examined normal sera from nonTg unvaccinated mice, nonTg mice vaccinated with Aβ peptide (to produce authentic anti-Aβ antibodies) or a monoclonal antibody against Aβ (6E10) using competitive-inhibition ELISA and Aβ epitope mapping assays. In addition, we examined use of a less stringent low pH procedure at pH 3.5, to ascertain if it had the same effects as the pH 2.5 procedure.     

Pigment epithelium-derived factor protects retinal ganglion cells

Background  

Retinal ganglion cells (RGCs) are responsible for the transmission of visual signals to the brain. Progressive death of RGCs occurs in glaucoma and several other retinal diseases, which can lead to visual impairment and blindness. Pigment epithelium-derived factor (PEDF) is a potent antiangiogenic, neurotrophic and neuroprotective protein that can protect neurons from a variety of pathologic insults. We tested the effects of PEDF on the survival of cultured adult rat RGCs in the presence of glaucoma-like insults, including cytotoxicity induced by glutamate or withdrawal of trophic factors.