Nonlinear Grassmann Sigma Models in Any Dimension and An Infinite Number of Conserved Currents

We first consider nonlinear Grassmann sigma models in any dimension and next construct their submodels. For these models we construct an infinite number of nontrivial conserved currents. Our result is independent of time-space dimensions and, therfore, is a full generalization of that of authors (Alvarez, Ferreira and Guillen). Our result also suggests that our method may be applied to other nonlinear sigma models such as chiral models, $G/H$ sigma models in any dimension.Comment: 11 pages, AMSLaTe

Possible time-variability of the fine-structure constant expected from the accelerating universe

We present a theoretical calculation on the time-variability of the fine-structure constant to fit the result of the recent precise analysis of the measurement of the QSO absorption lines. We find the parameters and initial values of the scalar-tensor theory to be determined much more accurately than fitting the accelerating universe itself, but leading not to easy detections of the effect on the equation of state of the dark energy in the earlier epochs.Comment: 9 pages, 9 figures. Revised interpretation of the theoretical fit; more recent reference

Choosing a conformal frame in scalar-tensor theories of gravity with a cosmological constant

Cosmological solutions of the Brans-Dicke theory with an added cosmological constant are investigated with an emphasis to select a conformal frame in order to implement the scenario of a decaying cosmological constant, featuring an ever growing scalar field. We focus particularly on Jordan frame, the original frame with the nonminimal coupling, and conformally transformed Einstein frame without it. For the asymptotoic attractor solutions as well as the "hesitation behavior," we find that none of these conformal frames can be accepted as the basis of analyzing primordial nucleosynthesis. As a remedy, we propose to modify the prototype BD theory, by introducing a scale-invariant scalar-matter coupling, thus making Einstein frame acceptable. The invariacne is broken as a quantum anomaly effect due to the non-gravitational interactions, entailing naturally the fifth force, characterized by a finite force-range and WEP violation. A tentative estimate shows that the theoretical prediction is roughly consistent with the observational upper bounds. Further efforts to improve the experimental accuracy is strongly encouraged.Comment: Latex 29 pages, including 9 figure