Stability in Generalized Modified Gravity

The stability issue of a large class of modified gravitational models is discussed with particular emphasis to de Sitter solutions. Three approaches are briefly presented and the generalization to more general cases is mentioned.Comment: 6 pages, talk delivered at DSU08 Cair

Zeta-function regularization, the multiplicative anomaly and the Wodzicki residue

The multiplicative anomaly associated with the zeta-function regularized determinant is computed for the Laplace-type operators L_1=-\lap+V_1 and L_2=-\lap+V_2, with $V_1$, $V_2$ constant, in a D-dimensional compact smooth manifold $M_D$, making use of several results due to Wodzicki and by direct calculations in some explicit examples. It is found that the multiplicative anomaly is vanishing for $D$ odd and for D=2. An application to the one-loop effective potential of the O(2) self-interacting scalar model is outlined.Comment: LaTeX, 17 pages, 3 figures. Small corrections, two new formulas, and an addition to the references. To appear in Commun. Math. Phy

HIGH TEMPERATURE EXPANSION OF STRING FREE ENERGY IN HYPERBOLIC SPACE

The high temperature behaviour of the open bosonic string free energy in the space $S^1 \otimes H^N$ with vanishingly small curvature is investigated. The leading term of the high temperature expansion of the one-loop free energy, near the Hagedorn instability, is obtained. The problem of infrared regularization of thermodynamical quantities is pointed out. For minimally coupling quantum fields related to the normal modes of strings, the results are similar to the ones valid for Rindler space. In the lower mass string states regime a connection with the quantum corrections to the black hole entropy is outlined.Comment: 7 pages, latex file, no figures