Strongly Coupled Inflaton

We continue to investigate properties of the strongly coupled inflaton in a setup introduced in arXiv:0807.3191 through the AdS/CFT correspondence. These properties are qualitatively different from those in conventional inflationary models. For example, in slow-roll inflation, the inflaton velocity is not determined by the shape of potential; the fine-tuning problem concerns the dual infrared geometry instead of the potential; the non-Gaussianities such as the local form can naturally become large.Comment: 12 pages; v3, minor revision, comments and reference added, JCAP versio

Non-universal critical Casimir force in confined 4^4He near the superfluid transition

We present the results of a one-loop calculation of the effect of a van der Waals type interaction potential $\sim | {\bf x} |^{-d-\sigma}$ on the critical Casimir force and specific heat of confined $^4$He near the superfluid transition. We consider a $^4$He film of thickness $L$. In the region $L \gtrsim \xi$ (correlation length) we find that the van der Waals interaction causes a leading non-universal non-scaling contribution of $O (\xi^2 L^{-d-\sigma})$ to the critical temperature dependence of the Casimir force above $T_\lambda$ that dominates the universal scaling contribution $\sim e^{- L/\xi}$ predicted by earlier theories. For the specific heat we find subleading non-scaling contributions of $O(L^{-1})$ and $O(L^{-d-\sigma})$.Comment: 2 pages, submitted to LT23 Proceedings on June 14, 2002, accepted for publication in Physica B on September 12, 200

Violation of Finite-Size Scaling in Three Dimensions

We reexamine the range of validity of finite-size scaling in the $\phi^4$ lattice model and the $\phi^4$ field theory below four dimensions. We show that general renormalization-group arguments based on the renormalizability of the $\phi^4$ theory do not rule out the possibility of a violation of finite-size scaling due to a finite lattice constant and a finite cutoff. For a confined geometry of linear size $L$ with periodic boundary conditions we analyze the approach towards bulk critical behavior as $L \to \infty$ at fixed $\xi$ for $T > T_c$ where $\xi$ is the bulk correlation length. We show that for this analysis ordinary renormalized perturbation theory is sufficient. On the basis of one-loop results and of exact results in the spherical limit we find that finite-size scaling is violated for both the $\phi^4$ lattice model and the $\phi^4$ field theory in the region $L \gg \xi$. The non-scaling effects in the field theory and in the lattice model differ significantly from each other.Comment: LaTex, 51 page