In a 5D open FRW model, negative curvature sustains tracker-like radion evolution that enables dynamical compactification via Casimir stabilization before 4D inflation dilutes curvature remnants.
Kirsten,Basic zeta functions and some applications in physics,MSRI Publ.57(2010) 101–143, [1005.2389]
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abstract
It is the aim of these lectures to introduce some basic zeta functions and their uses in the areas of the Casimir effect and Bose-Einstein condensation. A brief introduction into these areas is given in the respective sections. We will consider exclusively spectral zeta functions, that is zeta functions arising from the eigenvalue spectrum of suitable differential operators. There is a set of technical tools that are at the very heart of understanding analytical properties of essentially every spectral zeta function. Those tools are introduced using the well-studied examples of the Hurwitz, Epstein and Barnes zeta function. It is explained how these different examples of zeta functions can all be thought of as being generated by the same mechanism, namely they all result from eigenvalues of suitable (partial) differential operators. It is this relation with partial differential operators that provides the motivation for analyzing the zeta functions considered in these lectures. Motivations come for example from the questions "Can one hear the shape of a drum?" and "What does the Casimir effect know about a boundary?". Finally "What does a Bose gas know about its container?"
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Analytical expressions for quantum corrections to the Casimir effect and topological mass are derived for perturbative rough plates using WKB approximation and zeta-function regularization.
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Curvature-Assisted Dynamical Compactification in a Pre-Inflationary Higher-Dimensional Universe
In a 5D open FRW model, negative curvature sustains tracker-like radion evolution that enables dynamical compactification via Casimir stabilization before 4D inflation dilutes curvature remnants.
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One-Loop Quantum Corrections to the Casimir Effect for Rough Plates in the Low-Temperature Regime
Analytical expressions for quantum corrections to the Casimir effect and topological mass are derived for perturbative rough plates using WKB approximation and zeta-function regularization.