Zero modes, gauge fixing, monodromies, ζ\zeta-functions and all that

We discuss various issues associated with the calculation of the reduced functional determinant of a special second order differential operator \boldmath{F}$=-d^2/d\tau^2+\ddot g/g$, $\ddot g\equiv d^2g/d\tau^2$, with a generic function $g(\tau)$, subject to periodic and Dirichlet boundary conditions. These issues include the gauge-fixed path integral representation of this determinant, the monodromy method of its calculation and the combination of the heat kernel and zeta-function technique for the derivation of its period dependence. Motivations for this particular problem, coming from applications in quantum cosmology, are also briefly discussed. They include the problem of microcanonical initial conditions in cosmology driven by a conformal field theory, cosmological constant and cosmic microwave background problems.Comment: 17 pages, to appear in J. Phys. A: Math. Theor. arXiv admin note: substantial text overlap with arXiv:1111.447

Nonperturbative late time asymptotics for heat kernel in gravity theory

Recently proposed nonlocal and nonperturbative late time behavior of the heat kernel is generalized to curved spacetimes. Heat kernel trace asymptotics is dominated by two terms one of which represents a trivial covariantization of the flat-space result and another one is given by the Gibbons-Hawking integral over asymptotically-flat infinity. Nonlocal terms of the effective action generated by this asymptotics might underly long- distance modifications of the Einstein theory motivated by the cosmological constant problem. New mechanisms of the cosmological constant induced by infrared effects of matter and graviton loops are briefly discussed.Comment: 22 pages, LaTeX, final version, to be published in Phys. Rev.

Unified Gauge Models and One-Loop Quantum Cosmology

This paper studies the normalizability criterion for the one-loop wave function of the universe in a de Sitter background, when various unified gauge models are considered. It turns out that, in the absence of interaction between inflaton field and other matter fields, the supersymmetric version of such unified models is preferred. By contrast, the interaction of inflaton and matter fields, jointly with the request of normalizability at one-loop order, picks out non-supersymmetric versions of unified gauge models.Comment: 10 pages, Late

Operator ordering and consistency of the wavefunction of the Universe

We demonstrate in the context of the minisuperspace model consisting of a closed Friedmann-Robertson-Walker universe coupled to a scalar field that Vilenkin's tunneling wavefunction can only be consistently defined for particular choices of operator ordering in the Wheeler-DeWitt equation. The requirement of regularity of the wavefunction has the particular consequence that the probability amplitude, which has been used previously in the literature in discussions of issues such as the prediction of inflation, is likewise ill-defined for certain choices of operator ordering with Vilenkin's boundary condition. By contrast, the Hartle-Hawking no-boundary wavefunction can be consistently defined within these models, independently of operator ordering. The significance of this result is discussed within the context of the debate about the predictions of semiclassical quantum cosmology. In particular, it is argued that inflation cannot be confidently regarded as a "prediction" of the tunneling wavefunction, for reasons similar to those previously invoked in the case of the no-boundary wavefunction. A synthesis of the no-boundary and tunneling approaches is argued for.Comment: 9 pages, epsf, revTeX-3.1, 1 figure. In revised version (v2) a new section etc with additional arguments increases the length of paper by 3 pages of Physical Review; several references added. v3: small typos fixe

Spectral action beyond the weak-field approximation

The spectral action for a non-compact commutative spectral triple is computed covariantly in a gauge perturbation up to order 2 in full generality. In the ultraviolet regime, $p\to\infty$, the action decays as $1/p^4$ in any even dimension.Comment: 17 pages Few misprints correcte

Thermodynamics via Creation from Nothing: Limiting the Cosmological Constant Landscape

The creation of a quantum Universe is described by a {\em density matrix} which yields an ensemble of universes with the cosmological constant limited to a bounded range $\Lambda_{\rm min}\leq \Lambda \leq \Lambda_{\rm max}$. The domain $\Lambda<\Lambda_{\rm min}$ is ruled out by a cosmological bootstrap requirement (the self-consistent back reaction of hot matter). The upper cutoff results from the quantum effects of vacuum energy and the conformal anomaly mediated by a special ghost-avoidance renormalization. The cutoff $\Lambda_{\rm max}$ establishes a new quantum scale -- the accumulation point of an infinite sequence of garland-type instantons. The dependence of the cosmological constant range on particle phenomenology suggests a possible dynamical selection mechanism for the landscape of string vacua.Comment: RevTex, 4 pages, 4 figure