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Guido Cognola

Publications and source records attributed to Guido Cognola.

At least 37 records · Page 2Linked to original sources
arXiv2006

Heat-kernel expansion on non compact domains and a generalised zeta-function regularisation procedure

Heat-kernel expansion and zeta function regularisation are discussed for Laplace type operators with discrete spectrum in non compact domains. Since a general theory is lacking, the heat-kernel expansion is investigated by means of several examples. It is pointed out that for a class of exponential (analytic) interactions, generically the non-compactness of the domain gives rise to logarithmic terms in the heat-kernel expansion. Then, a meromorphic continuation of the associated zeta function is investigated. A simple model is considered, for which the analytic continuation of the zeta function is not regular at the origin, displaying a pole of higher order. For a physically meaningful evaluation of the related functional determinant, a generalised zeta function regularisation procedure is proposed.

hep-th↗
arXiv2006

Dark energy in modified Gauss-Bonnet gravity: late-time acceleration and the hierarchy problem

Dark energy cosmology is considered in a modified Gauss-Bonnet (GB) model of gravity where an arbitrary function of the GB invariant, $f(G)$, is added to the General Relativity action. We show that such theory is endowed with a quite rich cosmological structure: it may naturally lead to an effective cosmological constant, quintessence or phantom cosmic acceleration, with a possible transition from deceleration to acceleration. It is demonstrated in the paper that this theory is perfectly viable, since it is compliant with Solar System constraints. Specific properties of $f(G)$ gravity in a de Sitter universe, such as dS and SdS solutions, their entropy and its explicit one-loop quantization are studied. The issue of a possible solution of the hierarchy problem in modified gravities is addressed too.

hep-th↗
arXiv2005

One-loop f(R) Gravitational Modified Models

The one-loop quantisation of a general class of modified gravity models around a classical de Sitter background is presented. Application to the stability of the models is addressed.

hep-th↗
arXiv2005

One-loop f(R) gravity in de Sitter universe

Motivated by the dark energy issue, the one-loop quantization approach for a family of relativistic cosmological theories is discussed in some detail. Specifically, general $f(R)$ gravity at the one-loop level in a de Sitter universe is investigated, extending a similar program developed for the case of pure Einstein gravity. Using generalized zeta regularization, the one-loop effective action is explicitly obtained off-shell, what allows to study in detail the possibility of (de)stabilization of the de Sitter background by quantum effects. The one-loop effective action maybe useful also for the study of constant curvature black hole nucleation rate and it provides the plausible way of resolving the cosmological constant problem.

hep-th↗
arXiv2004

Late-time phantom universe in ${\bf SO(1,1)}$ dark energy model with exponential potential

We discuss the late-time property of universe and phantom field in the SO(1,1) dark energy model for the potential $V=V_0e^{-βΦ^α}$ with $α$ and $β$ two positive constants. We assume in advance some conditions satisfied by the late-time field to simplify equations, which are confirmed to be correct from the eventual results. For $α<2$, the filed falls exponentially off and the phantom equation of state rapidly approaches -1. When $α=2$, the kinetic energy $ρ_k$ and the coupling energy $ρ_c$ become comparable but there is always $ρ_k<-ρ_c$ so that the phantom property of field proceeds to hold. The analysis on the perturbation to the late-time field $Φ$ illustrates the square effective mass of the perturbation field is always positive and thus the phantom is stable. The universe considered currently may evade the future sudden singularity and will evolve to de Sitter expansion phase.

gr-qc↗
arXiv2004

One-loop effective potential from higher-dimensional AdS black holes

We study the quantum effects in a brane-world model in which a positive constant curvature brane universe is embedded in a higher-dimensional bulk AdS black hole, instead of the usual portion of the AdS$_5$. By using zeta regularisation, in the large mass regime, we explicitly calculate the one-loop effective potential due to the bulk quantum fields and show that it leads to a non-vanishing cosmological constant, which can definitely acquire a positive value.

hep-th↗
arXiv2004

Generalised zeta-function regularization for scalar one-loop effective action

The one-loop effective action for a scalar field defined in the ultrastatic space-time where non standard logarithmic terms in the asymptotic heat-kernel expansion are present, is investigated by a generalisation of zeta-function regularisation. It is shown that additional divergences may appear at one-loop level. The one-loop renormalisability of the model is discussed and the one-loop renormalisation group equations are derived.

hep-th↗
arXiv2003

Effective action for scalar fields and generalised zeta-function regularisation

Motivated by the study of quantum fields in a Friedman-Robertson-Walker (FRW) spacetime, the one-loop effective action for a scalar field defined in the ultrastatic manifold $R\times H^3/Γ$, $H^3/Γ$ being the finite volume, non-compact, hyperbolic spatial section, is investigated by a generalisation of zeta-function regularisation. It is shown that additional divergences may appear at one-loop level. The one-loop renormalisability of the model is discussed and making use of a generalisation of zeta-function regularisation, the one-loop renormalisation group equations are derived.

hep-th↗
arXiv2002

Fluctuations of quantum fields via zeta function regularization

Explicit expressions for the expectation values and the variances of some observables, which are bilinear quantities in the quantum fields on a D-dimensional manifold, are derived making use of zeta function regularization. It is found that the variance, related to the second functional variation of the effective action, requires a further regularization and that the relative regularized variance turns out to be 2/N, where N is the number of the fields, thus being independent on the dimension D. Some illustrating examples are worked through.

hep-th↗
arXiv2001

Casimir Energies for Spherically Symmetric Cavities

A general calculation of Casimir energies --in an arbitrary number of dimensions-- for massless quantized fields in spherically symmetric cavities is carried out. All the most common situations, including scalar and spinor fields, the electromagnetic field, and various boundary conditions are treated with care. The final results are given as analytical (closed) expressions in terms of Barnes zeta functions. A direct, straightforward numerical evaluation of the formulas is then performed, which yields highly accurate numbers of, in principle, arbitrarily good precision.

hep-th↗
arXiv2001

On the Dimensional Reduction Procedure

The issue related to the so-called dimensional reduction procedure is revisited within the Euclidean formalism. First, it is shown that for symmetric spaces, the local exact heat-kernel density is equal to the reduced one, once the harmonic sum has been succesfully performed. In the general case, due to the impossibility to deal with exact results, the short time heat-kernel asymptotics is considered. It is found that the exact heat-kernel and the dimensionally reduced one coincide up to two non trivial leading contributions in the short time expansion. Implications of these results with regard to dimensional-reduction anomaly are discussed.

hep-th↗
arXiv1999

Thermodynamics of Kerr-Newman-AdS Black Holes and Conformal Field Theories

We study the thermodynamics of four-dimensional Kerr-Newman-AdS black holes both in the canonical and the grand-canonical ensemble. The stability conditions are investigated, and the complete phase diagrams are obtained, which include the Hawking-Page phase transition in the grand-canonical ensemble. In the canonical case, one has a first order transition between small and large black holes, which disappears for sufficiently large electric charge or angular momentum. This disappearance corresponds to a critical point in the phase diagram. Via the AdS/CFT conjecture, the obtained phase structure is also relevant for the corresponding conformal field theory living in a rotating Einstein universe, in the presence of a global background U(1) current. An interesting limit arises when the black holes preserve some supersymmetry. These BPS black holes correspond to highly degenerate zero temperature states in the dual CFT, which lives in an Einstein universe rotating with the speed of light.

hep-th↗
arXiv1999

Dirac Functional Determinants in Terms of the Eta Invariant and the Noncommutative Residue

The zeta and eta-functions associated with massless and massive Dirac operators, in a D-dimensional (D odd or even) manifold without boundary, are rigorously constructed. Several mathematical subtleties involved in this process are stressed, as the intrisic ambiguity present in the definition of the associated fermion functional determinant in the massless case and, also, the unavoidable presence (in some situations) of a multiplicative anomaly, that can be conveniently expressed in terms of the noncommutative residue. The ambiguity is here seen to disappear in the massive case, giving rise to a phase of the Dirac determinant - that agrees with very recent calculations appeared in the mathematical literature - and to a multiplicative anomaly - also in agreement with other calculations, in the coinciding situations. After explicit, nontrivial resummation of the mass series expansions involving zeta and eta functions, the results are expressed in terms of quite simple formulas.

hep-th↗
arXiv1999

Consistent, covariant and multiplicative anomalies

It is shown that the multiplicative anomaly in the vector-axial-vector model, which apparently has nothing to do with the breaking of classical current symmetries, nevertheless is strictly related to the well known consistent and covariant anomalies.

hep-th↗
arXiv1998

Applications in physics of the multiplicative anomaly formula involving some basic differential operators

In the framework leading to the multiplicative anomaly formula ---which is here proven to be valid even in cases of known spectrum but non-compact manifold (very important in Physics)--- zeta-function regularisation techniques are shown to be extremely efficient. Dirac like operators and harmonic oscillators are investigated in detail, in any number of space dimensions. They yield a non-zero anomaly which, on the other hand, can always be expressed by means of a simple analytical formula. These results are used in several physical examples, where the determinant of a product of differential operators is not equal to the product of the corresponding functional determinants. The simplicity of the Hamiltonian operators chosen is aimed at showing that such situation may be quite widespread in mathematical physics. However, the consequences of the existence of the determinant anomaly have often been overlooked.

hep-th↗
arXiv1998

Back reaction of vacuum and the renormalization group flow from the conformal fixed point

We consider the GUT-like model with two scalar fields which has infinitesimal deviation from the conformal invariant fixed point at high energy region. In this case the dominating quantum effect is the conformal trace anomaly and the interaction between the anomaly-generated propagating conformal factor of the metric and the usual dimensional scalar field. This interaction leads to the renormalization group flow from the conformal point. In the supersymmetric conformal invariant model such an effect produces a very weak violation of sypersymmetry at lower energies.

hep-th↗