Partial summation of the nonlocal expansion for the gravitational effective action in 4 dimensions

The vacuum action for the gravitational field admits a known expansion in powers of the Ricci tensor with nonlocal operator coefficients (form factors). We show that going over to a different basis of curvature invariants makes possible a partial summation of this expansion. Only the form factors of the Weyl-tensor invariants need be calculated. The full action is then uniquely recovered to all orders from the knowledge of the trace anomaly. We present an explicit expression for the partially summed action, and point out simplifications resulting in the vertex functions. An application to the effect of the vacuum gravitational waves is discussed.Comment: 12 pages, LaTe

Quantum Dirac constraints, Ward identities and path integral in relativistic gauge

Quantum Dirac constraints in generic constrained system are solved by directly calculating in the one-loop approximation the path integral with relativistic gauge fixing procedure. The calculations are based on the reduction algorithms for functional determinants extended to gauge theories. Explicit mechanism of transition from relativistic gauge conditions to unitary gauges, participating in the construction of this solution, is revealed by the method of Ward identities.Comment: 12 pages, LaTe

Effective equations in quantum cosmology

We develop a general framework for effective equations of expectation values in quantum cosmology and pose for them the quantum Cauchy problem with no-boundary and tunneling wavefunctions. Cosmological configuration space is decomposed into two sectors that give qualitatively different contributions to the radiation currents in effective equations. The field-theoretical sector of inhomogeneous modes is treated by the method of Euclidean effective action, while the quantum mechanical sector of the spatially homogeneous inflaton is handled by the technique of manifest quantum reduction to gauge invariant cosmological perturbations. We apply this framework in the model with a big negative non-minimal coupling, which incorporates a recently proposed low energy (GUT scale) mechanism of the quantum origin of the inflationary Universe and study the effects of the quantum inflaton mode.Comment: 33 pages, LaTeX2

Open inflation from quantum cosmology with a strong nonminimal coupling

We propose the mechanism of quantum creation of the open Universe in the observable range of values of $\Omega$. This mechanism is based on the no-boundary quantum state with the Hawking-Turok instanton applied to the model with a strong nonminimal coupling of the inflaton field. We develop the slow roll perturbation expansion for the instanton solution and obtain a nontrivial contribution to the classical instanton action. The interplay of this classical contribution with the loop effects due to quantum effective action generates the probability distribution peak with necessary parameters of the inflation stage without invoking any anthropic considerations. In contrast with a similar mechanism for closed models, existing only for the tunneling quantum state of the Universe, the observationally justified open inflation originates from the no-boundary cosmological wavefunction.Comment: 28 pages, LaTe

Nonlocal action for long-distance modifications of gravity theory

We construct the covariant nonlocal action for recently suggested long-distance modifications of gravity theory motivated by the cosmological constant and cosmological acceleration problems. This construction is based on the special nonlocal form of the Einstein-Hilbert action explicitly revealing the fact that this action within the covariant curvature expansion begins with curvature-squared terms. Nonlocal form factors in the action of both quantum and brane-induced nature are briefly discussed. In particular, it is emphasized that for certain class of quantum initial value problems nonlocal nature of the Euclidean action does not contradict the causality of effective equations of motion.Comment: 13 pages, LaTeX, final version to appear in Phys. Lett.

Wheeler-DeWitt equation and Feynman diagrams

We present a systematic expansion of all constraint equations in canonical quantum gravity up to the order of the inverse Planck mass squared. It is demonstrated that this method generates the conventional Feynman diagrammatic technique involving graviton loops and vertices. It also reveals explicitly the back reaction effects of quantized matter and graviton vacuum polarization. This provides an explicit correspondence between the frameworks of canonical and covariant quantum gravity in the semiclassical limit.Comment: 35 pages, LATEX, 1 figur

Effective action and decoherence by fermions in quantum cosmology

We develop the formalism for the one-loop no-boundary state in a cosmological model with fermions. We use it to calculate the reduced density matrix for an inflaton field by tracing out the fermionic degrees of freedom, yielding both the fermionic effective action and the standard decoherence factor. We show that dimensional regularisation of ultraviolet divergences would lead to an inconsistent density matrix. Suppression of these divergences to zero is instead performed through a nonlocal Bogoliubov transformation of the fermionic variables, which leads to a consistent density matrix. The resulting degree of decoherence is less than in the case of bosonic fields.Comment: Latex, 26 page

New nonlocal effective action

We suggest a new method for the calculation of the nonlocal part of the effective action. It is based on resummation of perturbation series for the heat kernel and its functional trace at large values of the proper time parameter. We derive a new, essentially nonperturbative, nonlocal contribution to the effective action in spacetimes with dimensions $d>2$.Comment: 28 pages, latex, no figures, typos are corrected, presentation improve

Heat kernel expansion in the covariant perturbation theory

Working within the framework of the covariant perturbation theory, we obtain the coincidence limit of the heat kernel of an elliptic second order differential operator that is applicable to a large class of quantum field theories. The basis of tensor invariants of the curvatures of a gravity and gauge field background, to the second order, is derived, and the form factors acting on them are obtained in two integral representations. The results are verified by the functional trace operation, by the short proper time (Schwinger-DeWitt) expansions, as well as by the computation of the Green function for the two-dimensional scalar field model.Comment: LaTeX, 33 page

Non-minimal coupling, boundary terms and renormalization of the Einstein-Hilbert action

A consistent variational procedure applied to the gravitational action requires according to Gibbons and Hawking a certain balance between the volume and boundary parts of the action. We consider the problem of preserving this balance in the quantum effective action for the matter non-minimally coupled to metric. It is shown that one has to add a special boundary term to the matter action analogous to the Gibbons-Hawking one. This boundary term modifies the one-loop quantum corrections to give a correct balance for the effective action as well. This means that the boundary UV divergences do not require independent renormalization and are automatically renormalized simultaneously with their volume part. This result is derived for arbitrary non-minimally coupled matter. The example of 2D Maxwell field is considered in much detail. The relevance of the results obtained to the problem of the renormalization of the black hole entropy is discussed.Comment: 14 pages, latex. More discussion added, the case of 2D Maxwell field considered in more detail