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We make a conceptual overview of a particular approach to the initial-value problem in canonical gauge theories. We stress how the first-class phase-space constraints may be relaxed if we interpret them as fixing the values of new degrees of freedom. This idea goes back to Fock and Stueckelberg, leading to restrictions of the gauge symmetry of a theory, and it corresponds, in certain cases, to promoting constants of Nature to physical fields. Recently, different versions of this formulation have gained considerable attention in the literature, with several independent iterations, particularly in classical and quantum descriptions of gravity, cosmology, and electromagnetism. In particular, in the case of canonical quantum gravity, the Fock--Stueckelberg approach is relevant to the so-called problem of time. Our overview recalls and generalizes the work of Fock and Stueckelberg and its physical interpretation with the aim of conceptually unifying the different iterations of the idea that appear in the literature and of motivating further research., Comment: v2: conceptual clarifications and brief appendix added; improvements to the text; results unchanged; references updated

We investigate the impact of conformal transformations on the physical properties of solution trajectories in nonmetricity gravity. Specifically, we explore the phase-space and reconstruct the cosmological history of a spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker universe within scalar-nonmetricity theory in both the Jordan and Einstein frames. A detailed analysis is conducted for three different connections defined in both the coincident and non-coincident gauges. Our findings reveal the existence of a unique one-to-one correspondence for equilibrium points in the two frames. Furthermore, we demonstrate that solutions describing accelerated universes remain invariant under the transformation that relates these conformally equivalent theories., Comment: 35 pages, 5 figures, Latex2e source file

We analyze the consequences of different evolutions of the Hubble parameter on the spectrum of scalar inflationary perturbations. The analysis is restricted to inflationary phases described by a transient evolution, when uncommon features arise in the inflationary spectra that may lead to an amplitude enhancement. We then discuss how the spectrum is, respectively, amplified or blue-tilted in the presence or absence of a growing solution of the Mukhanov-Sasaki equation. The cases of general relativity with a minimally coupled inflaton and that of induced gravity are considered explicitly. Finally, some remarks on constant roll inflation are discussed., Comment: references updated, conceptual clarifications added. Matches published version

We discuss applications of perturbative quantum gravity in the theory of very early quantum Universe and quantum cosmology. Consistency of the theoretical formalism for quantum effects of matter and correspondence with observational status of modern precision cosmology impose stringent bounds on and establish strong links with high energy particle phenomenology. Within this line of reasoning we study various aspects of one-loop approximation for the cosmological wave function, review Higgs inflation model intertwining the physics of electroweak sector of the Standard Model with the characteristics of the observable cosmic microwave background and, finally, consider the problem of quantum initial conditions for inflationary Universe. We formulate a cosmological quantum state in the form of the microcanonical density matrix -- a universal equipartition of eigenstates of the Wheeler-DeWitt equations. We demonstrate elimination of the inalienable infrared catastrophe of vanishing cosmological constant for the no-boundary quantum state of the Universe and derive initial conditions for inflation in the form of a special garland-type cosmological instanton -- the saddle point of quantum gravity path integral. Applied to the cosmological model of the Universe with a hidden sector of numerous conformally invariant higher spin fields, this setup suggests a solution to the problem of hierarchy between the Planck and the inflation energy scales and, thus, admits applicability of perturbative semiclassical expansion methods., Comment: Comments about hill-top inflation and special case of closed Universe along with several new references are added. arXiv admin note: text overlap with arXiv:0910.1041

In the context of canonical quantum gravity, we consider the effects of a non-standard expression for the gravitational wave function on the evolution of inflationary perturbations. Such an expression and its effects may be generated by a sudden variation in the (nearly constant) inflaton potential. The resulting primordial spectra, up to the leading order, are affected in the short and in the long wavelength regime, where an oscillatory behavior with a non-negligible amplitude is superimposed on the standard semiclassical result. Moreover, a novel, non-perturbative, approach is used to study the evolution. Finally, a simplified application is fully illustrated and commented., Comment: references updated, conceptual clarifications added. Matches published version

We consider a procedure of elimination of cosmological singularities similar to that suggested in the recent paper by Simpson and Visser for the construction of regular black holes. It is shown that by imposing a non-singular cosmological evolution with a bounce in a flat Friedmann universe filled with a minimally coupled scalar field, we obtain a transition between the standard scalar field and its phantom counterpart. In this case, the potential of the scalar field has a non-analyticity of the cusp type. This result is also readily reproduced in the case of an anisotropic Bianchi I universe. We have also found a spherically symmetric static solution of the Einstein equations, free of singularities and sustained by a scalar field., Comment: slightly expanded, with updated references and conceptual clarifications. Matches the published version

We investigate a model of gravitational collapse of matter inhomogeneities where the latter are modelled as Bianchi type IX (BIX) spacetimes. We found that this model contains, as limiting cases, both the standard spherical collapse model and the Zeldovich solution for a 1-dimensional perturbation. We study how these models are affected by small anisotropic perturbations within the BIX potential. For the spherical collapse case, we found that the model is equivalent to a closed FLRW Universe filled with matter and two perfect fluids representing the anisotropic contributions. From the linear evolution up to the turnaround, the anisotropies effectively shift the value of the FLRW spatial curvature, because the fluids have effective Equation of State (EoS) parameters $w \approx -1/3$. Then we estimate the impact of such anisotropies on the number density of haloes using the Press-Schechter formalism. If a fluid description of the anisotropies is still valid after virialization, the averaged over time EoS parameters are $w\approx 1/3$. Using this and demanding hydrostatic equilibrium, we find a relation between the mass $M$, the average radius $R$ and the pressure $p$ of the virialized final structure. When we consider perturbations of the Zeldovich solution, our qualitative analysis suggests that the so called \textit{pancakes} exhibit oscillatory behavior, as would be expected in the case of a vacuum BIX spacetime., Comment: v2, replaced to match the accepted version. Comments are welcome!

We examine long-wavelength correlation functions of massive scalar fields in de Sitter spacetime. For the theory with a quartic self-interaction, the two-point function is calculated up to two loops. Comparing our results with the Hartree-Fock approximation and with the stochastic approach shows that the former resums only the cactus type diagrams, whereas the latter contains the sunset diagram as well and produces the correct result. We also demonstrate that the long-wavelength expectation value of the commutator of two fields is equal to zero both for spacelike and timelike separated points., Comment: Presentation expanded, matches published version

We analyze the issue of dynamical evolution and time in quantum cosmology. We emphasize the problem of choice of phase space variables that can play the role of a time parameter in such a way that for expectation values of quantum operators the classical evolution is reproduced. We show that it is neither necessary nor sufficient for the Poisson bracket between the time variable and the super-Hamiltonian to be equal to unity in all of the phase space. We also discuss the question of switching between different internal times as well as the Montevideo interpretation of quantum theory., Comment: 30 pages, published in Universe 7, 219 (2021) in the Special Issue on "Quantum Cosmology", Ed. Paulo Vargas Moniz

We review a number of issues in foundations of quantum theory and quantum cosmology including, in particular, the problem of the preferred basis in the many-worlds interpretation of quantum mechanics, the relation between this interpretation and the decoherence phenomenon, application of decoherence approach to quantum cosmology, the relation between the many-worlds interpretation and Anthropic Principle along with the notion of quantum-classical duality. We also discuss the concept of fundamentally mixed quantum state of the Universe represented by a special microcanonical density matrix and its dynamical realization in the form of the semiclassically treated path integral over spacetime geometries and quantum matter fields. These issues can be considered as a part of the scientific legacy of H. D. Zeh generously left to us in his two seminal papers published at the beginning of seventies in Foundations of Physics., Comment: 25 pages, 3 figures, prepared for the publication in the Springer series "Fundamental Theories of Physics", in the volume, dedicated to the memory of H. D. Zeh. arXiv admin note: text overlap with arXiv:1302.5545

We develop a method for treating a series of secularly growing terms obtained from quantum perturbative calculations: autonomous first-order differential equations are constructed such that they reproduce this series to the given order. The exact solutions of these equations are free of secular terms and approach a finite limit at late times. This technique is illustrated for the well-known problem of secular growth of correlation functions of a massless scalar field with a quartic self-interaction in de Sitter space. For the expectation value of the product of two fields at coinciding space-time points we obtain a finite late-time result that is very close to the one following from Starobinsky's stochastic approach., Comment: 20 pages

We consider different scenarios of the evolution of the universe, where the singularities or some non-analyticities in the geometry of the spacetime are present, trying to answer the following question: is it possible to conserve some kind of notion of particle corresponding to a chosen quantum field present in the universe when the latter approaches the singularity? We study scalar fields with different types of Lagrangians, writing down the second-order differential equations for the linear perturbations of these fields in the vicinity of a singularity. If both independent solutions are regular, we construct the vacuum state for quantum particles as a Gaussian function of the corresponding variable. If at least one of two independent solutions has a singular asymptotic behavior, then we cannot define the creation and the annihilation operators and construct the vacuum. This means that the very notion of particle loses sense. We show that at the approaching to the Big Rip singularity, particles corresponding to the phantom scalar field driving the evolution of the universe must vanish, while particles of other fields still can be defined. In the case of the model of the universe described by the tachyon field with a special trigonometric potential, where the Big Brake singularity occurs, we see that the (pseudo) tachyon particles do not pass through this singularity. Adding to this model some quantity of dust, we slightly change the characteristics of this singularity and tachyon particles survive. Finally, we consider a model with the scalar field with the cusped potential, where the phantom divide line crossing occurs. Here the particles are well defined in the vicinity of this crossing point., Comment: 13 pages, 1 figure. Final version to be published in PRD

We study the solutions of the Einstein equations in the presence of a thick infinite slab with constant energy density. When there is an isotropy in the plane of the slab, we find an explicit exact solution that matches with the Rindler and Weyl-Levi-Civita spacetimes outside the slab. We also show that there are solutions that can be matched with general anisotropic Kasner spacetime outside the slab. In any case, it is impossible to avoid the presence of the Kasner type singularities in contrast to the well-known case of spherical symmetry, where by matching the internal Schwarzschild solution with the external one, the singularity in the center of coordinates can be eliminated., Comment: 5 pages, to be published in JETP Letters

We find exact static solutions of the Einstein equations in the spacetime with plane symmetry, where an infinite slab with finite thickness and homogeneous energy (mass) density is present. In the first solution the pressure is isotropic, while in the second solution the tangential components of the pressure are equal to zero. In both cases the pressure vanishes at the boundaries of the slab. Outside the slab these solutions are matched with the Rindler spacetime and with the Weyl-Levi-Civita spacetime, which represent special cases of the Kasner solution., Comment: Final version, published in Physics Letters B

We study static spherically and hyperbolically symmetric solutions of the Einstein equations in the presence of a conformally coupled scalar field and compare them with those in the space filled with a minimally coupled scalar field. We then study the Kantowski-Sachs cosmological solutions, which are connected with the static solutions by the duality relations. The main ingredient of these relations is an exchange of roles between the radial and the temporal coordinates, combined with the exchange between the spherical and hyperbolical two-dimensional geometries. A brief discussion of questions such as the relation between the Jordan and the Einstein frames and the description of the singularity crossing is also presented., Comment: The final version, published in Physical Review D, the title is changed and some references and comments are added

We compare two different approaches to the treatment of the Wheeler-DeWitt equation and the introduction of time in quantum cosmology. One approach is based on the gauge-fixing procedure in theories with first-class constraints, while the other uses the Born-Oppenheimer method. We apply both to a very simple cosmological model and observe that they give similar predictions. We also discuss the problem of time in non-relativistic quantum mechanics and some questions concerning the correspondence between classical and quantum theories., Comment: 9 pages

We check the cancellation of the vacuum energy in the Wess-Zumino model at the two-loop order in the component field formalisms with and without auxiliary fields. We show that in both cases the vacuum energy is equal to zero. However, in the formalism where the auxiliary fields are excluded, the vanishing of the vacuum energy arises due to the cancellation between the potential and kinetic energies, while in the formalism with the auxiliary fields, both terms vanish separately., Comment: 13 pages

We illustrate and examine diverse approaches to the quantum matter-gravity system which refer to the Born-Oppenheimer (BO) method. In particular we first examine a quantum geometrodynamical approach introduced by other authors in a manner analogous to that previously employed by us, so as to include back reaction and non-adiabatic contributions. On including such effects it is seen that the unitarity violating effects previously found disappear. A quantum loop space formulation (based on a hybrid quantisation, polymer for gravitation and canonical for matter) also refers to the BO method. It does not involve the classical limit for gravitation and has a highly peaked initial scalar field state. We point out that it does not resemble in any way to our traditional BO approach. Instead it does resemble an alternative, canonically quantised, non BO approach which we have also previously discussed., Comment: 14 pages, no figures

We consider a rather simple method for the description of the Big Bang - Big Crunch cosmological singularity crossing. For the flat Friedmann universe this method gives the same results as more complicated methods, using Weyl symmetry or the transitions between the Jordan and Einstein frames. It is then easily generalized for the case of a Bianchi-I anisotropic universe. We also present early-time and late-time asymptotic solutions for a Bianchi-I universe, filled with a conformally coupled massless scalar field., Comment: 11 pages, v2: accepted for publication in Phys. Rev. D

We study different aspects of the Ho\v{r}ava-Lifshitz inspired Bianchi-II cosmology and its relations with the mixmaster universe model. First, we present exact solutions for a toy model, where only the cubic in spatial curvature terms are present in the action; then we briefly discuss some exotic singularities, which can appear in this toy model. We study also the toy model where only the quadratic in spatial curvature terms are present in the action. We establish relations between our results and those obtained by using the Hamiltonian formalism. Finally, we apply the results obtained by studying Bianchi-II cosmology to describe the evolution of the mixmaster universe in terms of the Belinsky-Khalatnikov-Lifshitz formalism. Generally, our analysis gives some arguments in favour of the existence of the oscillatory approach to the singularity in a universe governed by the Ho\v{r}ava-Lifshitz type gravity., Comment: 25 pages, final version to appear in Classical and Quantum Gravity, the title is changed and two sections are added

We study the relation between the Jordan-Einstein frame transition and the possible description of the crossing of singularities in flat Friedmann universes, using the fact that the regular evolution in one frame can correspond to crossing singularities in the other frame. We show that some interesting effects arise in simple models such as one with a massless scalar field or another wherein the potential is constant in the Einstein frame. The dynamics in these models and in their conformally coupled counterparts are described in detail, and a method for the continuation of such cosmological evolutions beyond the singularity is developed. We compare our approach with some other, recently developed, approaches to the problem of the crossing of singularities., Comment: 15 pages, v2: title changed, presentation improved, references added, accepted for publication in Phys. Rev. D

The evolution of a closed Friedmann universe filled by a tachyon scalar field with a trigonometric potential and cold dark matter (CDM) is investigated. A subset of the evolutions consistent to 1$\sigma $ confidence level with the Union 2.1 supernova data set is identified. The evolutions of the tachyon field are classified. Some of them evolve into a de Sitter attractor, while others proceed through a pseudo-tachyonic regime into a sudden future singularity. Critical evolutions leading to Big Brake singularities in the presence of CDM are found and a new type of cosmological evolution characterized by singularity avoidance in the pseudo-tachyon regime is presented., Comment: 7 pages, 5 figures, to be published in Phys. Rev. D

In the framework of a general scalar-tensor theory, we investigate the equivalence between two different parametrizations of fields that are commonly used in cosmology - the so-called Jordan frame and Einstein frame. While it is clear that both parametrizations are mathematically equivalent at the level of the classical action, the question about their mathematical equivalence at the quantum level as well as their physical equivalence is still a matter of debate in cosmology. We analyze whether the mathematical equivalence still holds when the first quantum corrections are taken into account. We explicitly calculate the one-loop divergences in both parametrizations by using the generalized Schwinger-DeWitt algorithm and compare both results. We find that the quantum corrections do not coincide off shell and hence induce an off shell dependence on the parametrization. According to the equivalence theorem, the one-loop divergences should however coincide on shell. For a cosmological background, we show explicitly that the on shell equivalence is indeed realized by a nontrivial cancellation., Comment: 18 pages, 1 figure, revised version accepted for publication in Physical Review D, new title, section V, VI and VIII of previous arXiv version removed, references updated

We investigate particular cosmological models, based either on tachyon fields or on perfect fluids, for which soft future singularities arise in a natural way. Our main result is the description of a smooth crossing of the soft singularity in models with an anti-Chaplygin gas or with a particular tachyon field in the presence of dust. Such a crossing is made possible by certain transformations of matter properties. Some of these cosmological evolutions involving tachyons are compatible with SNIa data. We compute numerically their dynamics involving a first soft singularity crossing, a turning point and a second soft singulatity crossing during recollapse, ending in a Big Crunch singularity., Comment: published version, 13 pages, 2 figure panels, new subsection III.D added

Both dark energy models and modified gravity theories could lead to cosmological evolutions different from either the recollapse into a Big Crunch or exponential de Sitter expansion. The newly arising singularities may represent true endpoints of the evolution or allow for the extension of geodesics through them. In the latter case the components of the Riemann tensor representing tidal forces diverge. Sudden Future Singularities (SFS) occur at finite time, finite scale factor and finite Hubble parameter, only the deceleration parameter diverges. The energy density of a perfect fluid is regular and its pressure diverges at the SFS. A particular SFS, the Big Brake occurs when the energy density vanishes and the expansion arrives at a full stop at the singularity. Such scenarios are generated by either a particular scalar field (the tachyon field) or the anti-Chaplygin gas. By adding matter to these models, an unwanted feature appears: at the finite scale factor of the SFS the energy density of matter remains finite, implying (for a spatially flat universe) a finite Hubble parameter, hence finite expansion rate, rather then full stop. The universe would further expand through the singularity, this nevertheless seems forbidden as the energy density of the tachyonic field / anti-Chaplygin gas would become ill-defined. This paradox is relieved in the case of the anti-Chaplygin gas by redefining its energy density and pressure in terms of distributions peaked on the singularity. The regular cosmological quantities, continuous across the SFS are the energy density and the square of the Hubble parameter; those allowing for a jump at the SFS are the Hubble parameter and expansion rate (both being mirror-symmetric). The pressure and the decelaration parameter will contain Dirac delta-function contributions peaked on the SFS, however they anyhow would diverge at the singularity., Comment: 4 pages, in the Proceedings of the Multiverse and Fundamental Cosmology (Multicosmofun'12) Conference

We investigate a very general class of cosmological models with scalar fields non-minimally coupled to gravity. A particular representative in this class is given by the non-minimal Higgs inflation model in which the Standard Model Higgs boson and the inflaton are described by one and the same scalar particle. While the predictions of the non-minimal Higgs inflation scenario come numerically remarkably close to the recently discovered mass of the Higgs boson, there remains a conceptual problem in this model that is associated with the choice of the cosmological frame. While the classical theory is independent of this choice, we find by an explicit calculation that already the first quantum corrections induce a frame dependence. We give a geometrical explanation of this frame dependence by embedding it into a more general field theoretical context. From this analysis, some conceptional points in the long lasting cosmological debate: "Jordan frame vs. Einstein frame" become more transparent and in principle can be resolved in a natural way., Comment: 4 pages, 3 figures. To appear in the proceedings of the Multiverse and Fundamental Cosmology Conference (Multicosmofun 2012), Szczecin, Poland

A cosmological model of a flat Friedmann universe filled with a mixture of anti-Chaplygin gas and dust-like matter exhibits a future soft singularity, where the pressure of the anti-Chaplygin gas diverges (while its energy density is finite). Despite infinite tidal forces the geodesics pass through the singularity. Due to the dust component, the Hubble parameter has a non-zero value at the encounter with the singularity, therefore the dust implies further expansion. With continued expansion however, the energy density and the pressure of the anti-Chaplygin gas would become ill-defined, hence from the point of view of the anti-Chaplygin gas only a contraction is allowed. Paradoxically, the universe in this cosmological model would have to expand and contract simultaneously. This obviosly could not happen. We solve the paradox by redefining the anti-Chaplygin gas in a distributional sense. Then a contraction could follow the expansion phase at the singularity at the price of a jump in the Hubble parameter. Although such an abrupt change is not common in any cosmological evolution, we explicitly show that the set of Friedmann, Raychaudhuri and continuity equations are all obeyed both at the singularity and in its vicinity. We also prove that the Israel junction conditions are obeyed through the singular spatial hypersurface. In particular we enounce and prove a more general form of the Lanczos equation., Comment: 12 pages; to be published in Phys.Rev.D

We review the application of the spectral zeta-function to the 1- loop properties of quantum field theories on manifolds with boundary, with emphasis on Euclidean quantum gravity and quantum cosmology. As was shown in the literature some time ago, the only boundary conditions that are completely invariant under infinitesimal diffeomorphisms on metric perturbations suffer from a drawback, i.e. lack of strong ellipticity of the resulting boundary-value problem. Nevertheless, at least on the Euclidean 4-ball background, it remains possible to evaluate the zeta(0) value, which describes in this case a universe which, in the limit of small 3-geometry, has vanishing probability of approaching the cosmological singularity. An assessment of this result is here performed, discussing its physical and mathematical implications., Comment: 40 pages, Latex, submitted to the Stuart Dowker special issue of J. Phys. A

We show that the string gas - a perfect fluid with the equation of state $p = -\frac13 \rho$ possesses rather interesing properties. In Friedmann universes its presence can can change the observable topology of the space; in the spherically symmetric spacetimes it produces rather bizzare geometries and in a way its influence on the rotation curves mimics the dark matter effects., Comment: 9 pages, 1 figure

Using the generalized Schwinger-DeWitt technique, we calculate the divergent part of the one-loop effective action for gravity non-minimally coupled to a multiplet of scalar fields. All the calculations are consistently done in the Jordan frame., Comment: revised version, to appear in Phys. Rev. D

We investigate a Friedmann universe filled with a tachyon scalar field, which behaves as dustlike matter in the past, while it is able to accelerate the expansion rate of the universe at late times. The comparison with type Ia supernovae (SNIa) data allows for evolutions driving the universe into a Big Brake. Some of the evolutions leading to a Big Brake exhibit a large variation of the equation of state parameter at low redshifts which is potentially observable with future data though hardly detectable with present SNIa data. The soft Big Brake singularity occurs at finite values of the scale factor, vanishing energy density and Hubble parameter, but diverging deceleration and infinite pressure. We show that the geodesics can be continued through the Big Brake and that our model universe will recollapse eventually in a Big Crunch. Although the time to the Big Brake strongly depends on the present values of the tachyonic field and of its time derivative, the time from the Big Brake to the Big Crunch represents a kind of invariant timescale for all field parameters allowed by SNIa., Comment: v2: slightly expanded, 14 pages, 5 figures, 3 tables; version to be published in Phys.Rev.D

We suggest a path integral formulation for the tunneling cosmological state, which admits a consistent renormalization and renormalization group (RG) improvement in particle physics applications of quantum cosmology. We apply this formulation to the inflationary cosmology driven by the Standard Model (SM) Higgs boson playing the role of an inflaton with a strong non-minimal coupling to gravity. In this way a complete cosmological scenario is obtained, which embraces the formation of initial conditions for the inflationary background in the form of a sharp probability peak in the distribution of the inflaton field and the ongoing generation of the Cosmic Microwave Background (CMB) spectrum on this background. Formation of this probability peak is based on the same RG mechanism which underlies the generation of the CMB spectrum which was recently shown to be compatible with the WMAP data in the Higgs mass range $135.6 {\rm GeV} \lesssim M_H\lesssim 184.5 {\rm GeV}$. This brings to life a convincing unification of quantum cosmology with the particle phenomenology of the SM, inflation theory, and CMB observations., Comment: 18 pages, 3 figures, LaTeX

An exact solution of the Einstein equations for a Bianchi-I universe in the presence of dust, stiff matter and a negative cosmological constant, generalising the well-known Heckmann-Schucking solution is presented. This solution describes a universe existing during a finite period of cosmic time, where the beginning and the end of its evolution are characterized by the presence of Kasner type cosmological singularities., Comment: 10 pages

We construct a scalar field based cosmological model, possessing a cosmological singularity characterized by a finite value of the cosmological radius and an infinite scalar curvature. Using the methods of the qualitative theory of differential equations, we give a complete description of the cosmological evolutions in the model under consideration. There are four classes of evolutions, two of which have finite lifetimes, while the other two undergo an infinite expansion., Comment: 6 pages, 3 figures

A vanishing one-loop wave function of the Universe in the limit of small three-geometry is found, on imposing diffeomorphism-invariant boundary conditions on the Euclidean 4-ball in the de Donder gauge. This result suggests a quantum avoidance of the cosmological singularity driven by full diffeomorphism invariance of the boundary-value problem for one-loop quantum theory. All of this is made possible by a peculiar spectral cancellation on the Euclidean 4-ball, here derived and discussed., Comment: 7 pages, latex file. Paper prepared for the Conference "QFEXT05: Quantum Field Theory Under the Influence of External Conditions", Barcelona, September 5 - September 9, 2005. In the final version, the presentation has been further improved, and yet other References have been added

Recent work on Euclidean quantum gravity on the four-ball has proved regularity at the origin of the generalized zeta-function built from eigenvalues for metric and ghost modes, when diffeomorphism-invariant boundary conditions are imposed in the de Donder gauge. The hardest part of the analysis involves one of the four sectors for scalar-type perturbations, the eigenvalues of which are obtained by squaring up roots of a linear combination of Bessel functions of integer adjacent orders, with a coefficient of linear combination depending on the unknown roots. This paper obtains, first, approximate analytic formulae for such roots for all values of the order of Bessel functions. For this purpose, both the descending series for Bessel functions and their uniform asymptotic expansion at large order are used. The resulting generalized zeta-function is also built, and another check of regularity at the origin is obtained. For the first time in the literature on quantum gravity on manifolds with boundary, a vanishing one-loop wave function of the Universe is found in the limit of small three-geometry, which suggests a quantum avoidance of the cosmological singularity driven by full diffeomorphism invariance of the boundary-value problem for one-loop quantum theory., Comment: 21 Pages, Latex and .eps files with JHEP3 style. The discussion in Section 5 has been improved, and Ref. 26 has been added

A general method exists for studying Abelian and non-Abelian gauge theories, as well as Euclidean quantum gravity, at one-loop level on manifolds with boundary. In the latter case, boundary conditions on metric perturbations h can be chosen to be completely invariant under infinitesimal diffeomorphisms, to preserve the invariance group of the theory and BRST symmetry. In the de Donder gauge, however, the resulting boundary-value problem for the Laplace type operator acting on h is known to be self-adjoint but not strongly elliptic. The present paper shows that, on the Euclidean four-ball, only the scalar part of perturbative modes for quantum gravity is affected by the lack of strong ellipticity. Interestingly, three sectors of the scalar-perturbation problem remain elliptic, while lack of strong ellipticity is confined to the remaining fourth sector. The integral representation of the resulting zeta-function asymptotics on the Euclidean four-ball is also obtained; this remains regular at the origin by virtue of a peculiar spectral identity obtained by the authors. There is therefore encouraging evidence in favour of the zeta(0) value with fully diff-invariant boundary conditions remaining well defined, at least on the four-ball, although severe technical obstructions remain in general., Comment: 26 pages, Latex file with Latex macros. In the final version, style of References has been further improved

A general method is known to exist for studying Abelian and non-Abelian gauge theories, as well as Euclidean quantum gravity, at one-loop level on manifolds with boundary. In the latter case, boundary conditions on metric perturbations h can be chosen to be completely invariant under infinitesimal diffeomorphisms, to preserve the invariance group of the theory and BRST symmetry. In the de Donder gauge, however, the resulting boundary-value problem for the Laplace type operator acting on h is known to be self-adjoint but not strongly elliptic. The latter is a technical condition ensuring that a unique smooth solution of the boundary-value problem exists, which implies, in turn, that the global heat-kernel asymptotics yielding one-loop divergences and one-loop effective action actually exists. The present paper shows that, on the Euclidean four-ball, only the scalar part of perturbative modes for quantum gravity are affected by the lack of strong ellipticity. Further evidence for lack of strong ellipticity, from an analytic point of view, is therefore obtained. Interestingly, three sectors of the scalar-perturbation problem remain elliptic, while lack of strong ellipticity is confined to the remaining fourth sector. The integral representation of the resulting zeta-function asymptotics is also obtained; this remains regular at the origin by virtue of a spectral identity here obtained for the first time., Comment: 25 pages, Revtex-4. Misprints in Eqs. (5.11), (5.14), (5.16) have been corrected

One of the most interesting features of braneworld models is the existence of massive gravitational modes in addition to the usual massless one. Mixing of the modes which depends nontrivially on the inter-brane distance can be interpreted as radion-induced gravitational-wave oscillations, a classical analogy to meson and neutrino oscillations. We show that these oscillations arising in M-theory inspired two-brane setups could lead to effects detectable by gravitational-wave interferometers., Comment: 5 pages. Talk given by A. Rathke at SUGRA 20 Conference, Northeastern University, Boston, March 17-20 2003

We discuss the theory and phenomenology of the interplay between the massless graviton and its massive Kaluza-Klein modes in the Randall-Sundrum two-brane model. The equations of motion of the transverse traceless degrees of freedom are derived by means of a Green function approach as well as from an effective nonlocal action. The second procedure clarifies the extraction of the particle content from the nonlocal action and the issue of its diagonalization. The situation discussed is generic for the treatment of two-brane models if the on-brane fields are used as the dynamical degrees of freedom. The mixing of the effective graviton modes of the localized action can be interpreted as radion-induced gravitational-wave oscillations, a classical analogy to meson and neutrino oscillations. We show that these oscillations arising in M-theory-motivated braneworld setups could lead to effects detectable by gravitational-wave interferometers. The implications of this effect for models with ultra-light gravitons are discussed., Comment: 27 pages, to appear in Annalen Phys

A brief review is presented of motivations and results in one-loop supergravity on manifolds with boundary, whose consideration is suggested by quantum cosmology., Comment: 6 pages, Latex, invited contribution to the "Concise Encyclopedia of Supersymmetry", edited by J. Bagger, S. Duplij and W. Siegel (Dordrecht: Kluwer Academic Publishers)

The zero-point energy of a conducting spherical shell is studied by imposing the axial gauge via path-integral methods, with boundary conditions on the electromagnetic potential and ghost fields. The coupled modes are then found to be the temporal and longitudinal modes for the Maxwell field. The resulting system can be decoupled by studying a fourth-order differential equation with boundary conditions on longitudinal modes and their second derivatives. Complete agreement is found with a previous path-integral analysis in the Lorenz gauge, and with Boyer's value. This investigation leads to a better understanding of how gauge independence is achieved in quantum field theory on backgrounds with boundary., Comment: 4 pages, plain Tex, paper prepared for the QG6 parallel session on Casimir effect at 9th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories (MG 9), Rome, Italy, 2-8 July 2000

The zero-point energy of a conducting spherical shell is studied by imposing the axial gauge via path-integral methods, with boundary conditions on the electromagnetic potential and ghost fields. The coupled modes are then found to be the temporal and longitudinal modes for the Maxwell field. The resulting system can be decoupled by studying a fourth-order differential equation with boundary conditions on longitudinal modes and their second derivatives. The exact solution of such equation is found by using a Green-function method, and is obtained from Bessel functions and definite integrals involving Bessel functions. Complete agreement with a previous path-integral analysis in the Lorenz gauge, and with Boyer's value, is proved in detail., Comment: 9 pages, Revtex