arXiv subjects
Publications and source records attributed to Ilya L. Shapiro.
The divergent part of the one-loop Vilkovisky unique effective action for quantum Einstein gravity is evaluated in the general parametrization of the quantum field, including the separated conformal factor. The output of this calculation explicitly demonstrates the parametrization and conformal gauge independence of the unique effective action with the configuration space metric chosen following Vilkovisky's prescription.
Theoretically, the running of the cosmological constant in the IR region is not ruled out. On the other hand, from the QFT viewpoint, the energy released due to the variation of the cosmological constant in the late universe cannot go to the matter sector. For this reason, the phenomenological bounds on such a running are not sufficiently restrictive. The situation can be different in the early universe when the gravitational field was sufficiently strong to provide an efficient creation of particles from the vacuum. We develop a framework for systematically exploring this ossibility. It is supposed that the running occurs in the epoch when the Dark Matter already decoupled and is expanding adiabatically, while baryons are approximately massless and can be abundantly created from vacuum due to the decay of vacuum energy. By using the handy model of Reduced Relativistic Gas for describing the Dark Matter, we consider the dynamics of both cosmic background and linear perturbations and evaluate the impact of the vacuum decay on the matter power spectrum and to the first CMB peak. Additionally, using the combined data of CMB+BAO+SNIa we find the best fit values for the free parameters of our model.
The effective action in quantum general relativity is strongly dependent on the gauge-fixing and parametrization of the quantum metric. As a consequence, in the effective approach to quantum gravity, there is no possibility to introduce the renormalization-group framework in a consistent way. On the other hand, the version of effective action proposed by Vilkovisky and DeWitt does not depend on the gauge-fixing and parametrization off-shell, opening the way to explore the running of the cosmological and Newton constants as well as the coefficients of the higher-derivative terms of the total action. We argue that in the effective framework the one-loop beta functions for the zero-, two- and four-derivative terms can be regarded as exact, that means, free from corrections coming from the higher loops. In this perspective, the running describes the renormalization group flow between the present-day Hubble scale in the IR and the Planck scale in the UV.
It is known than the inclusion of spatial curvature can modify the evolution of matter perturbations and affect the Large Scale Structure (LSS) formation. We quantify the effects of the non-zero space curvature in terms of LSS formation for a cosmological model with a running vacuum energy density and a warm dark matter component. The evolution of density perturbations and the modified shape of its power spectrum are constructed and analyzed.
We review and present full detail of the Feynman diagram - based and heat-kernel method - based calculations of the simplest nonlocal form factors in the one-loop contributions of a massive scalar field. The paper has a pedagogical and introductory purposes and is intended to help the reader in better understanding the existing literature on the subject. The functional calculations are based on the solution by Avramidi and Barvinsky \& Vilkovisky for the heat kernel and are performed in curved spacetime. One of the important points is that the main structure of non-localities is the same as in the flat background.
We investigate the gauge symmetry and gauge fixing dependence properties of the effective average action for quantum gravity models of general form. Using the background field formalism and the standard BRST-based arguments, one can establish the special class of regulator functions that preserves the background field symmetry of the effective average action. Unfortunately, regardless the gauge symmetry is preserved at the quantum level, the non-invariance of the regulator action under the global BRST transformations leads to the gauge fixing dependence even under the use of the on-shell conditions.
We study the Yukawa model with one scalar and one axial scalar fields, coupled to $N$ copies of Dirac fermions, in curved spacetime background. The theory possesses a reach set of coupling constants, including the scalar terms with odd powers of scalar fields in the potential, and constants of non-minimal coupling of the scalar fields to gravity. Using the heat-kernel technique and dimensional regularization, we derive the one-loop divergences, describe the renormalization of the theory under consideration and calculate the full set of beta- and gamma-functions for all coupling constants and fields. As a next step, we construct the renormalized one-loop effective potential of the scalar fields up to the terms linear in scalar curvature. This calculation includes only the contributions from quantum scalar fields, and is performed using covariant cut-off regularization and local momentum representation. Some difficulties of the renormalization group approach to the effective potential in the case under consideration are discussed.
We consider, in more details than it was done previously, the effective low-energy behavior in the quantum theory of a light scalar field coupled to another scalar with much larger mass. The main target of our work is an IR decoupling of heavy degrees of freedom, including in the diagrams with mixed light-heavy contents in the loops. It is shown that the one-loop diagrams with mixed internal lines produce an IR non-local contributions which are exactly the same as the ones in the theory of the light scalar alone, with the effective self-interaction which can be obtained by the functional integration of the heavy scalar, almost neglecting its kinetic term. The same effect takes place in curved space, regardless of a larger amount of non-localities which show up in the effective model.
We employ stochastic quantization for a self-interacting nonminimal massive scalar field in curved spacetime. The covariant background field method and local momentum space representation are used to obtain the Euclidean correlation function and evaluate multi-loop quantum corrections through simultaneous expansions in the curvature tensor and its covariant derivatives and in the noise fields. The stochastic correlation function reproduces the well-known result by Bunch and Parker and is used to construct the effective potential in curved spacetime in an arbitrary dimension $D$ up to the first order in curvature. Furthermore, we present a sample of numerical simulations for $D=3$ in the first order in curvature.
We present a reformulation of the background field method for Yang-Mills type theories, based on using a superalgebra of generators of BRST and background field transformations. The new approach enables one to implement and consistently use non-linear gauges in a natural way, by using the requirement of invariance of the fermion gauge-fixing functional under the background field transformations.
Using the background field method for the functional renormalization group approach in the case of a generic gauge theory, we study the background field symmetry and gauge dependence of the background average effective action, when the regulator action depends on external fields. The final result is that the symmetry of the average effective action can be maintained for a wide class of regulator functions, but in all cases the dependence of the gauge fixing remains on-shell. The Yang-Mills theory is considered as the main particular example.
The study of stability of gravitational perturbations in higher derivative gravity has shown that at the linear level the massive unphysical ghost is not generated from vacuum if the initial seed of metric perturbation has frequency essentially below the Planck threshold. The mathematical knowledge indicated that the linear stability is supposed to hold even at the nonperturbative level, but in such a complicated case it is important to perform a verification of this statement. We compare the asymptotic stability solutions at the linear and full nonperturbative levels for the Bianchi-I metric with small anisotropies, which can be regarded as an extreme, zero frequency limit of a gravitational wave. As one should expect from the combination of previous analysis and general mathematical theorems, there is a good correspondence between linear stability and the nonperturbative asymptotic behavior.
Using the Batalin-Vilkovisky technique and the background field method the proof of gauge invariant renormalizability is elaborated for a generic model of quantum gravity which is diffeomorphism invariant and has no other, potentially anomalous, symmetries. The gauge invariant renormalizability means that in all orders of loop expansion of the quantum effective action one can control deformations of the generators of gauge transformations which leave such an action invariant. In quantum gravity this means that one can maintain general covariance of the divergent part of effective action when the mean quantum field, ghosts and antifields are switched off.
We explore the classical and quantum properties of a sterile scalar field coupled to $N$ copies of Dirac fermions in an external gravitational field. We find that the self-interaction scalar potential of a model that is consistent at the quantum level, includes odd (first and third) powers of a scalar. In particular, one has to consider, besides the standard non-minimal coupling of the form $ξφ^2 R$, the new type of non-minimal coupling of the form $fφR$ with new non-minimal parameter $f$. We study the one-loop renormalization of such a theory including renormalization of the new non-minimal coupling. Also, we calculate the one-loop effective potential using the renormalization group and show how the renormalization group analysis should be extended compared to the standard expression which was derived in 1980-ies. This conclusion is supported by the direct calculation of effective potential using normal coordinates and covariant cut-off regularization. The important features of the classical theory with a sterile scalar are related to the presence of the qualitatively new terms in the induced action of gravity, coming from the odd terms. We show that this new feature of the theory may have phenomenologically relevant consequences, both in the low-energy gravitational physics and at the high energies, corresponding to inflation.
Total derivative terms play an important role in the integration of conformal anomaly. In four dimensional space $4D$ there is only one such term, namely $\,{\square}R$. In the case of six dimensions $6D$ the structure of surface terms is more complicated, and it is useful to construct a basis of linear independent total derivative terms. We briefly review the general scheme of integrating anomaly and present the reduction of the minimal set of the surface terms in $6D$ from eight to seven.
We extend previous calculations of the non-local form factors of semiclassical gravity in $4D$ to include the Einstein-Hilbert term. The quantized fields are massive scalar, fermion and vector fields. The non-local form factor in this case can be seen as the sum of a power series of total derivatives, but it enables us to derive the beta function of Newton's constant and formally evaluate the decoupling law in the new sector, which turns out to be the standard quadratic one.
The $R+R^2$ model is successful in describing inflation, as it provides an excellent fit to the full set of available observational data. On the other hand, the same model is the simplest extension of general relativity which does not produce higher derivative ghosts and related instabilities. Long ago, it was proposed to treat all terms which cause higher derivative instabilities as small perturbations that could avoid the presence of ghosts in the spectrum. We put this proposal into practice and consider an explicit example of treating more complicated higher derivative terms as small perturbations over the $R+R^2$ model by introducing the $R\Box R$ term into the action. Within the described scheme, it is possible to obtain an upper bound on the coefficient of this non-scale-free sixth-derivative term by mapping the theory into a one-scalar field potential. It is shown that the result differs from treating this term on equal footing with other terms that requires mapping to a two-scalar field model, and in general leads to different observational consequences.
We review some of the recent results which can be useful for better understanding of the problem of stability of vacuum and in general classical solutions in higher derivative quantum gravity. The fourth derivative terms in the purely gravitational vacuum sector are requested by renormalizability already in both semiclassical and complete quantum gravity theories. However, because of these terms the spectrum of the theory has unphysical ghost states which jeopardize the stability of classical solutions. At the quantum level ghosts violate unitarity, and and thus ghosts look incompatible with the consistency of the theory. The `dominating' or `standard' approach is to treat higher derivative terms as small perturbations at low energies. Such an effective theory is supposed to glue with an unknown fundamental theory in the high energy limit. We argue that the perspectives for such a scenario are not clear, to say the least. On the other hand, recently there was certain progress in understanding physical conditions which can make ghosts not offensive. We survey these results and discuss the properties of the unknown fundamental theory which can provide these conditions satisfied.