arXiv subjects

Ilya L. Shapiro

Publications and source records attributed to Ilya L. Shapiro.

At least 73 records · Page 4Linked to original sources

arXiv2018

Renormalization group in super-renormalizable quantum gravity

One of the main advantages of super-renormalizable higher derivative quantum gravity models is the possibility to derive exact beta functions, by making perturbative one-loop calculations. We perform such a calculation for the Newton constant by using the Barvinsky-Vilkovisky trace technology. The result is well-defined in a large class of models of gravity in the sense that the renormalization group beta functions do not depend on the gauge-fixing condition. Finally, we discuss the possibility to apply the results to a large class of nonlocal gravitational theories which are free of massive ghost-like states at the tree-level.

hep-th↗

arXiv2018

Gravitational form factors and decoupling in 2D

We calculate and analyse non-local gravitational form factors induced by quantum matter fields in curved two-dimensional space. The calculations are performed for scalars, spinors and massive vectors by means of the covariant heat kernel method up to the second order in the curvature and confirmed using Feynman diagrams. The analysis of the ultraviolet (UV) limit reveals a generalized "running" form of the Polyakov action for a nonminimal scalar field and the usual Polyakov action in the conformally invariant cases. In the infrared (IR) we establish the gravitational decoupling theorem, which can be seen directly from the form factors or from the physical beta function for fields of any spin.

hep-th↗

arXiv2018

Light bending in $F\left[g(\square)R\right]$ extended gravity theories

We show that in the weak field limit the light deflection alone cannot distinguish between different $R + F[g(\square)R]$ models of gravity, where $F$ and $g$ are arbitrary functions. This does not imply, however, that in all these theories an observer will see the same deflection angle. Owed to the need to calibrate the Newton constant, the deflection angle may be model-dependent after all necessary types of measurements are taken into account.

gr-qc↗

arXiv2018

Cosmic anisotropy with Reduced Relativistic Gas

The dynamics of cosmological anisotropies is investigated for Bianchi type I universe filled by a relativistic matter represented by the reduced relativistic gas model (RRG), with equation of state interpolating between radiation and matter. Previously it was shown that the interpolation is observed in the background cosmological solutions for homogeneous and isotropic universe and also for the linear cosmological perturbations. We extend the application of RRG to the Bianchi type I anisotropic model and find that the solutions evolve to the isotropic universe with the pressureless matter contents.

gr-qc↗

arXiv2018

Gauge and parametrization ambiguity in quantum gravity

The gauge and parametrization dependence is discussed in quantum gravity in an arbitrary dimension $D$. Explicit one-loop calculations are performed within the most general parametrization of quantum metric with seven arbitrary parameters. On the other hand, some of the gauge fixing parameters are fixed to make the calculations relatively simple. We confirm the general theorem stating that the on-shell local terms in the one-loop effective action are independent on the gauge and parametrization ambiguity.

hep-th↗

arXiv2018

On the ghost-induced instability on de Sitter background

It is known that the perturbative instability of tensor excitations in higher derivative gravity may not take place if the initial frequency of the gravitational waves are below the Planck threshold. One can assume that this is a natural requirement if the cosmological background is sufficiently mild, since in this case the situation is qualitatively close to the free gravitational wave in flat space. Here, we explore the opposite situation and consider the effect of a very far from Minkowski radiation-dominated or de Sitter cosmological background with a large Hubble rate, e.g., typical of an inflationary period. It turns out that, then, for initial Planckian or even trans-Planckian frequencies, the instability is rapidly suppressed by the very fast expansion of the universe.

gr-qc↗

arXiv2017

Low-energy effects in a higher-derivative gravity model with real and complex massive poles

The most simple superrenormalizable model of quantum gravity is based on the general local covariant six-derivative action. In addition to graviton such a theory has massive scalar and tensor modes. It was shown recently that in the case when the massive poles emerge in complex conjugate pairs, the theory has also unitary $S$-matrix and hence can be seen as a candidate to be a consistent quantum gravity theory. In the present work we construct the modified Newton potential and explore the gravitational light bending in a general six-derivative theory, including the most interesting case of complex massive poles. In the case of the light deflection the results are obtained within classical and semiclassical approaches.

gr-qc↗

arXiv2017

Renormalization group flows and fixed points for a scalar field in curved space with nonminimal $F(ϕ)R$ coupling

Using covariant methods, we construct and explore the Wetterich equation for a non-minimal coupling $F(ϕ)R$ of a quantized scalar field to the Ricci scalar of a prescribed curved space. This includes the often considered non-minimal coupling $ξϕ^2 R$ as a special case. We consider the truncations without and with scale- and field-dependent wave function renormalization in dimensions between four and two. Thereby the main emphasis is on analytic and numerical solutions of the fixed point equations and the behavior in the vicinity of the corresponding fixed points. We determine the non-minimal coupling in the symmetric and spontaneously broken phases with vanishing and non-vanishing average fields, respectively. Using functional perturbative renormalization group methods, we discuss the leading universal contributions to the RG flow below the upper critical dimension $d=4$.

hep-th↗

arXiv2017

On the gravitational seesaw in higher-derivative gravity

Local gravitational theories with more than four derivatives are superrenormalizable, and also may be unitary in the Lee-Wick sense. Thus, it is relevant to study the low-energy properties of these theories, especially to identify observables which might be useful for experimental detection of higher derivatives. Using an analogy with the neutrino Physics, we explore the possibility of a gravitational seesaw mechanism, in which several dimensional parameters of the same order of magnitude produce a hierarchy in the masses of propagating particles. Such a mechanism could make a relatively light degree of freedom detectable in low-energy laboratory and astrophysical observations, such as torsion balance experiments and the bending of light. We demonstrate that such a seesaw mechanism in the six- and more-derivative theories is unable to reduce the lightest mass more than in the simplest four-derivative model. Adding more derivatives to the four-derivative action of gravity makes heavier masses even greater, while the lightest massive ghost is not strongly affected. This fact is favorable for protecting the theory from instabilities, but makes the experimental detection of higher derivatives more difficult.

gr-qc↗

arXiv2017

Massive vector field on curved background: non-minimal coupling, quantization and divergences

We study the effective action for the massive vector field theory non-minimally coupled to external gravitational field. Such a theory is an interesting model both from the theoretical side and also due to the various phenomenological applications to cosmology and astrophysics. The present work pretends to initiate a systematic study of its properties at the quantum level, by exploring free massive vector coupled to an external symmetric second-rank tensor. Stueckelberg scalar field is used to restore the gauge invariance. After that, by using a special gauge fixing and non-local in external fields change of variables, we diagonalize the bilinear form of the action and develop a consistent procedure to study the effective action. As a result we derive a complete non-linear structure of divergences of the effective action and discuss its properties.

hep-th↗

arXiv2017

Integration of trace anomaly in 6D

The trace anomaly in six-dimensional space is given by the local terms which have six derivatives of the metric. We find the effective action which is responsible for the anomaly. The result is presented in non-local covariant form and also in the local covariant form which employs two auxiliary scalar fields.

hep-th↗

arXiv2016

Torsion as a Dark Matter Candidate from the Higgs Portal

Torsion is a metric-independent component of gravitation, which may provide a more general geometry than the one taking place within general relativity. On the other hand torsion could lead to interesting phenomenology in both particle physics and cosmology. In the present work it is shown that a torsion field interacting with the SM Higgs doublet and having a negligible coupling to SM fermions is protected from decaying by a $Z_2$ symmetry, and therefore becomes a promising Dark Matter (DM) candidate. In order to check the consistency of this scenario we evaluate the DM relic density and explore direct DM detection and collider constraints on this model. It turns out that in the model when the Higgs boson is only partly responsible for the generation of torsion mass, there is a region of parameter space where torsion contributes 100% to the DM budget of the Universe. Furthermore, we show that the LHC currently has a limited sensitivity to the torsion parameter space via mono-jet signature and will be able to considerably improve its coverage of the torsion parameter space with the projected high luminosity.

hep-ph↗

arXiv2016

Gravitational "seesaw" and light bending in higher-derivative gravity

Local gravitational theories with more than four derivatives have remarkable quantum properties, e.g., they are super-renormalizable and may be unitary in the Lee-Wick sense. Therefore, it is important to explore also the IR limit of these theories and identify observable signatures of the higher derivatives. In the present work we study the scattering of a photon by a classical external gravitational field in the sixth-derivative model whose propagator contains only real, simple poles. Also, we discuss the possibility of a gravitational seesaw-like mechanism, which could allow the make up of a relatively small physical mass from the huge massive parameters of the action. If possible, this mechanism would be a way out of the Planck suppression, affecting the gravitational deflection of low energy photons. It turns out that the mechanism which actually occurs works only to shift heavier masses to the further UV region. This fact may be favourable for protecting the theory from instabilities, but makes experimental detection of higher derivatives more difficult.

gr-qc↗

arXiv2016

From stable to unstable anomaly-induced inflation

Quantum effects derived through conformal anomaly lead to an inflationary model that can be either stable or unstable. The unstable version requires a large dimensionless coefficient of about $5\times 10^8$ in front of the $R^2$ term that results in the inflationary regime in the $R+R^2$ ("Starobinsky") model being a generic intermediate attractor. In this case the non-local terms in the effective action are practically irrelevant, and there is a 'graceful exit' to a low curvature matter-like dominated stage driven by high-frequency oscillations of $R$ -- scalarons, which later decay to pairs of all particles and antiparticles, with the amount of primordial scalar (density) perturbations required by observations. The stable version is a genuine generic attractor, so there is no exit from it. We discuss a possible transition from stable to unstable phases of inflation. It is shown that this transition is automatic if the sharp cut-off approximation is assumed for quantum corrections in the period of transition. Furthermore, we describe two different quantum mechanisms that may provide a required large $\,R^2$-term in the transition period.

hep-th↗

arXiv2016

Non-local form factors for curved-space antisymmetric fields

In the recent paper Buchbinder, Kirillova and Pletnev presented formal arguments concerning quantum equivalence of free massive antisymmetric tensor fields of second and third rank to the free Proca theory and massive scalar field with minimal coupling to gravity, respectively. We confirm this result using explicit covariant calculations of non-local form factors based on the heart-kernel technique, and discuss the discontinuity of quantum contributions in the massless limit.

hep-th↗

arXiv2016

On the conformal properties of topological terms in even dimensions

Conformal properties of the topological gravitational terms in $D=2$, $D=4$ and $D=6$ are discussed. It is shown that in the last two cases the integrands of these terms, when being settled into the dimension $D-1$ and multiplied by a scalar, become conformal invariant. Furthermore we present a simple covariant derivation of the Paneitz operator in $D=4$ and formulate two general conjectures concerning the conformal properties of topological structures in even dimensions.

gr-qc↗

arXiv2016

Superrenormalizable quantum gravity with complex ghosts

We suggest and briefly review a new sort of superrenormalizable models of higher derivative quantum gravity. The higher derivative terms in the action can be introduced in such a way that all the unphysical massive states have complex poles. According to the literature on Lee-Wick quantization, in this case the theory can be formulated as unitary, since all massive ghosts-like degrees of freedom are unstable.

hep-th↗

arXiv2016

Tensor instabilities at the end of the LCDM universe

The unphysical spin-2 massive degrees of freedom in higher derivative gravity may be either massive unphysical ghosts or tachyonic ghosts. In the last case there is no Planck-scale threshold protecting vacuum cosmological solutions from instabilities. Within the anomaly-induced action formalism the photon-driven IR running of the coefficient of the Weyl-squared term makes the ghost eventually becoming tachyon, that should produce a gravitational explosion of vacuum. This effect is stable under higher loop corrections and takes place also in known versions of perturbative quantum gravity. However, the contribution of massless fields in the far IR are not the same in flat and de~Sitter spaces. In the asymptotically deSitter case one can observe a kind of IR decoupling, which protects the cosmological solution from the future tachyonic instabilities.

gr-qc↗