arXiv subjects

Alexey S. Koshelev

Publications and source records attributed to Alexey S. Koshelev.

At least 19 recordsLinked to original sources

arXiv2026

Is there ghost and tachyon free bounce in UV complete gravity theory?

Analytic infinite derivative gravity theories provide a renormalizable and ghost-free description of gravity around covariantly constant backgrounds. These theories can have non-singular bouncing Universe solutions. In this paper we aim to address a question whether it is possible to realize a bouncing solution without the presence of a ghost or a tachyon instability in this framework. We perform a detailed analysis of degrees of freedom in $(1+3)$ formalism around Minkowski and de Sitter space-times. As a result it becomes clear that on a very general basis one cannot construct an instability free bounce without a negative cosmological constant. An analysis of known bouncing solutions in this model shows that an analyticity of higher derivative form factors in combination with solutions parameters result in the presence of a ghost radiation. Being motivated by the idea of resolving the cosmological singularity problem we proceed by analyzing scalar and tensor modes anyway. Scalar modes appear to not influence Cosmic Microwave Background observations at all, while tensor modes spectrum is computed and the corresponding implications are discussed.

gr-qc↗

arXiv2026

Cancellation of UV divergences in ghost-free infinite derivative gravity

We consider the most general covariant gravity action up to terms that are quadratic in curvature. These can be endowed with generic form factors, which are functions of the d'Alembert operator. If they are chosen in a specific way as an exponent of an entire function, the theory becomes ghost-free and renormalizable at the price of non-locality. Furthermore, according to power-counting arguments, if these functions grow sufficiently fast along the real axis, divergences may only appear at the first order in loop expansion. Using the heat kernel technique, we compute the one-loop logarithmic divergences in the ultraviolet limit and determine the conditions under which they vanish completely, apart from the Gauss--Bonnet term and a surface term, both of which can be neglected on a four-dimensional manifold without a boundary. We identify form factors both within the Tomboulis class and beyond it that lead to vanishing logarithmic divergences. The general expression for the one-loop beta functions of the dimensionless couplings in quadratic gravity with asymptotically monomial form factors is given.

hep-th↗

arXiv2026

Convergent sum of EFT corrections to Schwarzschild metric requires UV locality

Corrections to vacuum black hole solutions of general relativity (GR) are considered in an effective field theory (EFT) framework, perturbatively in EFT coefficients, focusing on the Schwarzschild solution of GR. We find dominant corrections to the Schwarzschild metric in all orders in the derivative expansion far away from the horizon. These corrections can be summed up in a closed form through EFT coefficients up to all orders in derivatives and to the second order in curvature. It occurs that such a summation is convergent only for localizable theories, making a direct connection between the graviton scattering amplitudes properties and the applicability of a perturbative treatment of an EFT of gravity. We further apply our results to logarithmic form-factors which appear in the 1-loop effective action for GR in four dimensions. We find out that the corresponding corrections to the Schwarzschild metric are stronger than those from the tree-level EFT operators. The developed framework can be extended to account for the corrections to the other BH solutions in GR, such as the Kerr metric.

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arXiv2025

Visions in Quantum Gravity

To deepen our understanding of Quantum Gravity and its connections with black holes and cosmology, building a common language and exchanging ideas across different approaches is crucial. The Nordita Program "Quantum Gravity: from gravitational effective field theories to ultraviolet complete approaches" created a platform for extensive discussions, aimed at pinpointing both common grounds and sources of disagreements, with the hope of generating ideas and driving progress in the field. This contribution summarizes the twelve topical discussions held during the program and collects individual thoughts of speakers and panelists on the future of the field in light of these discussions.

hep-th↗

arXiv2025

Energy conditions for regular black holes in EFT of gravity

As Einstein's gravity is a non-renormalizable theory, it can be a good description of physics only at the scales of energy or spacetime curvature below the Planck mass. Moreover, it requires the presence of an infinite tower of higher-derivative corrections, as required in the framework of effective field theory (EFT). Black holes, known to be vacuum solutions in Einstein's gravity, necessarily have singularities in the center, where both Einstein's gravity and low-energy EFT expansions break down. In this work, we address the question of whether, in the presence of matter, regular solutions looking like black holes from outside do exist. We show that the matter distribution supporting the regular black hole solution in the presence of Riemann tensor cube and Riemann tensor to the fourth power EFT corrections satisfies positivity of energy (also called weak energy condition, WEC) and null energy condition (NEC) everywhere outside the horizon. Unlike the case of singular solutions, the EFT description is also valid in the interior of such an object, given that the maximal curvature is bounded and does not exceed the cut-off scale. We found that in a wide range of parameters, WEC is satisfied inside the horizon, but NEC is violated inside the horizon in all cases.

gr-qc↗

arXiv2025

Cosmic inflation in non-perturbative quantum gravity

String field theory motivated infinite-derivative models lead to non-local gravity modifications which form a promising class of quantum gravity candidates. In this paper we investigate effects of non-locality on the three-point function (the bi-spectrum) during cosmic inflation. The study is done in an Einstein frame with an infinite-derivative scalar field Lagrangian minimally coupled to the Einstein-Hilbert term. A non-local generalization of the Mukhanov-Sasaki equation is derived. Infinite-derivative operators present in this equation lead to an appearance of infinitely many new background induced states in the perturbation spectrum during inflation with complex masses on top of a usual nearly massless inflaton. On contrary to a flat background such states can be classically stable in a de Sitter space-time. This helps preserving observational constraints on the scalar power-spectrum. We proceed by studying a particular configuration assuming that the generalized Mukhanov-Sasaki equation gives rise to an inflaton and one pair of new states with complex conjugate masses as perturbative degrees of freedom. The corresponding scalar bi-spectrum is computed numerically in squeezed and equilateral limits. We use the latest observational constraints on amplitude of the bi-spectrum $f_{NL}$ from Planck 2018 dataset as a guideline for possible values of masses of new emerging states. We find that $f_{NL}$ is non-trivially sensitive to the values of complex masses and this can reduce the parameter space of gravity modifications. In particular we find that the amplitude of the squeezed limit gets easily enhanced while of the equilateral limit can stay like in a local single-field model of inflation. We end up discussing open questions relevant for this class of models of inflation.

gr-qc↗

arXiv2024

Quasi-normal modes in non-perturbative quantum gravity

Non-pertrubative quantum gravity formulated as a unitary four-dimensional theory suggests that certain amount of non-locality, such as infinite-derivative operators, can be present in the action, in both cases of Analytic Infinite Derivative gravity and Asymptotically Safe gravity. Such operators lead to the emergence of Background Induced States on top of any background deviating from the flat spacetime. Quasi-normal modes (QNMs) corresponding to these excitations are analyzed in the present paper with the use of an example of a static nearly Schwarzschild black hole. We mainly target micro-Black Holes, given that they are strongly affected by the details of UV completion for gravity, while real astrophysical black holes can be well described in EFT framework. We find that frequencies of QNMs are deviating from those in a General Relativity setup and, moreover, that the unstable QNMs are also possible. This leads to the necessity of constraints on gravity modifications or lower bounds on masses of the stable micro-Black Holes or both.

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arXiv2024

Secondary Gravitational Waves in Non-local Starobinsky inflation

We show how infinite derivative modifications of gravity impact on the stochastic background of Gravitational Waves from early Universe. The generic property of the ghost-free theory fixed on Minkowski space-time is the emergence of an infinite number of complex mass states when other classical backgrounds are considered. These additional states are shown to enhance the power spectrum of scalar perturbations generated during inflation. Current and future space-based and terrestrial interferometers offer indirect testing methods for the infinite derivative gravity action, enabling the exploration of new parameter spaces. In particular, we identify unconventional blue-tilted Gravitational Wave spectra, presenting a novel approach for testing infinite derivative quantum gravity in the future.

gr-qc↗

arXiv2023

Non-perturbative Lee-Wick gauge theory: Towards Confinement and RGE with strong couplings

We consider a non-Abelian Lee--Wick gauge theory and discuss Becchi-Rouet-Stora-Tyutin (BRST) invariance. It contains fourth-order derivative as extensions of the kinetic term, leading to massive ghosts in the theory upon quantization. We particularly provide essential clues towards confinement conditions in strongly-coupled regimes, using the Kugo-Ojima approach, and obtain the $β-$functions in the non-perturbative regimes. This is achieved using a set of exact solutions of the corresponding local theory in terms of Jacobi elliptical functions. We obtain a similar $β-$function just as for the ordinary Yang-Mills theory but the main differences are that now, the cut-off arises naturally from the Lee-Wick heavy mass scales (M). We show that the fate of the ghosts is fixed in these regimes: they are no more the propagating degrees of freedom in the infrared (IR)-limit. As it also happens for the ordinary case, confinement is due to the non-Abelian nature of the theory. In the limit $M\rightarrow\infty $, one recovers the standard results for the local non-Abelian Yang-Mills theory.

hep-ph↗

arXiv2023

Generalized non-local $R^2$-like inflation

The $R^2$ inflation which is an extension of general relativity (GR) by quadratic scalar curvature introduces a quasi-de Sitter expansion of the early Universe governed by Ricci scalar being an eigenmode of d'Alembertian operator. In this paper, we derive a most general theory of gravity admitting $R^2$ inflationary solution which turned out to be higher curvature non-local extension of GR. We study in detail inflationary perturbations in this theory and analyse the structure of form-factors that leads to a massive scalar (scalaron) and massless tensor degrees of freedom. We argue that the theory contains only finite number of free parameters which can be fixed by cosmological observations. We derive predictions of our generalized non-local $R^2$-like inflation and obtain the scalar spectral index $n_s\approx 1-\frac{2}{N}$ and any value of the tensor-to-scalar ratio $r<0.036$. In this theory, tensor spectral index can be either positive or negative $n_t\lessgtr 0$ and the well-known consistency relation $r = -8n_t$ is violated in a non-trivial way. We also compute running of the tensor spectral index and discuss observational implications to distinguish this model from several classes of scalar field models of inflation. These predictions allow us to probe the nature of quantum gravity in the scope of future CMB and gravitational wave observations. Finally we comment on how the features of generalized non-local $R^2$-like inflation cannot be captured by established notions of the so-called effective field theory of single field inflation and how we must redefine the way we pursue inflationary cosmology.

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arXiv2023

Non-Gaussianities in generalized non-local $R^2$-like inflation

In [1], a most general higher curvature non-local gravity action was derived that admits a particular $R^2$-like inflationary solution predicting the spectral index of primordial scalar perturbations $n_s(N)\approx 1-\frac{2}{N}$, where $N$ is the number of e-folds before the end of inflation, $N\gg 1$, any value of the tensor-to-scalar ratio $r(N)<0.036$ and the tensor tilt $n_t(N)$ violating the $r= -8n_t$ condition. In this paper, we compute scalar primordial non-Gaussianities (PNGs) in this theory and effectively demonstrate that higher curvature non-local terms lead to reduced bispectrum $f_{\rm NL}\left( k_1,\,k_2,\,k_3 \right)$ mimicking several classes of scalar field models of inflation known in the literature. We obtain $\vert f_{\rm NL}\vert \sim O(1-10)$ in the equilateral, orthogonal, and squeezed limits and the running of these PNGs measured by the quantity $\vert\frac{d\ln f_{\rm NL}}{d\ln k}\vert\lesssim 1$. Such PNGs are sufficiently large to be measurable by future CMB and Large Scale Structure observations, thus providing a possibility to probe the nature of quantum gravity. Furthermore, we demonstrate that the $R^2$-like inflation in non-local modification of gravity brings non-trivial predictions which go beyond the current status of effective field theories (EFTs) of single field, quasi-single field and multiple field inflation. A distinguishable feature of non-local $R^2$-like inflation compared to local EFTs is that we can have running of PNGs at least an order of magnitude higher. In summary, through our generalized non-local $R^2$-like inflation, we obtain a robust geometric framework of inflation that can explain any detection of observable quantities related to scalar PNGs.

hep-th↗

arXiv2023

Cosmology in nonlocal gravity

In this chapter we review the recent developments of realizing $R^2$-like inflation in the framework of a most general UV nonlocal extension of Einstein's general theory of relativity (GR). It is a well-motivated robust approach towards quantum gravity. In the past decades, nonlocal gravitational theories which are quadratic in curvature have been understood to be ghost-free and super-renormalizable around maximally symmetric spacetimes. However, in the context of early Universe cosmology we show that one must go beyond the quadratic curvature nonlocal gravity in order to achieve a consistent ghost-free framework of Universe evolution from quasi de Sitter to Minkowski spacetime. In this regard, we discuss a construction of a most general nonlocal gravity action that leads to $R^2$-like inflation and discuss the corresponding observational predictions for the scalar and tensor spectral tilts, tensor-to-scalar ratio, and the primordial non-Gaussianities. We present an analysis of how the nonlocal inflationary cosmology goes beyond the established notions of effective field theories of inflation. Finally, we comment on some open questions and prospects of higher curvature nonlocal gravity on its way of achieving the UV completion.

hep-th↗

arXiv2023

Confining complex ghost degrees of freedom

We show a theorem proving that a non-local bosonic field upon a covariant interaction with a confining gauge field undergoes the confinement of its degrees of freedom present in the free theory changing completely the physical mass spectrum following Kugo-Ojima criterion. This is applicable to an infinite number of excitations of the bosonic field including ghosts whereas we pay special attention to the modes with the complex conjugate masses, states appearing in the string field theory motivated infinite-derivative models. The same recipe will obviously work for the Lee-Wick models.

hep-th↗

arXiv2022

Post-inflationary GW production in generic higher (infinite) derivative gravity

Gravity can be embedded into a renormalizable theory by means of adding quadratic in curvature terms. However, this at first leads to the presence of the Weyl ghost. It is possible to get rid of this ghost if the locality assumption is weakened and the propagator of the graviton is represented by an entire function of the d'Alembertian operator without new poles and zeros. Models of this type admit a cosmological solution describing the $R^2$, or Starobinsky, inflation. We study graviton production after inflation in this model and show that it is negligible despite the presence of the higher derivative operators which could potentially cause instabilities.

hep-th↗

arXiv2022

Unitarity of Minkowski non-local theories made explicit

In this work we explicitly show that the perturbative unitarity of analytic infinite derivative (AID) scalar field theories can be achieved using a modified prescription for computing scattering amplitudes. The crux of the new prescription is the analytic continuation of a result obtained in the Euclidean signature to the Minkowski external momenta. We intensively elaborate an example of a non-local $ϕ^4$ model for various infinite derivative operators. General UV properties of amplitudes in non-local theories are discussed.

hep-th↗

arXiv2021

Non-local self-healing of Higgs inflation

Higgs inflation is known to be a minimal extension of the Standard Model allowing for the description of the early Universe inflation. This model is considered as an effective field theory since it has a relatively low cutoff scale, thus requiring further extensions to be a valid description of the reheating phase. We present a novel unified approach to the problem of unitarization and UV completion of the Higgs inflation model without introducing new massive degrees of freedom. This approach is based on an analytic infinite derivative modification of the Higgs field kinetic term. We construct a unitary non-local UV completion of the original Higgs inflation model while the inflationary stage is kept stable with respect to quantum corrections.

hep-th↗

arXiv2020

Analytic infinite derivative gravity, $R^2$-like inflation, quantum gravity and CMB

Emergence of $R^2$ inflation which is the best fit framework for CMB observations till date comes from the attempts to attack the problem of quantization of gravity which in turn have resulted in the trace anomaly discovery. Further developments in trace anomaly and different frameworks aiming to construct quantum gravity indicate an inevitability of non-locality in fundamental physics at small time and length scales. A natural question would be to employ the $R^2$ inflation as a probe for signatures of non-locality in the early Universe physics. Recent advances of embedding $R^2$ inflation in a string theory inspired non-local gravity modification provides very promising theoretical predictions connecting the non-local physics in the early Universe and the forthcoming CMB observations.

hep-th↗

arXiv2020

Non-Gaussianities and tensor-to-scalar ratio in non-local $R^{2}$-like inflation

In this paper we will study $R^2$-like inflation in a non-local modification of gravity which contains quadratic in Ricci scalar and Weyl tensor terms with analytic infinite derivative form-factors in the action. It is known that the inflationary solution of the local $R+R^2$ gravity remains a particular exact solution in this model. It was shown earlier that the power spectrum of scalar perturbations generated during inflation in the non-local setup remains the same as in the local $R+R^2$ inflation, whereas the power spectrum of tensor perturbations gets modified due to the non-local Weyl tensor squared term. In the present paper we go beyond 2-point correlators and compute the non-Gaussian parameter $f_{NL}$ related to 3-point correlations generated during inflation, which we found to be different from those in the original local inflationary model and scenarios alike based on a local gravity. We evaluate non-local corrections to the scalar bi-spectrum which give non-zero contributions to squeezed, equilateral and orthogonal configurations. We show that $f_{NL}\sim O(1)$ with an arbitrary sign is achievable in this model based on the choice of form-factors and the scale of non-locality. We present the predictions for the tensor-to-scalar ratio, $r$, and the tensor tilt, $n_t$. In contrast to standard inflation in a local gravity, here the possibility $n_t$>0 is not excluded. Thus, future CMB data can probe non-local behaviour of gravity at high space-time curvatures.

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