Abstract:We discuss some properties of recently proposed models of a ghost-free gravity. For this purpose we study solutions of linearized gravitational equations in the framework of such a theory. We mainly focus on the version of the ghost-free theory with the exponential modification exp( /µ 2 ) −1 of the free propagator. The following three problems are discussed: (i) gravitational field of a point mass; (ii) Penrose limit of a point source boosted to the speed of light; and (iii) spherical gravitational collapse of null fluid. For the first problem we demonstrate that it can be solved by using the method of heat kernels and obtain a solution in a spacetime with arbitrary number of dimensions. For the second problem we also find the corresponding gyraton-type solutions of the ghost-free gravitational equations for any number of dimensions. For the third problem we obtain solutions for the gravitational field for the collapse of both "thin" and "thick" spherical null shells. We demonstrate how the ghost-free modification of the gravitational equations regularize the solutions of the linearized Einstein equations and smooth out their singularities.

Abstract:We consider the problem of Newtonian singularity in the wide class of higher derivative gravity models, including the ones which are renormalizable and superrenormalizable at the quantum level. The simplest version of the singularity-free theory has four derivatives and is pretty well-known. We argue that in all cases of local higherderivative theories, when the poles of the propagator are real and simple, the singularities disappear due to the cancelation of contributions from scalar and tensor massive modes.

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It is shown that polynomial gravity theories with more than four derivatives in each scalar and tensor sectors have a regular weak-field limit, without curvature singularities. This is achieved by proving that in these models the effect of the higher derivatives can be regarded as a complete regularization of the delta-source. We also show how this result implies that a wide class of non-local ghost-free gravities has a regular Newtonian limit too, and discuss the applicability of this approach to the case of weakly non-local models.1 We use the same sign conventions as [10]. Also, we set c = = 1. 2 That is, we shall consider non-local gravity models which are extensions of GR in the UV-limit, which means that for large momentum the propagator decays faster than in GR. Specifically, we require that f 0 (z) and f 2 (z) (defined in (3) and (4)) are constant or diverge at least linearly as z −→ ∞, and that f s (0) = 1. Owed to this improved behaviour in the UV, sometimes these models are called non-local HDG. The situation is quite different from non-local IR modifications of GR, such as those defined by form factors of the type F i ∝ ✷ −1 and F i ∝ ✷ −2 [24-26], or the logarithmic ones, F i ∝ ln ✷, which come from the integration of quantum matter fields in curved space-time [27][28][29][30][31].

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 × 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.

In the present work we show that, in the linear regime, gravity theories with more than four derivatives can have remarkable regularity properties if compared to their fourth-order counterpart. To this end, we derive the expressions for the metric potentials associated to a pointlike mass in a general higher-order gravity model in the Newtonian limit. It is shown that any polynomial model with at least six derivatives in both spin-2 and spin-0 sectors has regular curvature invariants. We also discuss the dynamical problem of the collapse of a small mass, considered as a spherical superposition of nonspinning gyratons. Similarly to the static case, for models with more than four derivatives the Kretschmann invariant is regular during the collapse of a thick null shell. We also verify the existence of the mass gap for the formation of mini black holes even if complex and/or degenerate poles are allowed, generalizing previous considerations on the subject and covering the case of Lee-Wick gravity. These interesting regularity properties of sixth-and higher-derivative models at the linear level reinforce the question of whether there can be nonsingular black holes in the full nonlinear model. MSC: 53B50, 83D05, PACS: 04.20.-q, 04.50.Kd

The investigation of UV divergences is a relevant step in better understanding of a new theory. In this work the one-loop divergences in the free field sector are obtained for the popular Galileons model. The calculations are performed by the generalized Schwinger-DeWitt technique and also by means of Feynman diagrams. The first method can be directly generalized to curved space, but here we deal only with the flat-space limit. We show that the UV completion of the theory includes the $\pi \Box^4\pi$ term. According to our previous analysis in the case of quantum gravity, this means that the theory can be modified to become superrenormalizable, but then its physical spectrum includes two massive ghosts and one massive scalar with positive kinetic energy. The effective approach in this theory can be perfectly successful, exactly as in the higher derivative quantum gravity, and in this case the non-renormalization theorem for Galileons remains valid in the low-energy region.Comment: One more section after Conclusions, including one extra reference, all concerning generalized second-derivative metric-scalar model. Version accepted in Physics Letters B. LaTeX, 19 pages, 5 figure

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.