Finite quantum gravity in dS and AdS spacetimes

Abstract

We hereby study the properties of a large class of weakly nonlocal gravitational theories around the (anti-) de Sitter spacetime background. In particular, we explicitly prove that the kinetic operator for the graviton field has the same structure as the one in Einstein-Hilbert theory around any maximally symmetric spacetime. Therefore, the perturbative spectrum is the same of standard general relativity, while the propagator on any maximally symmetric spacetime is a mere generalization of the one from Einstein's gravity derived and extensively studied in several previous papers. At quantum level the range of theories here presented is superrenormalizable or finite when proper (non affecting the propagator) terms cubic or higher in curvatures are added. Finally, it is proven that for a large class of nonlocal theories, which in their actions do involve neither the Weyl nor the Riemann tensor, the theory is classically equivalent to the Einstein-Hilbert one with cosmological constant by means of a metric field redefinition at any perturbative order.

24 pages, final version with journal corrections

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• Non-Gaussianities and tensor-to-scalar ratio in non-local $R^2$-like inflation
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• Non-unitarity of Minkowskian non-local quantum field theories
• Black-hole stability in non-local gravity
• Non-local self-healing of Higgs inflation
• Generalized non-local $R^2$-like inflation
• Renormalization Group in Six-derivative Quantum Gravity
• The Higgs mechanism in nonlocal field theory
• Unattainability of the Trans-Planckian regime in Nonlocal Quantum Gravity
• Introduction to Quantization of Conformal Gravity
• Infrared behavior of Weyl Gravity: Functional Renormalization Group approach
• Visions in Quantum Gravity
• On the causality properties in non-local gravity theories
• Cosmology in nonlocal gravity
• Confining complex ghost degrees of freedom
• New massless and massive infinite derivative gravity in three dimensions
• Dark side of Weyl gravity
• Spectral action approach to higher derivative gravity
• Quantum avoidance of Gödel's closed timelike curves
• Nonlocal Scalar Quantum Field Theory: Functional Integration, Basis Functions Representation and Strong Coupling Expansion
• Nonlocal Fractional Quantum Field Theory and Converging Perturbation Series
• Ultraviolet Finiteness or Asymptotic Safety in Higher Derivative Gravitational Theories
• Propagators in AdS for higher-derivative and nonlocal gravity: Heat kernel approach
• Strict renormalizability as a paradigm for fundamental physics
• The stability of the de-Sitter universe in nonlocal gravity
• A novel nonlocal spin-1/2 theory: classical and quantum aspects
• Tree-level scattering amplitudes in nonlocal field theories