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 as 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 presented here is superrenormalizable or finite when proper (not 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 a cosmological constant by means of a metric field redefinition at any perturbative order.
Highlights
In previous studies it has been extensively shown that a class of weakly nonlocal theories of gravity is unitary and perturbatively superrenormalizable or finite in the framework of quantum field theory [1,2,3,4,5,6,7,8,9,10,11]
To summarize the content of this section, we proved that the Einstein-Hilbert-Λcc theory (EH-Λ) and nonlocal gravity with the presence of a cosmological constant term are equivalent at the perturbative level
In the previous sections we have proved that the equations of motion (EOM) for both the theories, EH-Λ and nonlocal gravity, have the same solutions at the linear order in the gravitational perturbation, and, we inferred that the two theories have the same perturbative spectrum
Summary
In previous studies it has been extensively shown that a class of weakly nonlocal theories of gravity is unitary (ghost-free) and perturbatively superrenormalizable or finite in the framework of quantum field theory [1,2,3,4,5,6,7,8,9,10,11] These works mostly concentrated on the perturbative theory around the flat Minkowski spacetime. For one out of the two classes of theories, which we extensively study in this paper, we prove by the means of a field redefinition that at the perturbative level, but to all perturbative orders in the field redefinition, the nonlocal action is classically equivalent to the Einstein-Hilbert one in the presence of a cosmological constant. Most of the results obtained in this paper can be exported to Lee-Wick gravitational theories [35,36,37,38,39,40] just by replacing the nonlocal form factors with appropriate polynomials
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