Super-renormalizable Quantum Gravity

By L. Modesto. 2011

502 citations recorded by the source corpus.

In this paper we study perturbatively an extension of the Stelle higher derivative gravity involving an infinite number of derivative terms. We know that the usual quadratic action is renormalizable but suffers of the unitarity problem because of the presence of a ghost (state of negative norm) in the theory. The new theory is instead ghost-free since the introduction of (in general) two entire functions in the model with the property do not introduce new poles in the propagator. The local high derivative theory is recovered expanding the entire functions to the lowest order in the mass scale of the theory. Any truncation of the entire functions gives rise to the unitarity violation but if we keep all the infinite series we do not fall into these troubles. The theory is renormalizable at one loop and finite from two loops on. Since only a finite number of graphs are divergent then the theory is super-renormalizable. We analyze the fractal properties of the theory at high energy showing a reduction of the spacetime dimension at short scales. Black hole spherical symmetric solutions are also studied omitting the high curvature corrections in the equation of motions. The solutions are regular and the classical singularity is replaced by a "de Sitter-like core" in r=0. Black holes may show a "multi-horizon" structure depending on the value of the mass.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/217e9a0617eff1bba040ed4d5e96e969f99fd6bb

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Citations in the corpus

Dark Energy in Light of Multi-Messenger Gravitational-Wave Astronomy (2018, unknown): “Non-local interactions have been also proposed as a means to improve the ultra-violet behavior of gravity (Biswas et al., 2012; Modesto, 2012; Calcagni and Modesto, 2015).”
Notes on nonsingular models of black holes (2016, unknown): “[8] Leonardo Modesto, “Super-renormalizable Quantum Gravity,” Phys.”
Occurrence of exact R2 inflation in non-local UV-complete gravity (2016, background): “These operators scale as the propagator giving the following upper bound on the superficial degree of divergence d of any graph G [19], d(G) = DL+ (V − I)(2γ +D) (2.”
Towards understanding the ultraviolet behavior of quantum loops in infinite-derivative theories of gravity (2014, background): “In fact, a naive superficial divergence counting does suggest t hat diagrams with more than one loop should be finite [30, 31].”