Super-renormalizable or finite completion of the Starobinsky theory

Abstract

The recent Planck data of Cosmic Microwave Background (CMB) temperature anisotropies support the Starobinsky theory in which the quadratic Ricci scalar drives cosmic inflation. We build up a multi-dimensional quantum consisted ultraviolet completion of the model in a phenomenological "bottom-up approach". We present the maximal class of theories compatible with unitarity and (super-)renormalizability or finiteness which reduces to the Starobinsky theory in the low-energy limit. The outcome is a maximal extension of the Krasnikov-Tomboulis-Modesto theory including an extra scalar degree of freedom besides the graviton field. The original theory was afterwards independently discovered by Biswas-Gerwick-Koivisto-Mazumdar starting from first principles. We explicitly show power counting super-renormalizability or finiteness (in odd dimensions) and unitarity (no ghosts) of the theory. Any further extension of the theory is non-unitary confirming the existence of at most one single extra degree of freedom, the scalaron. A mechanism to achieve the Starobinsky theory in string (field) theory is also investigated at the end of the paper.

Asymptotically safe inflation from quadratic gravity

“…k 2 ∼ R (see also [41]). In a recent investigation a similar approach has been successfully applied to study the quantum gravity modifications of the Starobinsky model [42] (see also [43][44][45][46][47][48] for other examples of quantum deformed quadratic gravity inflationary models).…”

Finite entanglement entropy of black holes

“…In fact, the surface term of the effective action, which gives the area term of the conical entropy, will in general receive UV-divergent contributions which are gauge dependent and negative (in particular from gauge vector bosons and gravitons [8]). However, in the context of super-renormalizable gravitational theories [9][10][11][12][13][14][15][16][17][18][19][20][21][22], the beta functions are known to be gauge independent and furthermore they are completely determined at one loop [23]. On top of this, it has been explicitly shown in Ref.…”

“…The detailed reference about unitarity, superrenormalizability, and UV-finiteness issues in non-local theories around the Minkowski spacetime can be found in [9][10][11][12][13][14][15][16][17][18][19][20][21][22]49,50]. Moreover, recently it has been proved that a slight modification of the theory is stable around any maximally symmetric spacetime [57][58][59].…”

“…The most general D-dimensional theory weakly non-local (or quasi-local) and quadratic in the Riemann curvature reads [9][10][11][12][13][14][15][16][17][18][19][20][21][22][49][50][51],…”

“…In section II we briefly introduce a class of weakly non-local theories of gravity, which are unitary (ghost-free) and perturbatively super-renormalizable or finite in the quantum field theory framework [9][10][11][12][13][14][15][16][17][18][19][20][21][22]. At classical level evidences endorse that we are dealing with "singularity-free gravitational " the-ories [33][34][35][36][37][38][39][40][41] (see also the recent papers [42,43]).…”