Renormalizable and Unitary Model of Quantum Gravity

• Main Author: S. A. Larin
• Format: Article
• Language: English
• Published: MDPI AG 2019-10-01
• Series: Symmetry
• Subjects: modified theories of gravity; quantum gravity; renormalizability; unitarity
• Online Access: https://www.mdpi.com/2073-8994/11/11/1334

We consider <inline-formula> <math display="inline"> <semantics> <mrow> <mi>R</mi> <mo>+</mo> <msup> <mi>R</mi> <mn>2</mn> </msup> </mrow> </semantics> </math> </inline-formula> relativistic quantum gravity with the action where all possible terms quadratic in the curvature tensor are added to the Einstein-Hilbert term. This model was shown to be renormalizable in the work by K.S. Stelle. In this paper, we demonstrate that the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>R</mi> <mo>+</mo> <msup> <mi>R</mi> <mn>2</mn> </msup> </mrow> </semantics> </math> </inline-formula> model is also unitary contrary to the statements made in the literature, in particular in the work by Stelle. New expressions for the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>R</mi> <mo>+</mo> <msup> <mi>R</mi> <mn>2</mn> </msup> </mrow> </semantics> </math> </inline-formula> Lagrangian within dimensional regularization and the graviton propagator are derived. We demonstrate that the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>R</mi> <mo>+</mo> <msup> <mi>R</mi> <mn>2</mn> </msup> </mrow> </semantics> </math> </inline-formula> model is a good candidate for the fundamental quantum theory of gravity.