Starobinsky–Bel–Robinson Gravity

Abstract

A novel string-inspired gravitational theory in four spacetime dimensions is proposed as a sum of the modified (R+αR2) gravity motivated by the Starobinsky inflation and the leading Bel–Robinson-tensor-squared correction to the gravitational effective action of superstrings/M-theory compactified down to four dimensions. The possible origin of the theory from higher dimensions is revealed. The proposed Starobinsky–Bel–Robinson action has only two free parameters, which makes it suitable for verifiable physical applications in black hole physics, cosmological inflation and Hawking radiation.

On the superstring-inspired quantum correction to the Starobinsky model of inflation

“…The P 2 4 term does not contribute to the evolution equations in a spatially flat FLRW universe, so that the action JCAP12(2022)032 reduces to the particular case of the F (R, G) modified gravity on the FLRW background. Remarkably, the positivity of the new parameter β is a necessary condition for cosmological viability of the Einstein-Gauss-Bonnet models [34], while it is also a consequence of the origin of the Bel-Robinson tensor squared term from superstrings [30].…”

“…Since any viable inflationary model in modified gravity has to have the R 2 -term [7], the improved Starobinsky-Bel-Robinson (SBR) modified gravity action in four dimensions was proposed in ref. [30] by combining the R 2 and the BR tensor squared terms. Assuming that string dilaton and axion are stabilized, we can ignore their kinetic terms and keep only their mass terms, while the linear coupling of dilaton and axion to gravity in string theory is known via the Euler density and the Pontryagin density, respectively, in the leading approximation.…”

“…where µνλρ is the constant Levi-Civita symbol from Minkowski (flat) spacetime. The SBR gravity action is defined by [30] S…”

“…The constant β used here is different from the β parameter of ref [30]. by its normalization and sign.…”

“…by its normalization and sign. In the context of superstrings and M-theory[30], the constant β must be positive.…”