PREPRINT

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

Sergei V. Ketov, Ekaterina O. Pozdeeva, Sergey Yu. Vernov

Submitted on 2 November 2022

## Abstract

Superstring/M-theory is the theory of quantum gravity that can provide the UV-completion to viable inflation models. We modify the Starobinsky inflation model by adding the Bel-Robinson tensor ${T}^{\mu \nu \lambda \rho }$ squared term proposed as the leading quantum correction inspired by superstring theory. The $\left(R+\frac{1}{6{m}^{2}}{R}^{2}-\frac{\beta }{8{m}^{6}}{T}^{2}\right)$ model under consideration has two parameters: the inflaton mass $m$ and the string-inspired positive parameter $\beta$. We derive the equations of motion in the Friedmann-Lemaitre-Robertson-Walker universe and investigate its solutions. We find the physical bounds on the value of the parameter $\beta$ by demanding the absence of ghosts and consistency of the derived inflationary observables with the measurements of the cosmic microwave background radiation.

## Preprint

Comment: 22 pages, 5 figures, LaTeX

Subjects: General Relativity and Quantum Cosmology; Astrophysics - Cosmology and Nongalactic Astrophysics; High Energy Physics - Theory