# Covariant cosmological quantum space-time, higher-spin and gravity in the IKKT matrix model

## TL;DR

This paper presents a covariant quantum space-time model within the IKKT matrix framework that naturally incorporates higher-spin modes and gravity, offering a promising avenue for quantum gravity research.

## Contribution

It introduces a (3+1)-dimensional covariant quantum space-time with a Big Bounce cosmology derived from a fuzzy hyperboloid, and characterizes its higher-spin fluctuation spectrum including gravity.

## Key findings

- Includes a tower of higher-spin modes organized by SO(4,2) symmetry.
- Contains massless graviton and scalar modes propagating at the speed of light.
- Provides a gauge-invariant linearized Einstein-Hilbert action analog.

## Abstract

We discuss a $(3{+}1)$-dimensional covariant quantum space-time describing a FLRW cosmology with Big Bounce, obtained by a projection of the fuzzy hyperboloid $H^4_n$. This provides a background solution of the IKKT matrix model with mass term. We characterize the bosonic fluctuation spectrum, which consists of a tower of higher-spin modes. The modes are organized in terms of an underlying $SO(4,2)$ structure group, which is broken to the $SO(3,1)$ isometry of the background. The resulting higher-spin gauge theory includes all degrees of freedom required for gravity, and should be well suited for quantization. All modes propagate with the same speed of light, even though local boost invariance is not manifest. The propagating metric perturbation modes comprise those of a massless graviton, as well as a scalar mode. Gauge invariance allows to obtain the analog of the linearized Einstein-Hilbert action, which is expected to be induced upon quantization.