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 Hn4. 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, truncated at n. 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.
Highlights
The proper formulation of gravity as a quantum theory is a long-standing and controversial problem
It is plausible that the starting point of such a quantum theory could be very different from general relativity (GR), but GR should be approximately recovered at macroscopic scales, in the sense of an effective theory
Our objective is to find a suitable background space-time solution of the IKKT matrix model, which leads to the desired low-energy physics including gravity
Summary
The proper formulation of gravity as a quantum theory is a long-standing and controversial problem. It is plausible that the starting point of such a quantum theory could be very different from general relativity (GR), but GR should be approximately recovered at macroscopic scales, in the sense of an effective theory With this in mind, we choose the framework of matrix models of Yang-Mills type as a starting point. To avoid the dangerous UV/IR mixing which typically arises on non-commutative spaces [2], one is led to the maximally supersymmetric IKKT or IIB model [3], where UV/IR mixing is sufficiently mild.1 This model can be viewed as a constructive definition of IIB string theory, and it exhibits a rich set of brane-type solutions, such as [7,8,9,10,11,12] to mention only a few. Recent numerical simulations of the model [12,13,14,15] provide evidence that a 3+1-dimensional structure arises at the non-perturbative level
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