New Insights into Gravity from Pre-geometric Theories

A recent paper titled "Gravity from Pre-geometry" by Andrea Addazi, Salvatore Capozziello, Antonino Marciano, and Giuseppe Meluccio explores the emergence of gravitational interaction through a novel theoretical framework. The authors propose that gravity can be understood as a consequence of spontaneous symmetry breaking in a pre-geometric four-dimensional spacetime, which does not initially account for a spacetime metric.

The study begins with a formulation akin to Yang-Mills theory on principal bundles associated with the SO(1,4) or SO(3,2) groups. Through this approach, the authors recover the Einstein-Hilbert action by identifying an effective spacetime metric and spin connection that arise from the residual gauge symmetry of the spontaneously broken phase. This work suggests that the foundational principles of General Relativity, such as diffeomorphism invariance and the equivalence principle, may emerge from a more fundamental gauge principle.

Additionally, the paper discusses the emergence of two mass parameters significant to Einstein's theory: the Planck mass and the cosmological constant. The authors indicate that the sign of the cosmological constant is contingent upon whether the fundamental gauge group is de Sitter or anti-de Sitter. They conjecture that a phase transition from an unbroken to a spontaneously broken phase occurs near the Planck temperature, potentially driven by a scalar field that implements a Higgs mechanism, thereby providing mass to new particles.

The implications of this research extend to both cosmology and high-energy physics, offering a new perspective on the interplay between gravity and matter. The findings may pave the way for a deeper understanding of gravitational phenomena and contribute to the ongoing quest for a unified theory of physics.

For further details, the paper can be accessed at arXiv:2409.02200.