Gravity from Pre-geometry

Abstract: The gravitational interaction, as described by the Einstein-Cartan theory, is shown to emerge as the by-product of the spontaneous symmetry breaking of a gauge symmetry in a pre-geometric four-dimensional spacetime. Starting from a formulation `a la Yang-Mills on an SO(1,4) or SO(3,2) principal bundle and not accounting for a spacetime metric, the Einstein-Hilbert action is recovered after the identification of the effective spacetime metric and spin connection for the residual SO(1,3) gauge symmetry of the spontaneously broken phase - i.e. the stabiliser of the SO(1,4) or SO(3,2) gauge group. Thus, the two fundamental tenets of General Relativity, i.e. diffeomorphism invariance and the equivalence principle, can arise from a more fundamental gauge principle. The two mass parameters that characterise Einstein gravity, namely the Planck mass and the cosmological constant, are likewise shown to be emergent, with the correct sign for the cosmological constant depending on whether the fundamental gauge group is taken to be either the de Sitter or the anti-de Sitter group. The phase transition from the unbroken to the spontaneously broken phase is expected to happen close to the Planck temperature. This is conjectured to be dynamically driven by a scalar field that implements a Higgs mechanism, hence providing mass to new particles, with consequences for cosmology and high-energy physics. The couplings of gravity to matter are discussed after drawing up a dictionary that interconnects pre-geometric and effective geometric quantities. In the unbroken phase where the fundamental gauge symmetry is restored, the theory is potentially power-counting renormalisable without matter, offering a novel path towards a UV completion of Einstein gravity.

• The paper establishes that gravity can be viewed as an emergent phenomenon arising from underlying pre-geometric structures rather than a fundamental force.
• It explores theoretical models in which spacetime geometry is not primary but develops from more basic, often quantum, states.
• The study challenges traditional gravitational theories, suggesting new avenues for quantum gravity research and refined computational models.

"Gravity from Pre-geometry" is a concept in theoretical physics that aims to describe gravity not as a fundamental force but as an emergent phenomenon arising from more fundamental pre-geometric conditions. This approach often involves exploring models where spatiotemporal geometry itself is not primary but emerges from more basic principles or structures.

While the papers provided do not directly address "Gravity from Pre-geometry," they cover a range of studies involving gravity in diverse contexts. Here's an overview highlighting the concept's relevance and drawing parallels where applicable:

1. Trajectory Optimization: The paper on multiple gravity-assist trajectories (Vasile et al., 2011) discusses optimizing space missions using gravity assists, although it is more focused on practical applications within the traditional geometric framework of space travel.
2. Social Gravity in Graph Drawing: Another paper introduces "social gravity" for visualizing graph layouts by assigning mass to vertices based on network centrality (Bannister et al., 2012). While this involves a metaphorical use of gravity, it's outside the scope of pre-geometric theories.
3. Gravity in Camera Systems: Several papers discuss the practical application of gravity in computational problems, such as pose estimation (Ding et al., 2020), height estimation from video (Bieler et al., 2019), and panoramic image stitching (Ding et al., 2020). These utilize gravity as a reference within the geometric context but do not explore pre-geometric theories of gravity.
4. Computational Models of Gravity: The research on scalable forward models for computing gravity anomalies (May et al., 2011) presents sophisticated computational approaches to traditional gravitational problems, but again, this is within a recognized geometric and physical context.

In summary, while these papers provide a broad spectrum of applications and studies involving gravity, they do not specifically address the idea of gravity emerging from pre-geometric concepts. For a comprehensive understanding of "Gravity from Pre-geometry," one would typically look into theoretical physics literature, particularly in fields like quantum gravity, where researchers explore how spacetime itself might arise from more fundamental discrete structures or quantum states.