Condensed Tensor-Fabric Framework: Preliminary Spectrum Analysis of an Emergent Gravity Model

This preprint introduces a preliminary emergent-gravity framework based on a symmetric rank-2 tensor fabric field. In this alternative approach, macroscopic spacetime geometry is modeled as an effective manifestation of underlying tensor-fabric dynamics rather than a fundamental geometric background. By introducing a spontaneous vacuum condensate background, the fundamental field is decomposed into tensor, vector, and scalar excitation sectors.

The framework is analyzed at the quadratic level using a Fierz–Pauli-inspired kinetic structure combined with a symmetry-breaking potential. Preliminary spectrum analysis indicates the existence of massless tensor excitations alongside a massive scalar sector generated directly through the condensate formation.

As a foundational and preliminary theoretical framework, this work explicitly outlines open technical areas for future research, including a full Barnes–Rivers projector decomposition, exact propagator construction, rigorous degree-of-freedom counting, and ghost analysis