The Primary Particle Hypothesis: Quantitative Formulation of the Pre-Geometric Transition and Its Expected Cosmological Signatures

The Primary Particle Hypothesis (PPH) proposes that the emergence of spacetime and its perturbative structure originates from a dynamical transition involving a fundamental, short-lived object, the primary particle, defined within a pre-spacetime domain termed the quantized velocity space. In this framework, the inception of the universe is described not as a singularity, but as a transition from a non-expanding, flat background into an effective cosmological phase governed by standard relativistic dynamics. This paper provides a self-contained quantitative formulation of the PPH, consolidating and extending a series of conceptual developments from previous works. We introduce a heuristic pre-geometric Lagrangian to describe the collective dynamics of primordial particles in the pre-spacetime phase. Focusing on the cosmological implications, we derive leading-order predictions for the scalar and tensor power spectra generated during this pre-geometric transition. Explicit expressions for the scalar spectral index ( n s ) and the tensor-to-scalar ratio ( r ) are obtained as functions of the model’s fundamental parameters, including the quantized velocity increment ( ε ), which is intrinsically linked to the Planck mass and the total mass of the universe. These results provide testable signatures for current and forthcoming Cosmic Microwave Background (CMB) experiments, offering a theoretical alternative to the standard inflationary paradigm.