Bootstrap Origin without Singularity: Emergent Spacetime from a Discrete Conserved Network
Recognition Science, Recognition Physics Institute — Austin, Texas, USA
Summary
A singularity‑free origin: spacetime emerges from a discrete, conserved adjacency network. Minimal update‑cost selects an \(\\alpha\)‑attractor with \(\\alpha=\\varphi^2\), yielding standard slow‑roll predictions with two parameter‑free signatures: a log‑periodic modulation (cadence‑fixed) and a UV softening at \(\\lambda_{\\*}=L_P/\\sqrt{\\pi}\).
Abstract
We present a singularity‑free origin scenario in which spacetime emerges from a discrete, conserved adjacency network. Exact conservation enforces double‑entry balance and coarse‑grains to the standard continuity equation, while a minimal update‑cost principle selects an \(\\alpha\)‑attractor potential with \(\\alpha=\\varphi^2\). The resulting dynamics reproduce slow‑roll predictions for \(n_s\) and \(r\), and add two parameter‑free signatures: a log‑periodic modulation with cadence fixed by the network microperiod, and an ultraviolet softening at a closure extremum length \(\\lambda_{\\*}=L_P/\\sqrt{\\pi}\). The onset of macroscopic spacetime is an emergent‑metric phase transition that percolates the network and fixes \(c=\\ell_0/\\tau_0\). We quantify the comoving position of the spectral knee, the log‑modulation frequency and amplitude in light of current CMB/LSS bounds, and outline an EFT CP sector that yields the observed baryon asymmetry without additional mass scales. All scales and amplitudes descend from \((c,\\hbar,G)\), making the predictions directly testable with forthcoming CMB, large‑scale‑structure, and gravitational‑wave data.
Key Points
- Emergent spacetime, no singularity: Discrete conserved network with double‑entry closure and continuity.
- \(\\alpha\)‑attractor (fixed): Minimal cost selects \(\\alpha=\\varphi^2\); standard slow‑roll predictions for \(n_s\) and \(r\).
- Parameter‑free signatures: Cadence‑locked log‑periodic modulation; UV softening at \(\\lambda_{\\*}=L_P/\\sqrt{\\pi}\).
- R0 phase transition: Emergent‑metric percolation sets \(c=\\ell_0/\\tau_0\); scales descend from \((c,\\hbar,G)\).
- Baryogenesis: EFT CP sector yields observed asymmetry without new mass scales.