Space-Folding Bounce Cosmology Without Ghost: A R^2-Corrected Non-Singular Origin of the Big Bang

Abstract

The standard \LambdaCDM cosmological model inevitably encounters a spacetime singularity when extrapolated backward in time, where the scale factor a \to 0, density \rho \to \infty, and general relativity breaks down. While the Penrose-Hawking singularity theorems formalize this breakdown, they do not specify what physical mechanism replaces the singularity. Previous bounce models attempting to resolve this issue often rely on phantom scalar fields with negative kinetic energy, which introduce fatal ghost instabilities at the quantum level. In this work, we propose a ghost-free Space-Folding Bounce Model that eliminates the Big Bang singularity through a classical elastic rebound mechanism without invoking phantom fields or ad hoc quantum gravity inputs. The central hypothesis is that three-dimensional space possesses a foldable, elastic degree of freedom described by a canonical (positive-kinetic) scalar field \phi — the folding field — coupled to R^2 modified gravity. The action is constructed as S = \int d^4x\sqrt{-g}\left[\frac{M_{\rm Pl}^2}{2}\left(R + \frac{R^2}{6\rho_c}\right) + \frac{1}{2}\partial_\mu\phi\partial^\mu\phi - V_{\rm fold}(\phi)\right], where the saturating potential V_{\rm fold}(\phi) = V_0 + V_{\max}[1-(1+\phi/\phi_c)^{-\alpha}] encodes the finite compressibility of space. We demonstrate that: (i) the folding field has strictly positive energy density \rho_\phi = \frac{1}{2}\dot\phi^2 + V \ge 0, thereby evading ghost instabilities; (ii) the bounce occurs at finite a_{\min} > 0 driven by geometric corrections from R^2 terms, with H=0 and \ddot{a}/a > 0; (iii) the strong energy condition is violated by the effective total stress-energy at the bounce point; (iv) numerical integration of the coupled field equations with constraint-projected initial conditions confirms smooth solutions crossing the bounce with all physical quantities finite. The model reduces to standard \LambdaCDM in the low-folding limit \phi \to 0, with residual potential V_0 providing an effective cosmological constant. Observable predictions include a spectral index n_s \approx 0.964, tensor-to-scalar ratio r \approx 0.03, and local-type primordial non-Gaussianity f_{\rm NL}^{\rm local} \sim \mathcal{O}(1) — a characteristic fingerprint distinguishable from single-field slow-roll inflation. This model offers a complete, ghost-free, and observationally testable alternative to the singular Big Bang paradigm. AI Statement The theoretical framework, derivations, and numerical computations in this work were carried out by the authors. Large language model (LLM) tools were used to assist with text polishing, formula formatting, and code implementation. All results and conclusions have been independently verified and are the sole responsibility of the authors.