A Singularity-FreeEmergent Cosmology from the B-Project: Effective Einstein Dynamics with a Modular–Informational Equation of State

ABSTRACT We present a complete, singularity-free cosmological scenario emerging within standard Einstein gravity from the B-Project framework. The early-universe dynamics is described by an effective Einstein–Friedmann cosmology in which a modular– informational sector contributes to the total stress–energy tensor and can be consistently encoded as an effective fluid with a scale-factor-dependent equationof state 𝑤Ω(𝑎). Using a fully tabulated equation of state derived from the B-Project dynamics, we reconstruct the background evolution and show that all reconstructed background quantities remain finite and smooth over the numerical domain 𝑎 ∈ [𝑎min,1], with 𝑎min∼10−6. The model interpolates smoothly between a stiff early-time regime (𝑤Ω ≃1) and a late-time vacuum-like regime (𝑤Ω ≃−1), whileremainingboundedat alltimes. The resulting cosmology violates the strong energy condition over an extended epoch, thereby evading the assumptions of theHawking–PenrosesingularitytheoremswithoutmodifyingGeneralRelativity.AnexplicitreconstructionoftheHubblerate showsthat 𝐻(𝑎)remainsstrictlypositiveanddoesnotexhibitaclassicalbounce,sothescenarioisbestinterpretedasaregular emergentcosmology rather than acontraction–expansion transition. The model is implemented numerically using the Boltzmann solver CAMB, demonstrating full compatibility with standard cosmological pipelines. At late times the scenario is observationally indistinguishable from ΛCDM, while deviations are confinedtothe deep early universe,wherethey providea consistent, non-singular origin for cosmological evolution.摘要 本研究依托B-Project框架，在标准爱因斯坦引力理论下推导出一套完整且无奇点的宇宙学图景。早期宇宙动力学可通过有效爱因斯坦-弗里德曼宇宙学描述：其中模信息扇区对总能动量张量存在贡献，且可被一致编码为具有标度因子依赖状态方程𝑤_Ω(𝑎)的有效流体。 本研究采用基于B-Project动力学推导得到的全表格化状态方程，对宇宙学背景演化进行重构，结果显示所有重构得到的背景物理量在数值域𝑎 ∈ [𝑎_min, 1]内均保持有限且光滑，其中𝑎_min≈10^-6。该模型可在刚性早期演化阶段（𝑤_Ω≈1）与类真空晚期演化阶段（𝑤_Ω≈-1）之间实现光滑过渡，且全程物理量均有界。 该宇宙学模型在一段延展的时期内违背强能量条件，因此无需修改广义相对论即可规避霍金-彭罗斯奇点定理的前提假设。对哈勃速率的显式重构结果表明，𝐻(𝑎)始终严格为正，且未出现经典反弹现象，因此该宇宙学图景更适合被理解为正则涌现宇宙学，而非收缩-膨胀过渡模型。 本研究采用玻尔兹曼解算器CAMB对该模型进行数值实现，结果表明其与标准宇宙学分析流程完全兼容。在晚期宇宙中，该模型的观测特征与Λ冷暗物质（ΛCDM）模型完全无法区分，其偏差仅存在于极早期宇宙阶段，可为宇宙演化提供一套自洽且无奇点的起源解释。