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.