Unified covariant effective Big Beng cosmology: cyclic closure, stability, and an Einstein–Boltzmann benchmark

We present the fourth step of the Big Beng program, whose preceding papers separately establishedan effective cyclic background, a covariant nonsingular bounce construction, and a microscopic gaugeproductionchannel for contraction-side energy conversion. Here we consolidate those ingredientsinto a minimal renormalized effective architecture and test its low-density cosmological realizationin an Einstein–Boltzmann solver. The final candidate action contains Einstein gravity, a cuscutonconstraint sector, one canonical cyclic/EDE scalar φ, a Maxwell sector, and an axial interactionφF e F. The cyclic scalar potential combines the previously studied double-exponential EDE shapewith a positive late-time plateau and a bounded negative sech2 well. The final field content has twotensor polarizations, one propagating scalar, two transverse gauge helicities, and no independentcuscuton degree of freedom. The ekpyrotic tail has ceff = 10 and wek = 32.33, the reduced scalarkinetic coefficient remains positive on the audited final background, and finite-k mode amplification ismodest in the tested transition. A global background integration yields present acceleration, a futureturnaround, ekpyrotic contraction, a nonsingular bounce, gauge reheating, radiation domination,and a nonperiodic inter-cycle memory map.For the observational low-density branch we implement the full cyclic scalar potential in CLASSv3.3.4, where the high-density cuscuton correction is negligible. A clean benchmark gives a transientscalar fraction fmaxEDE = 0.0178871 at zc = 3799.93 while the same scalar today gives Ωφ,0 = 0.68941,wφ,0 = −0.98975, q0 = −0.52347, and Hphys0 = 68.042kms−1 Mpc−1. Using Planck-2018 low-ℓ TT,low-ℓ EE, high-ℓ TTTEEE-lite, and lensing likelihoods, matched BOBYQA profile minimizationsgive χ2CMB = 1008.9449 for the unified benchmark, compared with 1009.5735 for the old EDE controland 1010.9241 for the best matched ΛCDM control found in the same setup. These numbers areprofile benchmarks, not a posterior or Bayesian model-selection result. A complete MCMC analysisis deliberately deferred to a separate paper. The accompanying reviewer package contains the CLASSpatch, exact benchmark inputs, minimization YAML files, analytic audit data, figure-generationscripts, and validation scripts.