N_eff Constraints

The effective number of relativistic species N_eff parameterizes the total radiation energy density at the epoch of BBN and CMB decoupling beyond the photon contribution, conventionally normalized so that three massless neutrino species give N_eff = 3.044 (accounting for incomplete neutrino decoupling). Measurements from Planck CMB data give N_eff = 2.99 ± 0.17, consistent with the standard value, while BBN constraints from the helium-4 and deuterium abundances give N_eff values that are also broadly consistent but with uncertainties that allow for mild deviations at the level of ΔN_eff ~ 0.2–0.3. Any extra relativistic species — sterile neutrinos, dark radiation, early dark energy, or other light particles — would increase N_eff above 3.044 and leave detectable signatures in both BBN light element yields and CMB acoustic peak positions. Current data provides some tension hints toward N_eff slightly above the standard value, motivating searches for BSM relativistic species.

Successive Collision Theory predicts a small but physically determined contribution to N_eff beyond the standard neutrino value through two mechanisms, neither of which requires new particles. First, the gravitational superposition from overlapping nested comoving frames contributes an effective energy density to the total stress-energy tensor at all epochs, including the radiation-dominated era. This superposition energy density enters the Friedmann equation as an additional term that mimics extra radiation during BBN and CMB decoupling, producing an effective ΔN_eff at the level of a fraction of a relativistic species. The magnitude is set by the same superposition coefficient that explains the lensing amplitude excess and the helium-4 abundance elevation, providing a correlated prediction across three independent observables that is a unique fingerprint of the SCT superposition mechanism.

Second, the pre-existing matter from the colliding pockets introduced a small additional entropy contribution during the thermalization epoch that slightly modified the neutrino-to-photon temperature ratio from its standard value. This entropy injection — from the thermalization of stellar remnants, compact objects, and processed gas from the pre-existing pockets — heats the photon bath slightly relative to the neutrino background, which had already decoupled from the plasma before the full thermalization was complete. The result is a small decrease in T_ν/T_γ below its standard value, which appears observationally as a small downward shift in the effective N_eff from the standard 3.044. The two SCT contributions — superposition energy density pushing N_eff up, and entropy injection pushing N_eff down — partially cancel, with the net effect being a small deviation from 3.044 in a direction determined by which mechanism dominates in the specific collision parameters of our universe. SCT predicts this net ΔN_eff to be at the level of ±0.1 to ±0.2 — within current measurement uncertainties but potentially detectable by CMB-S4.