Linear Perturbations of the Scalar Temporal Field Ontology and Boltzmann-Code Predictions for the CMB Angular Power Spectrum

This paper derives the full linear perturbation theory of the Scalar Temporal Field Ontology (STFO) for a general temporal Lagrangian P(τ,X)P(\tau, X)P(τ,X) and provides an explicit mapping to Einstein–Boltzmann solvers such as CLASS and CAMB. The temporal field perturbation δτ\delta\tauδτ is shown to behave as a k-essence degree of freedom with an exact effective sound speed cs2=PX/(PX+2XPXX)c_s^2 = P_X / (P_X + 2 X P_{XX})cs2=PX/(PX+2XPXX), vanishing anisotropic stress, and well-defined stability conditions. Explicit expressions for the temporal energy density perturbation, pressure perturbation, and velocity divergence are derived, enabling direct computation of the CMB temperature and polarization angular power spectra CℓC_\ellCℓ. This work completes the transition of STFO from background cosmology to precision observable predictions and provides the technical foundation required to confront the theory with Planck and next-generation CMB data.