CAMB v2: cosmological power spectra for high-precision surveys

Upcoming cosmic microwave background (CMB) and large-scale-structure surveys require theoretical power spectra with numerical errors well below their observational uncertainties over the scales that carry most of the constraining power. We describe a substantial update to CAMB designed to provide fast, high-precision predictions for two key outputs: the lensed CMB and matter power spectra. The central development is a new treatment of the hyperspherical Bessel functions used for line-of-sight integration in non-flat cosmologies. A leading-order Olver construction maps the curved radial equation onto the flat spherical Bessel equation by matching their actions through the turning point. The resulting approximation is exact in the flat limit, remains smooth through the turning point, and reduces near flatness to a simple rescaling of the flat Bessel argument and amplitude. We also describe updated integrators, a recalibrated fast recombination model, stabilized parameterized post-Friedmann dark-energy evolution, and improvements to CMB lensing accuracy. Numerical convergence is assessed by comparing unboosted default results against more converged calculations. The defaults meet conservative 10-3 pointwise convergence targets over the main lensed-CMB and quasi-linear matter-power ranges relevant for future surveys. Errors measured in typical runs are substantially smaller than this. We also describe the convention dependence of the nominally linear matter power spectrum when a homogeneous calculation attempts to represent the effects of reionization heating. Essentially all of the new algorithms and code were developed with LLMs or AI agents under human supervision.