Primordial helium bounds on a leptonic electron-mass transition inside the BBN window

Abstract

The amplitude ε of a universal fractional shift in the electron mass that turns on inside the big-bang nucleosynthesis (BBN) temperature window is treated as a free parameter, and the measured primordial helium mass fraction Y_p is used to bound it. Bounds on constant or power-law variations of fundamental constants at BBN already exist; the narrow point here is only the temperature-dependent turn-on topology. The shift is switched on below a critical temperature T_c by a linear ramp, ε_eff(T) = ε max(0, 1 − T/T_c), which deforms the weak rates in the nuclear network without changing the relativistic degrees of freedom. At the single T_c where the helium response was measured in a production BBN code (T_c = 179 keV), that response is linear, dY_p/dε = 0.00163 per percent of ε, and reproduces a direct windowed run to a few percent of the window itself. Against the Aver et al. determination Y_p = 0.2453 ± 0.0034, that elasticity implies ε < 3.2% (2σ) at that measured T_c only. The EMPRESS determination cannot be used for the same purpose: standard BBN with ε = 0 already sits 2.9σ above it, so a measurement in tension with the null hypothesis does not constrain a deformation of that null. Deuterium is not used for a derivative bound, because its ε-response is a nonlinear bottleneck quantity; no chain-dependent absolute D/H is quoted. The result is a single-observable, chain-free upper edge on ε for one ramp point, with zero fitted parameters — not a first bound on varying m_e, and not a scan over the full free-T_c window.