Temperature-Dependent CPT Violation: Constraints from Big Bang Nucleosynthesis

TL;DR

The paper investigates CPT violation in the early universe via a temperature-dependent electron-positron mass difference characterized by $b_0(T)=\alpha T^2$, a scaling chosen to be both theoretically natural and phenomenologically viable at MeV temperatures. It extends the precision BBN code $\texttt{PRyMordial}$ to include dynamically solved chemical potentials and finite-mass/thermal corrections to weak rates, enabling robust constraints on $\alpha$ from Helium-4, Deuterium, and $N_{\rm eff}$. The analysis finds $\alpha \gtrsim 10^{-6}\ \mathrm{GeV}^{-1}$ for keV-scale mass differences at BBN, with no overall 1$\sigma$ overlap among all three observables, though pairwise overlaps depend on the Helium-4 data set (PDG vs EMPRESS). The authors also present three toy models that realize the $T^2$ scaling through different field-theoretic constructions, illustrating that such temperature-dependent CPT violation is theoretically plausible and would leave a distinctive imprint on early-universe cosmology, while remaining unconstrained by present-day laboratory tests. Together, the results establish BBN as a stringent probe of early-universe CPT violation of this form and motivate further UV-complete formulations and improved astrophysical measurements to sharpen the constraints.

Abstract

In this study, we explore temperature-dependent CPT violation during Big Bang Nucleosynthesis (BBN) through electron-positron mass asymmetries parametrized by $b_0(T) = αT^2$. The $T^2$ scaling naturally evades stringent laboratory bounds at zero temperature while allowing for significant CPT violation at MeV scales in the early universe \cite{ParticleDataGroup:2024cfk}. Using a modified version of the BBN code \faGithub \href{https://github.com/vallima/PRyMordial}{\,\texttt{PRyMordial}} with dynamically-solved chemical potentials and appropriate finite-mass corrections, we constrain electron-positron mass differences from observed abundances of Helium-4, Deuterium, and $N_{\rm eff}$. We find that $α$ must be greater than or approximately equal to $10^{-6}$ GeV$^{-1}$ for keV-scale mass differences at BBN. All three observables show no simultaneous $1σ$ overlap, though pairwise combinations allow for constrained regions of parameter space. We present three toy models demonstrating how $b_0(T) \propto T^2$ arises from field-theoretic mechanisms, including temperature-driven phase transitions. These results provide the most stringent constraints on early-universe CPT violation in this regime, probing parameter space inaccessible to laboratory experiments.

Figures (5)

• Figure 1: Change in the predicted Helium-4, Deuterium, and Lithium-7 abundances as well as $N_{\rm eff}$ with changing electron mass. Here, the electron and positron masses are assumed to be equal. Observational values for Helium-4 come from the PDG and the EMPRESS collaboration ParticleDataGroup:2024cfkMatsumoto:2022tlr. Observation values for Deuterium and Lithium-7 come from the PDG ParticleDataGroup:2024cfk. The observed value for $N_{\rm eff}$ comes from ACT ACT:2025tim.
• Figure 2: Change in the electron chemical potential over time for several combinations of electron and positron masses. The chemical potential $\mu_{e^-}(T)$ approaches $\frac{1}{2}(m_{e^-} - m_{e^+})$ at low temperature (dotted lines), validating our numerical solution against the analytical limit in Equation \ref{['eq:mu_approx']}.
• Figure 3: Change in $T_\nu / T_\gamma$ over time for several electron-positron mass differences.
• Figure 4: Change in the predicted values of Helium-4, Deuterium, Lithium-7, and $N_{\rm eff}$ with changing electron and positron masses. These plots were created under the assumptions outlined above, using dynamically solved non-zero chemical potentials for the electron and positron, the full neutron-proton interconversion rates, and appropriate modifications to the interactions between electrons, positrons, and neutrinos and QED plasma effects. Observational values for Helium-4 come from the PDG and the EMPRESS collaboration ParticleDataGroup:2024cfkMatsumoto:2022tlr. Observation values for Deuterium and Lithium-7 come from the PDG ParticleDataGroup:2024cfk. The observed value for $N_{\rm eff}$ comes from ACT ACT:2025tim.
• Figure 5: Overlap regions in ($m_{e^-}, m_{e^+}$) parameter space of the bounds from observation from Helium-4, Deuterium, and $N_{\rm eff}$. The plot on the left uses the EMPRESS value for Helium-4, and the plot on the right uses the PDG value. These plots were created under the assumptions outlined above, using dynamically solved non-zero chemical potentials for the electron and positron, the full neutron-proton interconversion rates, and appropriate modifications to the interactions between electrons, positrons, and neutrinos and QED plasma effects. Observational values for Helium-4 come from the PDG and the EMPRESS collaboration ParticleDataGroup:2024cfkMatsumoto:2022tlr. Observation values for Deuterium come from the PDG ParticleDataGroup:2024cfk. The observed value for $N_{\rm eff}$ comes from ACT ACT:2025tim.