Impact of non-standard neutrino-electron interactions on Big Bang Nucleosynthesis

The gist Neutrino non-standard interactions (NSI) with electrons are studied to update previous analyses of neutrino decoupling and to provide a full study of their effect on light element production during Big Bang Nucleosynthesis (BBN).

Neutrino Non-Standard Interactions with Electrons

Non-standard neutrino interactions arise in extensions of the Standard Model that generate neutrino masses and mixing [2]. For the range of cosmological temperatures during neutrino decoupling, the only abundant charged leptons are electrons and positrons, leading to a restriction to neutral-current NSI of neutrinos with electrons [4]. The effective Lagrangian density describing these interactions is given by L = LSM + LNC−NSIe (2.1) [4]. The SM contribution is described by LSM = −2√2 GF h (¯νeγ µPLe)(¯eγµPLνe) + gX (¯ναγ µPLνα)(¯eγµPXe) i. (2.2) [4]. The NSI contribution is described by LNC−NSIe = −2√2 GF ε X αβ (ναγ µPLνβ) (eγµPXe), (2.3) [4]. These dimensionless parameters εXαβ quantify the strength of the non-standard interactions between neutrinos of flavours α and β and electrons [4]. NSI can be flavour-changing when εαβ ≠ 0 for α ≠ β, corresponding to lepton flavour non-conserving interactions, or non-universal when εαα − εββ ≠ 0, which breaks lepton flavour universality [4]. Bounds on neutrino NSI with electrons are derived from data from neutrino oscillation experiments, neutrino–electron scattering measurements, and precision constraints from LEP [4].

Impact of Non-Standard Interactions on Neutrino Decoupling

The presence of NSI could modify the decoupling process of cosmological neutrinos by changing the thermal contact between neutrinos and the electromagnetic plasma [2]. Specifically, non-standard interactions with electrons would modify this contact and change their momentum spectra, leading to a different value of Neff [3]. The evolution of the neutrino density matrix is governed by quantum kinetic equations with NSI (3.2) [4]. The key point for assessing the impact on Neff is that the collisional integrals I(ϱ) depend on the couplings that appear in neutrino-electron scattering amplitudes [4]. In contrast to studies of decoupling, a full analysis of NSI effects on Big Bang Nucleosynthesis (BBN) has not been performed yet [3].

Results for Neff

A complete numerical computation using the publicly available code FortEPiaNO2 obtained Neff with a numerical error below 5×10−4 in the standard scenario [4]. The results presented are analogous to those reported in Ref. [14] and extend that analysis by exploring a wider region of the NSI parameter space to obtain a more complete picture of their effects on BBN [8]. One-parameter studies show that the minimum of Neff occurs at specific values, such as εLee = −g˜L ≃ −0.727 [25] for the left-handed electron sector, where the effective left-handed coupling to electrons vanishes, suppressing neutrino-electron interactions and leading to an earlier decoupling [8]. The increase in absolute value of non-standard couplings delays neutrino decoupling and more entropy is transferred from e± annihilations into the neutrino sea, resulting in a larger Neff [8].

Consequences for Big Bang Nucleosynthesis

BBN relies entirely on well-established SM physics and provides one of the most robust probes of the early universe [4]. The neutron-to-proton ratio is governed by charged-current weak interaction processes such as νe + n ←→ p + e − (4.1) [10]. Any deviation from the standard value of Neff alters the expansion rate, which in turn shifts the timing of freeze-out of weak interactions and impacts the neutron-to-proton ratio [4]. A larger value of Neff leads to a faster expansion, causing an earlier nn/np freeze-out and enhancing the production of 4He [10]. The deuterium abundance is affected by this faster expansion, which shortens the duration of deuterium burning before freeze-out, resulting in a higher 2H/H [10].

Results for Primordial Abundances

By varying only one NSI parameter at a time, the predictions for Yp and 2H/H follow the qualitative behavior observed for Neff in Fig. 1 [4]. The extrema of both Yp and 2H/H occur close to the values that minimize Neff, reflecting the dominant effect of NSI with electrons on the primordial abundances through modification of radiation density [4]. Direct effects on weak rates remain strongly subdominant and are only clearly visible in the helium abundance for sufficiently large electron NSI couplings [4]. For flavour-changing NSI, such as εL eτ, the dependence is approximately symmetric around εL eτ = 0 [12]. The results show that both abundances largely follow the behaviour expected from the NSI-induced changes in Neff [4].

Conclusions

The work explores cosmological implications of neutrino non-standard interactions with electrons during neutrino decoupling and BBN [5]. The study confirms that both primordial helium mass fraction Yp and deuterium abundance 2H/H largely track the NSI-induced changes in Neff, which is primarily driven by the modification of the radiation density [4]. Regions of parameter space leading to a larger radiation density generally produce larger values of Yp and 2H/H, consistent with the effect of a faster expansion rate during BBN [4]. The results provide complementary constraints to laboratory limits by probing neutrino properties at different energy and time scales [5]. Future improvements in the precision and robustness of primordial abundance measurements could further enhance the sensitivity of cosmological probes to non-standard neutrino interactions [5].

--- Page 17 ---

Acknowledgments

At IFIC Valencia, this work was supported by the Spanish grants PID2023-147306NBI00 and CEX2023-001292-S (MCIU/AEI/10.13039/501100011). J.M. is supported by the grant FPU24/0735. S.G. also acknowledges financial support through the Ram´on y Cajal contract RYC2023-044611-I funded by MICIU/AEI/10 and FSE+ [17]. S.G. and O.P. are supported by the Research grant TAsP (Theoretical Astroparticle Physics) funded by Istituto Nazionale di Fisica Nucleare (INFN) [17]. O.P. is also supported by Ministero dell’Universitâ e della Ricerca (MUR), PRIN2022 program (Grant PANTHEON 2022E2J4RK), Italy [17].

--- Page 18 ---

[1] P.F. de Salas et al., 2020 Global reassessment of the neutrino oscillation picture, JHEP 02 (2021) 071 [hep-ph/061137].

[4] J. Froustey, C. Pitrou and M.C. Volpe, Neutrino decoupling including flavour oscillations and primordial nucleosynthesis, JCAP 12 (2020) 015 [2008.01074].

[8] SPT-3G collaboration, SPT-3G D1: CMB temperature and polarization power spectra and cosmology from 2019 and 2026 observations of the SPT-3G main field, Phys. Rev. D 113 (2026) 083504 [2506.20707].

[14] P.F. de Salas, S. Gariazzo, P. Mart´ınez-Mirav´e, S. Pastor and M. T´ortola, Cosmological radiation density with non-standard neutrino-electron interactions, Phys. Lett. B 820 (2021) 136508 [2105.08168].

[4] JCAP 4 (L e e) and R (e e) for the left panel and right panel, for α = ϵLee in the left panel and εRee in the right panel, for α = εRee in the right panel [4].

[25] J. Erler and S. Su, The Weak Neutral Current, Prog. Part. Nucl. Phys. 71 (2013) 119 [1303.5522].

[4] The dashed red curve corresponds to the observational 1σ bound (Table 2) [4].

[8] The shaded vertical bands correspond to the 90% C.L. bounds shown in Table 1, in orange for the τ τ coupling and in blue for the ee ones [4].

[17] The white-shaded regions correspond to the expected future 1σ uncertainty [24] [4].

[18] A Bola˜nos, O.G. Miranda, A. Palazzo, M.A. T´ortola and J.W.F. Valle, Probing non-standard neutrino-electron interactions with solar and reactor neutrinos, Phys Rev D 79 (2009) 113012 [81].

1. Improve cosmological model testing by enabling direct comparison of neutrino non-standard interaction constraints from Big Bang Nucleosynthesis with terrestrial bounds, as they are complementary and can provide a test of neutrino physics at different temperature scales and epochs. This allows AI systems to evaluate the consistency between laboratory limits and early universe predictions simultaneously.

2. Enhance predictive capability for primordial light elements by allowing AI systems to calculate primordial helium mass fraction Yp and deuterium abundance 2H/H as functions of various non-standard neutrino interaction parameters, directly testing the effect of relic neutrinos on Big Bang Nucleosynthesis. This enables the system to map parameter space constraints onto observable cosmological benchmarks.

3. Develop a simulation engine capable of modeling the thermal history of the early universe under varying NSI conditions by utilizing Neff as a diagnostic quantity, as Neff becomes sensitive to the NSI parameters εL,Rαβ. This allows AI systems to predict how neutrino decoupling temperature and thermal equilibrium are shifted by new physics.

4. Implement a two-step computational workflow for BBN analysis where the system first computes the evolution of the neutrino momentum distributions throughout the decoupling epoch for different values of the NSI parameters before introducing them into nuclear reaction networks. This ensures that modifications to weak rates and spectral distortions are consistently incorporated into light element predictions.

5. Create a multidimensional parameter exploration tool that identifies degeneracies in NSI parameter space, such as those shown by iso-Neff contours, by analyzing the quadratic dependence of effective couplings on NSI parameters, as seen in Fig. 3 shows contours of constant Neff. This allows the system to efficiently search for regions where multiple non-standard interactions yield the same cosmological outcome.