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Hierarchical Bayesian Thermonuclear Rate for the 7 Be(n,p) 7 Li Big Bang Nucleosynthesis Reaction

Big Bang nucleosynthesis provides the earliest probe of standard model physics, at a time when the universe was less than 1000 seconds old. It determines the abundances of the lightest nuclides, which give rise to the subsequent history of the visible matter in the universe. This work derives new 7 Be(n,p) 7 Li thermonuclear reaction rates based on all available experimental information. This reaction sensitively impacts the primordial abundances of 7 Be and 7 Li during big bang nucleosynthesis. We critically evaluate all available data and disregard experimental results that are questionable. For the nuclear model, we adopt an incoherent sum of single-level, two-channel, R -matrix approximation expressions, which are implemented into a hierarchical Bayesian model, to analyze the remaining six data sets we deem most reliable. In the fitting of the data, we consistently model all known sources of uncertainty, including discrepant absolute normalizations of different data sets, and also take the variation of the neutron and proton channel radii into account, hence providing less biased estimates of the 7 Be(n,p) 7 Li thermonuclear rates. From the resulting posteriors, we extract R -matrix parameters ($E_r, γ^2_n, γ^2_p$) and derive excitation energies and partial and total widths. Our fit is sensitive to the contributions of the first three levels above the neutron threshold. Reaction rates were computed by integrating 10,000 samples of the reduced cross section. Our 7 Be(n,p) 7 Li thermonuclear rates have uncertainties between 1.5% and 2.0% at temperatures of ≤1 GK. Finally, we compare our rates to previous results and find that the 7 Be(n,p) 7 Li rates most commonly used in big bang simulations have uncertainties that are too optimistic.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Limits on non-relativistic matter during Big-bang nucleosynthesis

Big-bang nucleosynthesis (BBN) probes the cosmic mass-energy density at temperatures ~10 MeV to ~100 keV. Here, we consider the effect of a cosmic matter-like species that is non-relativistic and pressureless during BBN. Such a component must decay; doing so during BBN can alter the baryon-to-photon ratio, η, and the effective number of neutrino species. We use light element abundances and the cosmic microwave background (CMB) constraints on η and N ν to place constraints on such a matter component. We find that electromagnetic decays heat the photons relative to neutrinos, and thus dilute the effective number of relativistic species to N eff < 3 for the case of three Standard Model neutrino species. Intriguingly, likelihood results based on Planck CMB data alone find N ν = 2.800 ± 0.294, and when combined with standard BBN and the observations of D and 4 He give N ν = 2.898 ± 0.141. While both results are consistent with the Standard Model, we find that a nonzero abundance of electromagnetically decaying matter gives a better fit to these results. Our best-fit results are for a matter species that decays entirely electromagnetically with a lifetime τ X = 0.89 sec and pre-decay density that is a fraction ξ = (ρ X /ρ rad |10 MeV = 0.0026 of the radiation energy density at 10 MeV; similarly good fits are found over a range where ξτ X 1/2 is constant. On the other hand, decaying matter often spoils the BBN+CMB concordance, and we present limits in the (τ X ,ξ) plane for both electromagnetic and invisible decays. For dark (invisible) decays, standard BBN (i.e. ξ = 0) supplies the best fit. We end with a brief discussion of the impact of future measurements including CMB-S4.

79 ASTRONOMY AND ASTROPHYSICS↗

Analysis of the multicomponent relativistic Boltzmann equation for electron scattering in big bang nucleosynthesis

Big-bang nucleosynthesis (BBN) is valuable as a means to constrain the physics of the early universe and it is the only probe of the radiation-dominated epoch. A fundamental assumption in BBN is that the nuclear velocity distributions obey Maxwell-Boltzmann (MB) statistics as they do in stars. Specifically, the BBN epoch is characterized by a dilute baryon plasma for which the velocity distribution of nuclei is mainly determined by the dominant Coulomb elastic scattering with mildly relativistic electrons. One must therefore deduce the momentum distribution for reacting nuclei from the multicomponent relativistic Boltzmann equation. However, the full multicomponent relativistic Boltzmann equation has only recently been analyzed and its solution has only been worked out in special cases. Moreover, a variety of schemes have been proposed that introduce nonthermal components into the BBN environment which can alter the thermal distribution of reacting nuclei. Here, we construct the relativistic Boltzmann equation in the context of BBN. We also derive a Langevin model and perform relativistic Monte-Carlo simulations which clarify the baryon distribution during BBN and can be used to analyze any relaxation from a nonthermal injection. Further, we show by these analyses that the thermalization process leads to a nuclear distribution function that remains very close to MB statistics even during the most relativistic environment relevant to BBN. Hence, the predictions of standard BBN remain unchanged.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

New bounds on heavy QCD axions from big bang nucleosynthesis

We study big bang nucleosynthesis (BBN) constraints on heavy QCD axions. BBN offers a powerful probe of new physics that modifies the neutron-to-proton ratio during the process, thanks to the precisely measured primordial Helium-4 abundance. A heavy QCD axion provides an attractive target for this probe, because not only is it a well-motivated hypothetical particle by the strong 𝐶⁢𝑃 problem, but also it dominantly decays to hadrons if kinematically allowed. A range of its lifetime is thus excluded where the hadronic decays would significantly alter the neutron-to-proton ratio. We compute axion-induced modification of the neutron-to-proton ratio, and obtain robust upper bounds on the axion lifetimes, as low as 0.017 s for the axion mass higher than 300 MeV. Remarkably, this is stronger than projected future cosmic microwave background bounds via 𝑁 eff . Our bounds are largely insensitive to uncertainties in hadronic cross sections and the axion’s branching fractions into various hadrons, as well as to the precise value of the initial axion abundance. We also incorporate, for the first time, several key improvements, such as scattering processes by energetic 𝐾 𝐿 and secondary hadrons, that can also be important for studying general hadronic injections during BBN, not limited to those from axion decays.

Axions↗

Enhanced matter power spectrum from axion kination after Big Bang nucleosynthesis

Despite stringent constraints from Big Bang Nucleosynthesis (BBN) and cosmic microwave background (CMB) observations, it is still possible for well-motivated particle physics models to substantially alter the cosmic expansion history between BBN and recombination. In this work we consider two different axion models that can realize a period of first matter domination, then kination, in this epoch. We perform fits to both primordial element abundances as well as CMB data and determine that up to a decade of late axion domination is allowed by these probes of the early universe. We establish the implications of late axion domination for the matter power spectrum on the scales 1/Mpc ≲ k ≲ 10 3 /Mpc. Our 'log' model predicts a relatively modest bump-like feature together with a small suppression relative to the standard ΛCDM predictions on either side of the enhancement. Our 'two-field' model predicts a larger, plateau-like feature that realizes enhancements to the matter power spectrum of up to two orders of magnitude. These features have interesting implications for structure formation at the forefront of current detection capabilities.

79 ASTRONOMY AND ASTROPHYSICS↗

The impact of new d(p,γ)3 rates on Big Bang Nucleosynthesis

We consider the effect on Big Bang Nucleosynthesis (BBN) of new measurements of the d(p,γ) 3 He cross section by the LUNA Collaboration. These have an important effect on the primordial abundance of D/H which is also sensitive to the baryon density at the time of BBN. We have re-evaluated the thermal rate for this reaction, using a world average of cross section data, which we describe with model-independent polynomials; our results are in good agreement with a similar analysis by LUNA. We then perform a full likelihood analysis combining BBN and Planck cosmic microwave background (CMB) likelihood chains using the new rate combined with previous measurements and compare with the results using previous rates. Concordance between BBN and CMB measurements of the anisotropy spectrum using the old rates was excellent. The predicted deuterium abundance at the Planck value of the baryon density was (D/H) BBN+CMB old = (2.57 ± 0.13) × 10 –5 which can be compared with the value determined from quasar absorption systems (D/H) obs = (2.55 ± 0.03) × 10 –5 . Using the new rates we find (D/H) BBN+CMB = (2.51 ± 0.11) × 10 –5 . We thus find consistency among BBN theory, deuterium and 4He observations, and the CMB, when using reaction rates fit in our data-driven approach. We also find that the new reaction data tightens the constraints on the number of relativistic degrees of freedom during BBN, giving the effective number of light neutrino species N ν = 2.880 ± 0.144 in good agreement with the Standard Model of particle physics. Lastly, we note that the observed deuterium abundance continues to be more precise than the BBN+CMB prediction, whose error budget is now dominated by d(d,n) 3 He and d(d,p) 3 H.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Fast, differentiable, and extensible big bang nucleosynthesis package

Here, we introduce light isotope nucleosynthesis with JAX (LINX), a new differentiable public big bang nucleosynthesis code designed for fast parameter estimation. By leveraging JAX, LINX achieves both speed and differentiability, enabling the use of Bayesian inference, including gradient-based methods. We discuss the formalism used in LINX for rapid primordial elemental abundance predictions and give examples of how LINX can be used. When combined with differentiable cosmic microwave background power spectrum emulators, LINX can be used for joint cosmic microwave background and big bang nucleosynthesis analyses without requiring extensive computational resources, including on personal hardware.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Does inhomogeneous big bang nucleosynthesis produce an inhomogeneous element distribution today?

Inhomogeneous big bang nucleosynthesis (BBN) produces a spatially inhomogeneous distribution of element abundances at $T \sim 10^9$ K , but subsequent element diffusion will tend to erase these inhomogeneities. In this work, we calculate the cosmological comoving diffusion length for the BBN elements. This diffusion length is limited by atomic scattering and is therefore dominated by diffusion when the atoms are neutral, between the redshifts of recombination and reionization. We find that the comoving diffusion length today is $d_{\text{com}} ≈ 70$ pc for all of the elements of interest except 7 Li , for which $d_{\text{com}}$ is an order of magnitude smaller because 7 Li remains ionized throughout the relevant epoch. This comoving diffusion length corresponds to a substellar baryonic mass scale and is roughly equal to the horizon scale at BBN. These results lend support to the possibility that inhomogeneities on scales larger than the horizon at BBN could lead to a spatially inhomogeneous distribution of elements today, while purely subhorizon fluctuations at BBN can result only in a homogeneous element distribution at present.

79 ASTRONOMY AND ASTROPHYSICS↗

Cosmological parameter estimation with a joint-likelihood analysis of the cosmic microwave background and big bang nucleosynthesis

Here, we present a joint-likelihood analysis of big bang nucleosynthesis (BBN) and cosmic microwave background (CMB) data, consistently combining likelihoods and taking into account uncertainties in nuclear reaction rates for the first time. Bayesian inference is performed on the baryon abundance and the effective number of neutrino species, 𝑁 eff , using a CMB Boltzmann solver in combination with LINX , a new flexible and efficient BBN code. We marginalize over Planck nuisance parameters and nuclear rates to find 𝑁 eff =3.0⁢8$^{+0.15}_{−0.14}$, 2.9⁢4$^{+0.16}_{−0.15}$, or 2.96$^{+0.13}_{−0.14}$, for three separate reaction networks. This framework enables robust testing of the lambda cold dark matter paradigm and its variants with CMB and BBN data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Big-Bang Nucleosynthesis after Planck

We assess the status of big-bang nucleosynthesis (BBN) in light of the final Planck data release and other recent developments, and in anticipation of future measurements. Planck data from the recombination era fix the cosmic baryon density to 0.9% precision, and now damping tail measurements determine the helium abundance and effective number of neutrinos with precision approaching that of astronomical and BBN determinations respectively. All three parameters are related by BBN. In addition, new high-redshift measurements give D/H to better precision than theoretical predictions, and new Li/H data reconfirm the lithium problem. We present new 7 Be(n, p) 7 Li rates using new neutron capture measurements; we have also examined the effect of proposed changes in the d(p, γ) 3 He rates. Using these results we perform a series of likelihood analyses. We assess BBN/CMB consistency, with attention to how our results depend on the choice of Planck data, as well as how the results depend on the choice of non-BBN, non-Planck data sets. Most importantly the lithium problem remains, and indeed is more acute given the very tight D/H observational constraints; new neutron capture data reveals systematics that somewhat increases uncertainty and thus slightly reduces but does not essentially change the problem. We confirm that d(p, γ) 3 He theoretical rates brings D/H out of agreement and slightly increases 7 Li; new experimental data are needed at BBN energies. Setting the lithium problem aside, we find the effective number of neutrino species at BBN is Nν = 2.86±0.15. Future CMB Stage-4 measurements promise substantial improvements in BBN parameters: helium abundance determinations will be competitive with the best astronomical determinations, and Neff will approach sensitivities capable of detecting the effects of Standard Model neutrino heating of the primordial plasma.

79 ASTRONOMY AND ASTROPHYSICS↗

The Neutron Mean Life and Big Bang Nucleosynthesis

We explore the effect of neutron lifetime and its uncertainty on standard big bang nucleosynthesis (BBN). BBN describes the cosmic production of the light nuclides, 1H, D, 3H+3He, 4He, and 7Li+7Be, in the first minutes of cosmic time. The neutron mean life τn has two roles in modern BBN calculations: (1) it normalizes the matrix element for weak n↔p interconversions, and (2) it sets the rate of free neutron decay after the weak interactions freeze-out. We review the history of the interplay between τn measurements and BBN, and present a study of the sensitivity of the light element abundances to the modern neutron lifetime measurements. We find that τn uncertainties dominate the predicted 4He error budget, but these theory errors remain smaller than the uncertainties in 4He observations, even with the dispersion in recent neutron lifetime measurements. For the other light element predictions, τn contributes negligibly to their error budget. Turning the problem around, we combine present BBN and cosmic microwave background (CMB) determinations of the cosmic baryon density to predict a “cosmologically preferred” mean life of τn(BBN+CMB)=870±16s, which is consistent with experimental mean life determinations. We show that if future astronomical and cosmological helium observations can reach an uncertainty of σobs(Yp)=0.001 in the 4He mass fraction Yp, this could begin to discriminate between the mean life determinations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Big bang nucleosynthesis constraints on sterile neutrino and lepton asymmetry of the Universe

We consider the cosmological effects of sterile neutrinos with the masses of 150–450 MeV. The decay of sterile neutrinos changes the thermal history of the Universe and affects the energy density of radiation at the recombination and the big bang nucleosynthesis (BBN) results. We derive severe constraints on the parameters of sterile neutrinos from the primordial abundances of helium-4 and deuterium. We also find that in a particular model the constraints can be considerably relaxed by assuming a large lepton asymmetry in the active neutrinos. In this case, the consistent parameters result in N eff ≃ 3.2–3.4 and can alleviate the Hubble tension.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Kaluza-Klein graviton freeze-in and big bang nucleosynthesis

In models featuring extra spatial dimensions, particle collisions in the early Universe can produce Kaluza-Klein gravitons. Such particles will later decay, potentially impacting the process of big bang nucleosynthesis. In this paper, we consider scenarios in which gravity is free to propagate throughout n flat, compactified extra dimensions, while the fields of the Standard Model are confined to a ( 3 + 1 )-dimensional brane. We calculate the production and decay rates of the states that make up the Kaluza-Klein graviton tower and determine the evolution of their abundances in the early Universe. We then go on to evaluate the impact of these decays on the resulting light element abundances. We identify significant regions of previously unexplored parameter space that are inconsistent with measurements of the primordial helium and deuterium abundances. In particular, we find that for the case of one extra dimension (two extra dimensions), the fundamental scale of gravity must be M ⋆ ≳ 2 × 10 13 GeV ( M ⋆ ≳ 1 0 10 GeV ) unless the temperature of the early Universe was never greater than T ∼ 2 TeV ( T ∼ 1 GeV ). For larger values of n , these constraints are less stringent. For the case of n = 6 , for example, our analysis excludes all values of M ⋆ less than ∼ 10 6 GeV , unless the temperature of the Universe was never greater than T ∼ 3 TeV . The results presented here severely limit the possibility that black holes were efficiently produced through particle collisions in the early Universe’s thermal bath. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Direct and Indirect Measurements for a Better Understanding of the Primordial Nucleosynthesis

The Big Bang Nucleosynthesis (BBN) model is a great success of nuclear astrophysics due to the outstanding agreement between observational and predicted light elements abundances. One exception, however, is the so-called “lithium problem.” In this context, experimental efforts to measure the relevant reactions have been brought to an increased level of accuracy in measuring primordial abundances, and the introduction of indirect methods has allowed researchers to overcome the natural limitations of direct measurements in the energy range of interest for BBN. Here we review the results obtained from the application of the Trojan Horse Method to some of the most influential reactions of the standard network, such as 2 H(d,p) 3 H, 2 H(d,n) 3 He, 3 He(d,p) 4 He, 7 Li(p,α) 4 He, and 7 Be(n,α) 4 He. The relevant cross sections have been then used as new inputs to a classical BBN code, resulting in important constraints that make suggestions for a possible solution for the lithium problem outside of nuclear physics.

79 ASTRONOMY AND ASTROPHYSICS↗