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# The baryon density of the Universe from an improved rate of deuterium burning

## Abstract

Light elements were produced in the first few minutes of the Universe through a sequence of nuclear reactions known as Big Bang nucleosynthesis (BBN)1,2. Among the light elements produced during BBN1,2, deuterium is an excellent indicator of cosmological parameters because its abundance is highly sensitive to the primordial baryon density and also depends on the number of neutrino species permeating the early Universe. Although astronomical observations of primordial deuterium abundance have reached percent accuracy3, theoretical predictions4,5,6 based on BBN are hampered by large uncertainties on the cross-section of the deuterium burning D(p,γ)3He reaction. Here we show that our improved cross-sections of this reaction lead to BBN estimates of the baryon density at the 1.6 percent level, in excellent agreement with a recent analysis of the cosmic microwave background7. Improved cross-section data were obtained by exploiting the negligible cosmic-ray background deep underground at the Laboratory for Underground Nuclear Astrophysics (LUNA) of the Laboratori Nazionali del Gran Sasso (Italy)8,9. We bombarded a high-purity deuterium gas target10 with an intense proton beam from the LUNA 400-kilovolt accelerator11 and detected the γ-rays from the nuclear reaction under study with a high-purity germanium detector. Our experimental results settle the most uncertain nuclear physics input to BBN calculations and substantially improve the reliability of using primordial abundances to probe the physics of the early Universe.

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## Data availability

Experimental data taken at LUNA are proprietary to the collaboration but can be made available from the corresponding authors upon reasonable request. Values of the thermonuclear reaction rate for smaller temperature steps can be obtained upon request to O.P. (e-mail: pisanti@na.infn.it). Source data are provided with this paper.

## Code availability

The PArthENoPE code used for BBN calculations can be made available upon request to O.P. (e-mail: pisanti@na.infn.it).

## References

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## Acknowledgements

We thank D. Ciccotti for accelerator operation and maintenance, for mechanical setups and servicing of the vacuum systems during the course of the experiment; M. D’Incecco for work on custom electronics; M. De Deo for the data acquisition system; G. Sobrero for the new gas target control panel. We also thank the mechanical workshop at LNGS, INFN Bari and Dipartimento Interateneo di Fisica Bari. This work was supported by INFN, with contributions from DFG (BE4100/4-1), Helmholtz Association (ERC-RA-0016), NKFIH (K120666), COST Association (ChETEC CA16117), STFC-UK, University of Naples Compagnia di San Paolo grant STAR, research grant number 2017W4HA7S NAT-NET: ‘Neutrino and Astroparticle Theory Network’ under the programme PRIN 2017 funded by the Italian Ministry of Education, University and Research (MIUR) and INFN Iniziativa Specifica TAsP. R.D. acknowledges funding from the Italian Ministry of Education, University and Research (MIUR) through the ‘Dipartimenti di eccellenza’ project Science of the Universe.

## Author information

Authors

### Contributions

The experiment at LUNA was proposed by C.G. and coordinated by F.C. and D.T.; P.C., C.G., S.Z. and V.M. planned the setup; S.Z. and P.C. developed the Monte Carlo simulations; S.Z., F.C., P.C., C.G., V.M., K.S. and F.F. led the data analysis. Other authors contributed to the data-taking over a period of two years and to discussion and interpretation of the results obtained. M.J. also had overall responsibility for the accelerator operations and the underground site. G.M. and O.P. performed all BBN calculations and Bayesian analyses. L.E.M., A.K., M.V. performed ab initio calculations. M.A., F.C., C.G., G.M. and O.P. also wrote the paper.

### Corresponding authors

Correspondence to C. Gustavino or S. Zavatarelli.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Grigory Rogachev and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data figures and tables

### Extended Data Fig. 1 Typical γ-ray spectrum obtained underground with the high-purity germanium detector at proton beam energy Ep = 50 keV.

Typical γ-ray spectrum (blue) obtained with the deuterium gas target at P = 0.3 mbar, clearly showing the full-energy, single-escape and double-escape peaks from the D(p,γ)3He reaction. The continuum is mainly due to Compton scattering events in which photons deposit only part of their energy in the detector. In grey is the beam-induced background spectrum acquired in the control run under the same experimental conditions but with an inert 4He gas target. Both spectra are normalized to the integrated beam current. The region of interest (Eγ ≈ 4.5−5.8 MeV) is essentially background free owing to the million-fold shielding8 from cosmic-ray muons attained at the LUNA underground laboratory.

### Extended Data Fig. 2 Typical γ-ray spectrum taken at proton beam energy Ep = 395 keV.

In blue is the γ-ray spectrum obtained with the deuterium gas target at P = 0.3 mbar (the peaks from the D(p,γ)3He reaction are broadened by the Doppler effect at this higher beam energy). In grey is the beam-induced background spectrum (acquired with an inert 4He gas target) due to the 19F contaminant (see text). Its contribution was subtracted leading to net counts on the full-energy peak with a statistical uncertainty of 0.9%. Both spectra are normalized to the integrated beam current.

### Extended Data Fig. 3 Sensitivity of the primordial deuterium abundance to the D(p,γ)3He reaction cross-section as a function of centre-of-mass energy.

The greatest sensitivity is obtained around E = 80 keV, where underground measurements are especially effective. The grey area represents the energy region explored at LUNA (see Methods for details).

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Mossa, V., Stöckel, K., Cavanna, F. et al. The baryon density of the Universe from an improved rate of deuterium burning. Nature 587, 210–213 (2020). https://doi.org/10.1038/s41586-020-2878-4

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• DOI: https://doi.org/10.1038/s41586-020-2878-4

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