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

Giovanetti, Cara; Lisanti, Mariangela; Liu, Hongwan; Mishra-Sharma, Siddharth; Ruderman, Joshua T.

doi:10.1103/wspy-s948

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

Journal Article · Tue Sep 16 20:00:00 EDT 2025 · Physical Review. D.

DOI:https://doi.org/10.1103/wspy-s948· OSTI ID:3010850

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New York Univ. (NYU), NY (United States)
Princeton Univ., NJ (United States); Flatiron Institute, New York, NY (United States)
Boston Univ., MA (United States); Univ. of Chicago, IL (United States); Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)
The NSF AI Institute for Artificial Intelligence and Fundamental Interactions, Cambridge, MA (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Harvard Univ., Cambridge, MA (United States); Anthropic, San Francisco, CA (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Princeton Univ., NJ (United States); Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0007968; SC0012567; AC02-07CH11359

OSTI ID:: 3010850

Alternate ID(s):: OSTI ID: 3011158
OSTI ID: 2477430

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 6 Vol. 112; ISSN 2470-0010; ISSN 2470-0029

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (70)

Mirror twin Higgs cosmology: constraints and a possible resolution to the H0 and S8 tensions Bansal, Saurabh; Kim, Jeong Han; Kolda, Christopher Journal of High Energy Physics, Vol. 2022, Issue 5 https://doi.org/10.1007/JHEP05(2022)050	journal	May 2022
AlterBBN: A program for calculating the BBN abundances of the elements in alternative cosmologies Arbey, A. Computer Physics Communications, Vol. 183, Issue 8 https://doi.org/10.1016/j.cpc.2012.03.018	journal	August 2012
PArthENoPE reloaded Consiglio, R.; de Salas, P. F.; Mangano, G. Computer Physics Communications, Vol. 233 https://doi.org/10.1016/j.cpc.2018.06.022	journal	December 2018
AlterBBN v2: A public code for calculating Big-Bang nucleosynthesis constraints in alternative cosmologies Arbey, A.; Auffinger, J.; Hickerson, K. P. Computer Physics Communications, Vol. 248 https://doi.org/10.1016/j.cpc.2019.106982	journal	March 2020
MontePython 3: Boosted MCMC sampler and other features Brinckmann, Thejs; Lesgourgues, Julien Physics of the Dark Universe, Vol. 24 https://doi.org/10.1016/j.dark.2018.100260	journal	March 2019
NACRE II: an update of the NACRE compilation of charged-particle-induced thermonuclear reaction rates for nuclei with mass number A<16 Xu, Y.; Takahashi, K.; Goriely, S. Nuclear Physics A, Vol. 918 https://doi.org/10.1016/j.nuclphysa.2013.09.007	journal	November 2013
Precision big bang nucleosynthesis with improved Helium-4 predictions Pitrou, Cyril; Coc, Alain; Uzan, Jean-Philippe Physics Reports, Vol. 754 https://doi.org/10.1016/j.physrep.2018.04.005	journal	September 2018
Array programming with NumPy Harris, Charles R.; Millman, K. Jarrod; van der Walt, Stéfan J. Nature, Vol. 585, Issue 7825 https://doi.org/10.1038/s41586-020-2649-2	journal	September 2020
The baryon density of the Universe from an improved rate of deuterium burning Mossa, V.; Stöckel, K.; Cavanna, F. Nature, Vol. 587, Issue 7833 https://doi.org/10.1038/s41586-020-2878-4	journal	November 2020
SciPy 1.0: fundamental algorithms for scientific computing in Python Virtanen, Pauli; Gommers, Ralf; Oliphant, Travis E. Nature Methods https://doi.org/10.1038/s41592-019-0686-2	journal	February 2020
Resolving conclusions about the early Universe requires accurate nuclear measurements Pitrou, Cyril; Coc, Alain; Uzan, Jean-Philippe Nature Reviews Physics, Vol. 3, Issue 4 https://doi.org/10.1038/s42254-021-00294-6	journal	March 2021
Nested sampling for physical scientists Ashton, Greg; Bernstein, Noam; Buchner, Johannes Nature Reviews Methods Primers, Vol. 2, Issue 1 https://doi.org/10.1038/s43586-022-00121-x	journal	May 2022
Planck 2013 results. XVI. Cosmological parameters Ade, P. A. R.; Aghanim, N.; Armitage-Caplan, C. Astronomy & Astrophysics, Vol. 571 https://doi.org/10.1051/0004-6361/201321591	journal	October 2014
Planck 2015 results : XIII. Cosmological parameters Ade, P. A. R.; Aghanim, N.; Arnaud, M. Astronomy & Astrophysics, Vol. 594 https://doi.org/10.1051/0004-6361/201525830	journal	September 2016
Planck 2018 results: VI. Cosmological parameters Aghanim, N.; Akrami, Y.; Ashdown, M. Astronomy & Astrophysics, Vol. 641, A6 https://doi.org/10.1051/0004-6361/201833910	journal	September 2020
Planck 2018 results: V. CMB power spectra and likelihoods Aghanim, N.; Akrami, Y.; Ashdown, M. Astronomy & Astrophysics, Vol. 641 https://doi.org/10.1051/0004-6361/201936386	journal	September 2020
Efficient Computation of Cosmic Microwave Background Anisotropies in Closed Friedmann‐Robertson‐Walker Models Lewis, Antony; Challinor, Anthony; Lasenby, Anthony The Astrophysical Journal, Vol. 538, Issue 2 https://doi.org/10.1086/309179	journal	August 2000
The Cosmic Linear Anisotropy Solving System (CLASS). Part II: Approximation schemes Blas, Diego; Lesgourgues, Julien; Tram, Thomas Journal of Cosmology and Astroparticle Physics, Vol. 2011, Issue 07 https://doi.org/10.1088/1475-7516/2011/07/034	journal	July 2011
The Cosmic Linear Anisotropy Solving System (CLASS) IV: efficient implementation of non-cold relics Lesgourgues, Julien; Tram, Thomas Journal of Cosmology and Astroparticle Physics, Vol. 2011, Issue 09 https://doi.org/10.1088/1475-7516/2011/09/032	journal	September 2011
CMB power spectrum parameter degeneracies in the era of precision cosmology Howlett, Cullan; Lewis, Antony; Hall, Alex Journal of Cosmology and Astroparticle Physics, Vol. 2012, Issue 04 https://doi.org/10.1088/1475-7516/2012/04/027	journal	April 2012
The effects of He I λ10830 on helium abundance determinations Aver, Erik; Olive, Keith A.; Skillman, Evan D. Journal of Cosmology and Astroparticle Physics, Vol. 2015, Issue 07 https://doi.org/10.1088/1475-7516/2015/07/011	journal	July 2015
The Simons Observatory: science goals and forecasts Ade, Peter; Aguirre, James; Ahmed, Zeeshan Journal of Cosmology and Astroparticle Physics, Vol. 2019, Issue 02 https://doi.org/10.1088/1475-7516/2019/02/056	journal	February 2019
The BAO+BBN take on the Hubble tension Schöneberg, Nils; Lesgourgues, Julien; Hooper, Deanna C. Journal of Cosmology and Astroparticle Physics, Vol. 2019, Issue 10 https://doi.org/10.1088/1475-7516/2019/10/029	journal	October 2019
Refined bounds on MeV-scale thermal dark sectors from BBN and the CMB Sabti, Nashwan; Alvey, James; Escudero, Miguel Journal of Cosmology and Astroparticle Physics, Vol. 2020, Issue 01 https://doi.org/10.1088/1475-7516/2020/01/004	journal	January 2020
Big-Bang Nucleosynthesis after Planck Fields, Brian D.; Olive, Keith A.; Yeh, Tsung-Han Journal of Cosmology and Astroparticle Physics, Vol. 2020, Issue 03 https://doi.org/10.1088/1475-7516/2020/03/010	journal	March 2020
Erratum: Big-Bang Nucleosynthesis after Planck Fields, Brian D.; Olive, Keith A.; Yeh, Tsung-Han Journal of Cosmology and Astroparticle Physics, Vol. 2020, Issue 11 https://doi.org/10.1088/1475-7516/2020/11/E02	journal	November 2020
Improving helium abundance determinations with Leo P as a case study Aver, Erik; Berg, Danielle A.; Olive, Keith A. Journal of Cosmology and Astroparticle Physics, Vol. 2021, Issue 03 https://doi.org/10.1088/1475-7516/2021/03/027	journal	March 2021
The impact of new d(p,γ)3 rates on Big Bang Nucleosynthesis Yeh, Tsung-Han; Olive, Keith A.; Fields, Brian D. Journal of Cosmology and Astroparticle Physics, Vol. 2021, Issue 03 https://doi.org/10.1088/1475-7516/2021/03/046	journal	March 2021
Updated BBN constraints on electromagnetic decays of MeV-scale particles Depta, Paul Frederik; Hufnagel, Marco; Schmidt-Hoberg, Kai Journal of Cosmology and Astroparticle Physics, Vol. 2021, Issue 04 https://doi.org/10.1088/1475-7516/2021/04/011	journal	April 2021
Primordial Deuterium after LUNA: concordances and error budget Pisanti, O.; Mangano, G.; Miele, G. Journal of Cosmology and Astroparticle Physics, Vol. 2021, Issue 04 https://doi.org/10.1088/1475-7516/2021/04/020	journal	April 2021
Addendum: Refined bounds on MeV-scale thermal dark sectors from BBN and the CMB Sabti, Nashwan; Alvey, James; Escudero, Miguel Journal of Cosmology and Astroparticle Physics, Vol. 2021, Issue 08 https://doi.org/10.1088/1475-7516/2021/08/A01	journal	August 2021
What does cosmology tell us about the mass of thermal-relic dark matter? An, Rui; Gluscevic, Vera; Calabrese, Erminia Journal of Cosmology and Astroparticle Physics, Vol. 2022, Issue 07 https://doi.org/10.1088/1475-7516/2022/07/002	journal	July 2022
Dark radiation constraints on portal interactions with hidden sectors Adshead, Peter; Ralegankar, Pranjal; Shelton, Jessie Journal of Cosmology and Astroparticle Physics, Vol. 2022, Issue 09 https://doi.org/10.1088/1475-7516/2022/09/056	journal	September 2022
Probing physics beyond the standard model: limits from BBN and the CMB independently and combined Yeh, Tsung-Han; Shelton, Jessie; Olive, Keith A. Journal of Cosmology and Astroparticle Physics, Vol. 2022, Issue 10 https://doi.org/10.1088/1475-7516/2022/10/046	journal	October 2022
Do you smell something decaying? Updated linear constraints on decaying dark matter scenarios Alvi, S.; Brinckmann, T.; Gerbino, M. Journal of Cosmology and Astroparticle Physics, Vol. 2022, Issue 11 https://doi.org/10.1088/1475-7516/2022/11/015	journal	November 2022
The 2024 BBN baryon abundance update Schöneberg, Nils Journal of Cosmology and Astroparticle Physics, Vol. 2024, Issue 06 https://doi.org/10.1088/1475-7516/2024/06/006	journal	June 2024
dynesty: a dynamic nested sampling package for estimating Bayesian posteriors and evidences Speagle, Joshua S. Monthly Notices of the Royal Astronomical Society, Vol. 493, Issue 3 https://doi.org/10.1093/mnras/staa278	journal	February 2020
A new tension in the cosmological model from primordial deuterium? Pitrou, Cyril; Coc, Alain; Uzan, Jean-Philippe Monthly Notices of the Royal Astronomical Society, Vol. 502, Issue 2 https://doi.org/10.1093/mnras/stab135	journal	January 2021
Chemical abundances in seven metal-poor H ii regions and a determination of the primordial helium abundance Valerdi, Mabel; Peimbert, Antonio; Peimbert, Manuel Monthly Notices of the Royal Astronomical Society, Vol. 505, Issue 3 https://doi.org/10.1093/mnras/stab1543	journal	May 2021
A new determination of the primordial helium abundance using the analyses of H ii region spectra from SDSS Kurichin, O. A.; Kislitsyn, P. A.; Klimenko, V. V. Monthly Notices of the Royal Astronomical Society, Vol. 502, Issue 2 https://doi.org/10.1093/mnras/stab215	journal	January 2021
polychord: next-generation nested sampling Handley, W. J.; Hobson, M. P.; Lasenby, A. N. Monthly Notices of the Royal Astronomical Society, Vol. 453, Issue 4 https://doi.org/10.1093/mnras/stv1911	journal	September 2015
A precise deuterium abundance: remeasurement of the z = 3.572 absorption system towards the quasar PKS1937–101 Riemer-Sørensen, S.; Kotuš, S.; Webb, J. K. Monthly Notices of the Royal Astronomical Society, Vol. 468, Issue 3 https://doi.org/10.1093/mnras/stx681	journal	March 2017
The primordial deuterium abundance at zabs = 2.504 from a high signal-to-noise spectrum of Q1009+2956 Zavarygin, E. O.; Webb, J. K.; Dumont, V. Monthly Notices of the Royal Astronomical Society, Vol. 477, Issue 4 https://doi.org/10.1093/mnras/sty1003	journal	April 2018
A Bayesian direct method implementation to fit emission line spectra: application to the primordial He abundance determination Fernández, Vital; Terlevich, Elena; Díaz, Angeles I. Monthly Notices of the Royal Astronomical Society, Vol. 487, Issue 3 https://doi.org/10.1093/mnras/stz1433	journal	May 2019
polychord: nested sampling for cosmology Handley, W. J.; Hobson, M. P.; Lasenby, A. N. Monthly Notices of the Royal Astronomical Society: Letters, Vol. 450, Issue 1 https://doi.org/10.1093/mnrasl/slv047	journal	April 2015
Review of Particle Physics Zyla, P. A.; Barnett, R. M.; Beringer, J. Progress of Theoretical and Experimental Physics, Vol. 2020, Issue 8 https://doi.org/10.1093/ptep/ptaa104	journal	August 2020
Thermonuclear fusion rates for tritium + deuterium using Bayesian methods de Souza, Rafael S.; Boston, S. Reece; Coc, Alain Physical Review C, Vol. 99, Issue 1 https://doi.org/10.1103/PhysRevC.99.014619	journal	January 2019
Primordial lepton asymmetries in the precision cosmology era: Current status and future sensitivities from BBN and the CMB Escudero, Miguel; Ibarra, Alejandro; Maura, Victor Physical Review D, Vol. 107, Issue 3 https://doi.org/10.1103/PhysRevD.107.035024	journal	February 2023
Neutrino-dark sector equilibration and primordial element abundances Giovanetti, Cara; Schmaltz, Martin; Weiner, Neal Physical Review D, Vol. 111, Issue 4 https://doi.org/10.1103/PhysRevD.111.043526	journal	February 2025
Cosmological parameters from CMB and other data: A Monte Carlo approach Lewis, Antony; Bridle, Sarah Physical Review D, Vol. 66, Issue 10 https://doi.org/10.1103/PhysRevD.66.103511	journal	November 2002
Thermal Dark Matter Below a MeV Berlin, Asher; Blinov, Nikita Physical Review Letters, Vol. 120, Issue 2 https://doi.org/10.1103/PhysRevLett.120.021801	journal	January 2018
Measurement of d + Be 7 Cross Sections for Big-Bang Nucleosynthesis Rijal, N.; Wiedenhöver, I.; Blackmon, J. C. Physical Review Letters, Vol. 122, Issue 18 https://doi.org/10.1103/PhysRevLett.122.182701	journal	May 2019
Joint Cosmic Microwave Background and Big Bang Nucleosynthesis Constraints on Light Dark Sectors with Dark Radiation Giovanetti, Cara; Lisanti, Mariangela; Liu, Hongwan Physical Review Letters, Vol. 129, Issue 2 https://doi.org/10.1103/PhysRevLett.129.021302	journal	July 2022
Indications for a Nonzero Lepton Asymmetry from Extremely Metal-Poor Galaxies Burns, Anne-Katherine; Tait, Tim M. P.; Valli, Mauro Physical Review Letters, Vol. 130, Issue 13 https://doi.org/10.1103/PhysRevLett.130.131001	journal	March 2023
Fast, differentiable, and extensible big bang nucleosynthesis package Giovanetti, Cara; Lisanti, Mariangela; Liu, Hongwan Physical Review D, Vol. 112, Issue 6 https://doi.org/10.1103/f3tj-r882	journal	September 2025
Matplotlib: A 2D Graphics Environment Hunter, John D. Computing in Science & Engineering, Vol. 9, Issue 3 https://doi.org/10.1109/MCSE.2007.55	journal	January 2007
MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics Feroz, F.; Hobson, M. P.; Bridges, M. Monthly Notices of the Royal Astronomical Society, Vol. 398, Issue 4 https://doi.org/10.1111/j.1365-2966.2009.14548.x	journal	October 2009
PRyMordial: the first three minutes, within and beyond the standard model Burns, Anne-Katherine; Tait, Tim M. P.; Valli, Mauro The European Physical Journal C, Vol. 84, Issue 1 https://doi.org/10.1140/epjc/s10052-024-12442-0	journal	January 2024
Nested sampling for general Bayesian computation Skilling, John Bayesian Analysis, Vol. 1, Issue 4 https://doi.org/10.1214/06-BA127	journal	December 2006
Slice sampling Neal, Radford M. The Annals of Statistics, Vol. 31, Issue 3 https://doi.org/10.1214/aos/1056562461	journal	June 2003
corner.py: Scatterplot matrices in Python Foreman-Mackey, Daniel The Journal of Open Source Software, Vol. 1, Issue 2 https://doi.org/10.21105/joss.00024	journal	June 2016
schwimmbad: A uniform interface to parallel processing pools in Python M. Price-Whelan, Adrian; Foreman-Mackey, Daniel The Journal of Open Source Software, Vol. 2, Issue 17 https://doi.org/10.21105/joss.00357	journal	September 2017
THE PRIMORDIAL DEUTERIUM ABUNDANCE OF THE MOST METAL-POOR DAMPED Ly α SYSTEM Cooke, Ryan J.; Pettini, Max; Nollett, Kenneth M. The Astrophysical Journal, Vol. 830, Issue 2 https://doi.org/10.3847/0004-637X/830/2/148	journal	October 2016
Bayesian Estimation of Thermonuclear Reaction Rates for Deuterium+Deuterium Reactions Gómez Iñesta, Á.; Iliadis, C.; Coc, A. The Astrophysical Journal, Vol. 849, Issue 2 https://doi.org/10.3847/1538-4357/aa9025	journal	November 2017
One Percent Determination of the Primordial Deuterium Abundance Cooke, Ryan J.; Pettini, Max; Steidel, Charles C. The Astrophysical Journal, Vol. 855, Issue 2 https://doi.org/10.3847/1538-4357/aaab53	journal	March 2018
Astrophysical S -factors, Thermonuclear Rates, and Electron Screening Potential for the ³ He(d,p) ⁴ He Big Bang Reaction via a Hierarchical Bayesian Model de Souza, Rafael S.; Iliadis, Christian; Coc, Alain The Astrophysical Journal, Vol. 872, Issue 1 https://doi.org/10.3847/1538-4357/aafda9	journal	February 2019
Determination of the Primordial Helium Abundance Based on NGC 346, an H ii Region of the Small Magellanic Cloud Valerdi, Mabel; Peimbert, Antonio; Peimbert, Manuel The Astrophysical Journal, Vol. 876, Issue 2 https://doi.org/10.3847/1538-4357/ab14e4	journal	May 2019
Hierarchical Bayesian Thermonuclear Rate for the ⁷ Be(n,p) ⁷ Li Big Bang Nucleosynthesis Reaction de Souza, Rafael S.; Kiat, Tan Hong; Coc, Alain The Astrophysical Journal, Vol. 894, Issue 2 https://doi.org/10.3847/1538-4357/ab88aa	journal	May 2020
The PHLEK Survey: A New Determination of the Primordial Helium Abundance Hsyu, Tiffany; Cooke, Ryan J.; Prochaska, J. Xavier The Astrophysical Journal, Vol. 896, Issue 1 https://doi.org/10.3847/1538-4357/ab91af	journal	June 2020
Bayesian Estimation of the D(p,γ)³He Thermonuclear Reaction Rate Moscoso, Joseph; de Souza, Rafael S.; Coc, Alain The Astrophysical Journal, Vol. 923, Issue 1 https://doi.org/10.3847/1538-4357/ac1db0	journal	December 2021

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

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