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

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

doi:10.1103/wspy-s948

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

Cara Giovanetti ^1,*, Mariangela Lisanti ^2,3,†, Hongwan Liu ^4,5,6,‡, Siddharth Mishra-Sharma ^7,8,9,§,∥, and Joshua T. Ruderman ^1,¶

¹Center for Cosmology and Particle Physics, Department of Physics, New York University, New York, New York 10003, USA
²Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
³Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Ave, New York, New York 10010, USA
⁴Physics Department, Boston University, Boston, Massachusetts 02215, USA
⁵Kavli Institute for Cosmological Physics, University of Chicago, Chicago, Illinois 60637
⁶Theoretical Physics Department, Fermi National Accelerator Laboratory, Batavia, Illinois 60510
⁷ The NSF AI Institute for Artificial Intelligence and Fundamental Interactions
⁸Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
⁹Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

^*Contact author: cg3566@nyu.edu
^†Contact author: mlisanti@princeton.edu
^‡Contact author: hongwan@bu.edu
^§Contact author: smsharma@mit.edu
^∥Present address: Anthropic, San Francisco, CA 94104, USA.
^¶Contact author: ruderman@nyu.edu

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Phys. Rev. D 112, 063530 – Published 17 September, 2025

DOI: https://doi.org/10.1103/wspy-s948

Abstract

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 $N_{eff} = 3.0 8_{- 0.14}^{+ 0.15}, 2.9 4_{- 0.15}^{+ 0.16}$ , or ${2.96}_{- 0.14}^{+ 0.13}$ , 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.

Physical Review D

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

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Fast, differentiable, and extensible big bang nucleosynthesis package

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