AlterBBN: A program for calculating the BBN abundances of the elements in alternative cosmologies

• Comparing calculated light-element abundances with measurements probes Universe properties during nucleosynthesis, the most ancient observationally accessible period.In standard cosmology, the baryon-to-photon ratio at BBN determines abundances and can be deduced from Cosmic Microwave Background observations [1].Source: §1 · p. 3
• AlterBBN publicly calculates elemental abundances in standard and alternative cosmologies, enabling tests and parameter constraints for scenarios such as quintessence or reheating.The paper also describes the code’s physics, package, routines, compilation, inputs, outputs, examples, nuclear reactions, and experimental abundance limits.Source: §1 · p. 3
• The paper presents AlterBBN’s physics and equations, alternative expansion-rate and entropy-production models, program routines, compilation and use, and example results.Its appendices list nuclear reactions and experimental limits for constraining calculated abundances.Source: §1 · p. 3

2.1 BBN in the Cosmological Standard Model

• The standard-model equations describe the expansion rate, energy conservation, neutrino content, and evolution of nuclear abundances.In the absence of neutrino degeneracy, the treatment takes Nν = 3.Source: §2.1 · p. 4
• Nuclear-reaction abundance equations are linearized and then integrated with a Runge-Kutta method.The standard-model treatment also specifies initial conditions for solving the abundance equations.Source: §2.1 · pp. 3, 5

2.2 Modified Cosmological Scenarios

• AlterBBN considers alternative early-Universe descriptions because the properties of that period are not well known.The scenarios include modified expansion rates and entropy content.Source: §2.2 · p. 5

2.2.1 Modified expansion rate

• The modified-expansion scenario adds an effective dark-energy density ρD to the Universe’s total energy in the Friedmann equation.Its parametrization uses κρ, the ratio of effective dark-energy density to total energy density, and nρ to describe the density’s behavior.Source: §2.2.1 · p. 6

2.2.2 Modified entropy content

• The modified-entropy scenario parametrizes additional entropy through an effective dark entropy density sD and an energy-conservation equation.It uses two parametrizations: one for sD and another inspired by reheating scenarios, where entropy production ΣD evolves with temperature.Source: §2.2.2 · pp. 6–7

3 Content of the AlterBBN package

• The libbbn.a library contains the procedures needed for abundance calculations, and the package provides five programs.The parameter structure is defined in src/include.h.Source: §3 · p. 7, §3.1 · p. 7

3.1 Parameter structure

• The relicparam structure holds the parameters needed to compute abundances in standard and alternative cosmological models.Its fields include parameters for dark density, entropy density, entropy production, baryon-to-photon ratio, and neutrino number.Source: §3.1 · p. 7

3.2 Main routines

• Initialization routines set parameters to defaults or let users modify the baryon-to-photon ratio and neutrino number, while a separate procedure computes and stores weak-interaction reaction decay rates.The default initializer sets all parameters to 0 except the neutrino number, set to 3, and η = 6.19 × 10−10. Dark-density and dark-entropy initializers set the corresponding density to 0 at a temperature cutoff T_end.Source: §3.2 · p. 8
• The nucl routine calculates η and element-abundance ratios, while bbn_excluded reports whether the abundances satisfy Appendix B constraints or the calculation failed.nucl returns 0 on calculation failure and 1 otherwise; bbn_excluded returns 0 for abundances satisfying constraints, 1 otherwise, and −1 on failure.Source: §3.2 · p. 9

• AlterBBN is written for C99 and was tested successfully with GNU C and Intel C compilers on Linux and Mac.Source: §4 · p. 9
• The package includes src/, a Makefile, a README, and five sample programs for standard cosmology and modified cosmological inputs.The examples cover standard cosmology, user-set η, altered neutrino number, modified expansion or entropy, and reheating.Source: §4 · pp. 9–10
• Compile the library first to create libbbn.a, then use make name or make name.c to build a sample executable with the .x extension.Source: §4 · pp. 9–10

5 Input and output description

• The input/output examples cover standard cosmology, user-modified η or neutrino number, effective energy and entropy densities, and reheating.Users can write their own programs, using the supplied main programs as guides, to scan cosmological models.Source: §5 · p. 10, §5.5 · p. 12

5.1 Standard cosmology

• With WMAP η = 6.19 × 10−10, stand_cosmo.x returns Yp = 2.448e-01 and reports compatibility with BBN constraints.No parameter is required for this program.Source: §5.1 · p. 10

5.2 Standard cosmology with η modification

• With η = 3e-10, alter_eta.x returns H2/H = 7.967e-05 and reports exclusion by BBN constraints.The baryon-to-photon ratio is supplied as input.Source: §5.2 · p. 10

5.3 Standard cosmology with modified neutrino number

• With Nν = 4.5, alter_neutrinos.x returns Yp = 2.629e-01 and reports exclusion by BBN constraints.The number of neutrino families is supplied as input.Source: §5.3 · pp. 10–11

5.4 Effective energy and entropy densities

• alter_standmod.x computes element abundances in the standard cosmological model augmented by effective energy and/or entropy density, potentially changing early-Universe properties without observational consequences if chosen adequately; κρ and κs are dark-to-radiation energy and entropy ratios, respectively, at BBN time, while ns is the dark-entropy decrease exponent.Source: §5.4 · p. 11

5.5 Effective reheating model

• The program alter_standmod.x computes element abundances with added effective energy density and/or entropy production, which modify early-Universe properties without observational consequences if chosen adequately.Its inputs are κρ, the dark-energy-to-radiation density ratio at BBN; κΣ, the dark-to-radiation entropy-production ratio at BBN; and Tr, the GeV temperature below which both are set to zero.Source: §5.5 · pp. 11–12

• AlterBBN provides results in agreement with NUC123.Source: §6 · p. 12
• AlterBBN was planned for integration into SuperIso Relic so implemented cosmological models could face both BBN and particle-physics constraints.Source: §6 · p. 12
• Figure 1 maps Yp and 2H/H constraints over (nρ, κρ), with BBN-excluded regions between the Yp black lines and in the 2H/H upper-left corner.The plot colors encode different Yp and 2H/H values.Source: §6 · p. 12, Figure 1 · p. 13

• AlterBBN currently includes a network of 88 nuclear reactions, gathered in Table 1.Source: Appendix A · p. 14, Table 1 · p. 14

• The conservative constraints require 0.240 < Yp < 0.258 and 1.2 × 10^-5 < 2H/H < 5.3 × 10^-5.Source: Appendix B · p. 15
• They also require 0.57 < 3H/2H < 1.52, 7Li/H > 0.85 × 10^-10, and 6Li/7Li < 0.66.Source: Appendix B · p. 15
• Users can change the constraints in the bbn_excluded routine in src/bbn.c.Source: Appendix B · p. 15