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R. Consiglio, P. F. de Salas, G. Mangano, G. Miele, S. Pastor, O. Pisanti

arXiv:1712.04378v1astro-ph.COhep-ph

TL;DR

PArthENoPE 2.0 updates a BBN code used to calculate primordial light-element abundances, addressing the need for accurate predictions to test cosmological consistency and new physics. It replaces non-free numerical libraries and adds a GUI; the reported solver comparison retains precision despite requiring more steps.

  • Problem

    Accurate BBN predictions are needed to test cosmological consistency and investigate constraints on new physics beyond the present framework.

    Source: §I · p. 2, §VI · p. 10

  • Method

    PArthENoPE 2.0 replaces NAG routines with ODEPACK’s DLSODE solver and adds a GUI for interactive parameter and run-configuration choices.

    Source: A. PArthENoPE 2.0 · p. 6

  • Results

    About 5 times as many ODE solver steps are used per simulation, without changing code precision.

    Source: §IV · p. 7

  • Takeaways & Limitations

    The release makes the code’s libraries publicly available and provides a more user-friendly GUI while retaining the command-line option.

    Source: §VI · p. 11

Abstract

from arXiv · show

We describe the main features of a new and updated version of the program PArthENoPE, which computes the abundances of light elements produced during Big Bang Nucleosynthesis. As the previous first release in 2008, the new one, PArthENoPE 2.0, will be soon publicly available and distributed from the code site, http://parthenope.na.infn.it. Apart from minor changes, which will be also detailed, the main improvements are as follows. The powerful, but not freely accessible, NAG routines have been substituted by ODEPACK libraries, without any significant loss in precision. Moreover, we have developed a Graphical User Interface (GUI) which allows a friendly use of the code and a simpler implementation of running for grids of input parameters. Finally, we report the results of PArthENoPE 2.0 for a minimal BBN scenario with free radiation energy density.

I. INTRODUCTION

BBN tests the compatibility of cosmological models and can constrain extensions involving new physics. PArthENoPE 2.0 updates the public BBN code, with new libraries and a GUI, and the paper outlines its physics, performance comparison, and an extended-model analysis.

I. INTRODUCTION

  • BBN predictions test cosmological-model compatibility and can constrain new physics from the universe’s first minutes.Primordial abundances are compared with astrophysical observations; the standard scenario’s baryon-to-photon ratio inferred from deuterium and helium agrees with the CMB determination.Source: §I · pp. 1–2
  • The standard scenario’s satisfactory concordance makes BBN a way to quantitatively study extensions such as additional radiation density, often encoded by Neff.The introduction identifies a light sterile neutrino as a possible early-universe candidate for extra radiation.Source: §I · p. 2
  • Improved weak-rate, neutrino-decoupling, and nuclear-rate calculations reduced the theoretical uncertainty on the 4He mass fraction to 0.1%.The cited uncertainty is attributed to the neutron-lifetime uncertainty, τn = (880.2 ± 1.0) s.Source: §I · p. 2
  • PArthENoPE 2.0 replaces non-free NAG libraries with portable libraries and adds a GUI for easier code use.The paper also previews a comparison with the earlier code and a BBN analysis allowing free radiation energy density.Source: §I · p. 2

II. THE PHYSICS OF BBN

The section sets out the equations and inputs used to model BBN, including initial conditions and nuclear reaction networks. It also describes standard and non-standard parameters available in PArthENoPE 2.0 and notes scenarios that require source-code changes.

II. THE PHYSICS OF BBN

  • PArthENoPE 2.0 evolves the electron degeneracy parameter and nuclide abundances as functions of z = me/T by solving transformed BBN differential equations.The equations track Nnuc + 1 unknown quantities.Source: §II · p. 3
  • Users can select small, intermediate, or complete nuclear networks, ranging from lighter nuclides to networks including heavier nuclides.Initially, nuclides heavier than deuterium are set to the numerical zero Xmin, whose default is 10^-30.Source: §II · p. 4
  • In the standard scenario, η is the sole free parameter; the code accepts η10 and reports the corresponding Ωbh2 using the run’s Yp.The initial baryon-to-photon ratio is approximately ηi ≃ 2.73ηf at T = 10 MeV, before e+e− annihilation.Source: §II · p. 4
  • Non-standard inputs include extra radiation degrees of freedom ΔNeff, active-neutrino chemical potentials, and cosmological-constant energy density.The permitted ΔNeff range is −3.0 to 3.0; ξe and ξx = ξμ,τ may each range from −1 to 1.Source: §II · pp. 4–5
  • The treatment assumes a common neutrino temperature with the photon temperature above the effective decoupling temperature Td = 2.3 MeV, and does not include neutrino oscillations.The paper describes oscillation effects as sub-leading, citing earlier work.Source: §II · pp. 3–4
  • Other non-standard scenarios, including non-thermal neutrino distributions, quintessence fluids, and photon injection, can be considered by modifying the source code.Source: §II · p. 5

III. THE NEW RELEASE OF PARTHENOPE

PArthENoPE 2.0 updates the code’s numerical-library dependencies and introduces a more user-friendly interface. Users can retain the command-line workflow or choose the new graphical interface for interactive setup.

III. THE NEW RELEASE OF PARTHENOPE

  • PArthENoPE 2.0 replaces the non-free NAG libraries used by earlier versions with publicly available libraries.The prior versions used Backward Differentiation Formulas implemented in NAG routines for the BBN ODEs.Source: §III · p. 5
  • A Python-based GUI adds interactive selection of initial parameters and run configuration, alongside the existing command-line mode.The release includes the Fortran program files and the Python GUI file gui2.0.py.Source: §III · p. 5

A. PArthENoPE 2.0

PArthENoPE 2.0 updates the numerical routines used to solve the BBN equations and adds options for user customization.

A. PArthENoPE 2.0

  • The routine fcn retains its name but adopts the format required by the new solver.Source: A. PArthENoPE 2.0 · p. 5
  • The weak-rate calculation is separated into a wrate routine, making it easier to substitute a user-defined routine for non-standard physics scenarios.Source: A. PArthENoPE 2.0 · p. 5
  • OUTVAR now provides 20 free locations for user-defined output variables, with corresponding names and counts set in the code.Source: A. PArthENoPE 2.0 · p. 5
  • The earlier version allowed users to select only a discrete grid of values for ξ.Source: A. PArthENoPE 2.0 · p. 5
  • Brent’s method now solves the implicit equation, while an extended trapezoidal rule evaluates the one-dimensional integral and routines from compute modified Bessel functions.Source: A. PArthENoPE 2.0 · p. 6
  • PArthENoPE 2.0 uses ODEPACK’s DLSODE for the BBN equations, replacing the previous Backward Differentiation Method from NAG; DLSODE handles stiff and nonstiff systems.Source: A. PArthENoPE 2.0 · pp. 5–6
  • The update also fixes an underflow exception and makes minor modifications to the ODEPACK files.Source: A. PArthENoPE 2.0 · p. 6

B. The PArthENoPE Graphical User Interface

The GUI makes PArthENoPE easier to configure and run, including across grids of physical parameters, while retaining the command-line option.

B. The PArthENoPE Graphical User Interface

IV. COMPARISON WITH PARTHENOPE

PArthENoPE 2.0 reproduces the earlier code’s abundance predictions closely in a benchmark and across parameter variations, while using fewer solver steps.

IV. COMPARISON WITH PARTHENOPE

  • The benchmark uses ∆Neff = 0, η10 = 6.09389, and ξi = 0, and the authors report performance at least as good as the previous code.Source: §IV · p. 7
  • Below 1% for most nuclides and below ∼0.1% for deuterium and helium, the relative differences in final abundances remain small in the benchmark comparison.Source: §IV · p. 7
  • Across parameter-space checks varying η10, ξe = ξµ = ξτ, or ∆Neff, no relevant abundance-difference dependence appears except for 7Li versus baryon density at Ωbh2 values excluded by Planck results.Source: §IV · p. 7
  • The previous solver takes about 5 times as many steps per simulation as PArthENoPE 2.0, without a resulting change in precision.Source: §IV · p. 7

V. BBN ANALYSIS USING PARTHENOPE 2.0

The analysis uses deuterium and 4He abundances to constrain the baryon density with the effective number of neutrinos fixed or free. The fixed-standard fit agrees with Planck’s baryon-density range, while the predicted lithium abundance disagrees with measurement.

V. BBN ANALYSIS USING PARTHENOPE 2.0

  • The analysis compares theoretical light-element abundances with recent deuterium and 4He measurements using a χ² function that includes experimental and nuclear-rate uncertainties.Source: §V · pp. 7, 10
  • For Neff=3.045, η10=6.23+0.12/-0.14 and Ωbh2=0.0227±0.0005, consistent with Planck’s Ωbh2=0.02218±0.00015.Source: §V · p. 10
  • At the best-fit η10, predicted 7Li/H=4.69·10^-10 disagrees with the measured (1.58±0.31)·10^-10.Source: §V · p. 10
  • With Neff free, η10=6.13±0.13 (Ωbh2=0.0224±0.0005); Fig. 5 shows joint 1σ/2σ allowed regions and bounds from each element alone.Source: §V · p. 10, Figure 5 · p. 10

VI. CONCLUSIONS

PArthENoPE 2.0 updates the public BBN code while retaining its theoretical and numerical accuracy. Its changes include replacing non-free NAG libraries and adding a more user-friendly Python interface and GUI.

VI. CONCLUSIONS

  • The original PArthENoPE aimed to improve nuclide-abundance predictions and provide researchers a public tool combining precision and versatility.Its improvements included neutron-to-proton weak conversion rates, detailed neutrino decoupling, and nuclear-network rates.Source: §VI · p. 10
  • PArthENoPE 2.0 replaces the code’s non-free NAG libraries with publicly available libraries.The authors state that the new version shares PArthENoPE’s theoretical and numerical accuracy.Source: §VI · p. 11
  • A Python interface adds an interactive GUI for choosing initial parameters and running configurations.The interface enhances the previous version’s main.f interface.Source: §VI · p. 11

Appendix A: The PArthENoPE set of equations

Appendix A summarizes the equations used by PArthENoPE and corrects typos in the reference paper. It sets out the variables and transformations used to express abundance and conservation equations in the code.

Appendix A: The PArthENoPE set of equations

  • The appendix summarizes equations from the PArthENoPE reference paper to correct its typos and recalls the dimensionless variables z, x, and z̄.The variables are defined using the electron mass, temperature, scale factor, and neutrino temperature.Source: Appendix A · p. 11
  • The appendix develops entropy and total-baryon conservation equations using derivatives with respect to z, φ_e, and the nuclide abundances.It then derives ż for calculating the nuclear reaction rates per unit z.Source: Appendix A · pp. 11–12
  • The abundance equations are written in the form used by PArthENoPE.The appendix also gives an expression for dφ_e/dz used in the code, obtained by solving the transformed equation.Source: Appendix A · p. 12
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