The 2024 BBN baryon abundance update

This paper updates the 2024 Big Bang Nucleosynthesis baryon abundance by using the $\mathtt{PRyMordial}$ code to marginalize over nuclear reaction rates, revealing that theoretical versus experimental Deuterium burning rates drive significant differences in derived abundances and yielding conservative estimates of $\Omega_b h^2 \approx 0.022$ with constraints on ultra-relativistic relics.

The Gist

Here is an explanation of the paper "The 2024 BBN baryon abundance update," translated into simple language with creative analogies.

The Big Picture: The Universe's Receipt

Imagine the Big Bang as a massive cosmic kitchen where the universe was cooked up. In the first few minutes, this kitchen produced the basic ingredients of everything we see today: Hydrogen, Helium, and a tiny bit of Deuterium (heavy hydrogen).

Scientists call this Big Bang Nucleosynthesis (BBN).

The amount of "stuff" (matter) in the universe is called the baryon abundance. Knowing exactly how much matter there is is crucial. It's like knowing the exact amount of flour in a cake recipe; if you get it wrong, the cake (the universe) won't rise correctly, and the stars and galaxies won't form the way they do.

This paper is a 2024 update on how well we know that "flour amount." The author, Nils Schöneberg, is checking the receipts to see if our measurements are consistent.

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The Main Problem: The "Deuterium Burn"

To figure out how much matter exists, scientists look at how much Deuterium survived the Big Bang.

The Analogy: The Campfire
Imagine Deuterium as a pile of wet wood trying to catch fire.

• The Fire: The nuclear reactions that turn Deuterium into heavier elements (like Helium).
• The Water: The intense heat and radiation of the early universe.

If there is more matter (more baryons), the "fire" burns hotter and faster. The wet wood (Deuterium) gets burned up almost instantly.
If there is less matter, the fire is weaker, and more wet wood survives.

So, by measuring how much Deuterium is left today, we can calculate how much matter was there at the start. It's a reverse-engineering trick: Less Deuterium left = More Matter existed.

The Conflict: Two Different Cookbooks

The paper discovers that the biggest source of confusion isn't the measurements themselves, but the theoretical "cookbooks" (computer codes) scientists use to predict how fast that fire burns.

There are two main ways to write these cookbooks:

1. The "Lab-Tested" Method (Experimental): This approach uses data from actual experiments in particle accelerators (like the LUNA experiment). It says, "We measured this reaction in a lab, so let's use those numbers."
   • Result: This method suggests there is more matter in the universe.
2. The "First-Principles" Method (Theoretical): This approach uses pure math and quantum physics to calculate how the particles should behave without relying on lab data.
   • Result: This method suggests there is less matter in the universe.

The Metaphor:
Imagine two chefs trying to guess how much salt is in a soup.

• Chef A tastes the soup and checks the recipe book written by the person who made it (Experimental).
• Chef B calculates the salt based on the chemical properties of the ingredients (Theoretical).
• They get different answers. The paper asks: "Who is right?"

The Solution: The "PRyMordial" Safety Net

The author introduces a new tool called PRyMordial. Think of this as a super-safety net.

Instead of picking just one chef's recipe, PRyMordial says, "Let's assume both chefs might be slightly off, and let's average out all the possible mistakes." It takes a "conservative" approach, widening the margin of error to make sure the true answer is definitely inside the range.

The New Verdict:
By using this safety net, the author finds a very solid estimate for the amount of matter in the universe:

• $\Omega_b h^2 = 0.02218 \pm 0.00055$

In plain English: We are now very confident that the universe is made of roughly 2.2% matter (relative to the critical density), give or take a tiny bit. This number matches up well with other ways of measuring the universe, like looking at the Cosmic Microwave Background (the "afterglow" of the Big Bang).

The "Helium Anomaly" (The Weird Outlier)

There was a recent measurement from a telescope survey called EMPRESS that found much less Helium than expected.

• The Reaction: This is like finding a cake that has no sugar in it when the recipe says it should.
• The Paper's Conclusion: The author treats this as a "glitch" or an outlier. When they try to force this low Helium number into their models, the math breaks down unless they invent weird, exotic physics (like invisible particles). Until we have more proof, the paper says: "Ignore this weird measurement for now; it doesn't fit the rest of the story."

Why Does This Matter?

You might ask, "Who cares about the exact amount of flour in the cosmic cake?"

1. Calibrating the Ruler: The universe has a "standard ruler" called the Sound Horizon (ripples in the early universe). To measure how fast the universe is expanding (the Hubble Constant), we need to know the exact amount of matter to calibrate that ruler. If our "flour" measurement is wrong, our ruler is wrong, and we can't solve the mystery of why the universe is expanding faster than we thought.
2. Checking for New Physics: If our measurements of the "flour" (matter) don't match the "afterglow" (CMB), it means our model of the universe is missing something. This paper confirms that, for now, the standard model holds up, but the biggest uncertainty is still how fast Deuterium burns.

The Bottom Line

This paper is a quality control check. It says:

• We have a slight disagreement between lab data and theory on how fast Deuterium burns.
• By being very careful and conservative, we can still pin down the amount of matter in the universe with high precision.
• The "Helium anomaly" is likely a measurement error, not a sign of new physics.
• The future of this field depends on better lab experiments to measure those Deuterium burning rates more accurately.

In short: The universe's recipe is looking more consistent than ever, but we still need to refine our measurements of the "cooking speed" to get the perfect cake.

Technical Summary

Here is a detailed technical summary of the paper "The 2024 BBN baryon abundance update" by Nils Schöneberg.

1. Problem Statement

The baryon abundance ($\Omega_b h^2$) is a fundamental parameter of the $\Lambda$CDM cosmological model, critical for understanding the thermal history of the universe, Big Bang Nucleosynthesis (BBN), and the calibration of the sound horizon for Baryon Acoustic Oscillations (BAO). While the Cosmic Microwave Background (CMB) provides precise constraints, the emergence of the "Hubble tension" (discrepancies between early and late-universe measurements of $H_0$) necessitates independent internal consistency checks.

The primary challenge addressed in this paper is the systematic uncertainty in BBN predictions arising from nuclear reaction rates, specifically the Deuterium burning rates. There is a known tension between:

• Theoretical ab-initio calculations (e.g., PRIMAT), which tend to predict lower baryon abundances.
• Experimentally determined rates (e.g., PArthENoPE using NACRE II databases), which tend to predict higher abundances.

Additionally, recent high-precision measurements of Helium-4 ($Y_p$) by the EMPRESS survey suggest a value significantly lower than standard BBN predictions, creating a potential "Helium anomaly" that could bias baryon abundance estimates.

2. Methodology

The author performs a comprehensive re-evaluation of light element abundances (Deuterium and Helium) using data from early 2024. The methodology involves:

• Code Comparison: The study utilizes three distinct computational approaches to model BBN:
  1. PArthENoPE v2.0: Older code, does not include recent LUNA experiment data.
  2. PArthENoPE v3.0: Updated code incorporating LUNA radiative capture ($dp\gamma$) measurements and recent transfer reaction data.
  3. PRyMordial: A new code capable of running in two modes:
     • NACRE II Mode: Uses experimental thermonuclear rates (similar to PArthENoPE).
     • PRIMAT Mode: Uses theoretical ab-initio reaction rates.
• Marginalization Strategy: A key methodological innovation is the use of PRyMordial's explicit marginalization over nuclear reaction rate uncertainties. Unlike previous works that applied fixed theoretical uncertainties, this approach marginalizes over log-normally distributed rate uncertainties. This allows for a conservative estimate that encompasses both theoretical and experimental systematic differences.
• Datasets: The analysis tests sensitivity against three primary datasets for light element abundances:
  • "BAO+BBN papers" (Cooke+2017 for D/H, Aver+2015 for $Y_p$).
  • "PDG Aug 2023" (Particle Data Group recommendations).
  • "Yeh+2022" (used as a reference for PDG constraints).
  • Outlier Check: The EMPRESS survey measurement of $Y_p$ is tested separately to assess its impact.
• Parameter Space: The analysis varies the baryon abundance ($\Omega_b h^2$), the effective number of neutrino species ($\Delta N_{\text{eff}}$), and the neutron lifetime ($\tau_n$) using flat priors.

3. Key Contributions

• Quantification of Rate Uncertainties: The paper demonstrates that the largest source of variation in derived baryon abundances is the choice of Deuterium burning rates (theoretical vs. experimental).
• Conservative Marginalization: It establishes a robust framework for deriving baryon abundances by explicitly marginalizing over nuclear rate uncertainties. This prevents the over-precision often seen in analyses that rely solely on specific experimental fits or theoretical calculations.
• Resolution of Code Discrepancies: The study shows that while ab-initio and experimental codes yield different central values (differing by $\sim 1\sigma$), the application of conservative marginalization in PRyMordial brings these results into agreement.
• Assessment of the Helium Anomaly: The paper rigorously tests the low Helium abundance reported by EMPRESS. It finds that this measurement is incompatible with standard Deuterium abundances and $\Delta N_{\text{eff}} = 0$ unless nuclear rates are pushed to the extreme edges of their allowed regions or exotic neutrino models are invoked.

4. Key Results

A. Baryon Abundance ($\Omega_b h^2$)

Using the PRyMordial code with NACRE II rates and explicit marginalization (the recommended conservative approach):

• $\Lambda$CDM (Standard Model):
  • Using PDG-recommended abundances: $\Omega_b h^2 = 0.02218 \pm 0.00055$.
  • Using the "BAO+BBN" datasets: $\Omega_b h^2 = 0.02231 \pm 0.00055$.
• $\Lambda$CDM + $\Delta N_{\text{eff}}$ (Additional Relics):
  • Using PDG-recommended abundances: $\Omega_b h^2 = 0.02196 \pm 0.00063$.
  • Using "BAO+BBN" datasets: $\Omega_b h^2 = 0.02212 \pm 0.00072$.

Note: The uncertainties are intentionally inflated compared to previous literature to account for the systematic differences between theoretical and experimental nuclear rates.

B. Effective Neutrino Species ($\Delta N_{\text{eff}}$)

When marginalizing over $\Delta N_{\text{eff}}$ using light element abundances alone:

• The constraint is $\Delta N_{\text{eff}} = -0.14 \pm 0.21$ (using PDG abundances).
• This indicates no significant evidence for extra relativistic species, consistent with the standard model ($\Delta N_{\text{eff}} = 0$).

C. The Helium Anomaly (EMPRESS)

• The EMPRESS measurement ($Y_p = 0.2370 \pm 0.0034$) is found to be an outlier.
• When forced into the model, it creates a significant incompatibility ($\chi^2_{\text{min}} \approx 4.6$) with standard Deuterium measurements unless $\Delta N_{\text{eff}}$ is allowed to vary or nuclear rates are pushed to their limits.
• The paper concludes that until further evidence emerges, the EMPRESS result should be treated as inconsistent with the standard BBN framework.

D. Sensitivity Analysis

• Code Sensitivity: Switching from PArthENoPE v2.0 to v3.0 (incorporating LUNA data) shifts the mean $\Omega_b h^2$ by $\sim -0.9\sigma$. Switching from experimental (NACRE) to theoretical (PRIMAT) rates shifts it by $\sim -1.0\sigma$.
• Dataset Sensitivity: The choice of Deuterium/Helium datasets (PDG vs. Yeh+2022 vs. BAO+BBN) has a minor impact, typically shifting results by less than $0.3\sigma$, except when using the PRIMAT mode which is more sensitive to dataset choice.

5. Significance

This paper provides the most up-to-date and conservative estimate of the baryon abundance derived from Big Bang Nucleosynthesis as of early 2024. Its significance lies in:

1. Calibration of the Sound Horizon: The derived value of $\Omega_b h^2$ is crucial for calibrating the sound horizon ($r_s$), which is the standard ruler used in BAO analyses to measure the Hubble constant ($H_0$). A precise BBN determination helps resolve tensions in $H_0$ measurements.
2. Systematic Uncertainty Handling: By explicitly marginalizing over nuclear rate uncertainties, the authors provide a "safe" value for cosmological inference that does not rely on the specific preference for theoretical vs. experimental nuclear physics.
3. Future Direction: The paper identifies that the primary bottleneck for future precision is not cosmological data, but laboratory measurements of Deuterium burning rates (specifically the $ddn$ and $ddp$ transfer reactions). Future improvements in these nuclear cross-sections will be the key to reducing the error bars on $\Omega_b h^2$ derived from BBN.