3.11 The Lithium-7 Puzzle in Primordial Nucleosynthesis: Dual Corrections via Tension Rescaling and Background-Noise Injection

Home ／ Chapter 3: Macroscopic Universe

I. Terminology and Scope

To set the stage, we interpret the “low lithium-7” problem within the Energy–Sea–Tension picture. In the early universe, generalized unstable particles (GUP), during their brief lifetimes, collectively sculpt a background landscape described as statistical tensor gravity (STG); when they disintegrate or annihilate, their residual wavelets seed a faint, locally injected texture called tensor background noise (TBN). From here on, this chapter uses only the full English terms—generalized unstable particles, statistical tensor gravity, and tensor background noise. We also reference Big Bang nucleosynthesis (BBN) and the cosmic microwave background (CMB); after their first mention, we use the full terms only.

II. Observational Gap and Challenges

1. The abundance gap: Measurements in the atmospheres of metal-poor, old stars (the Spite plateau) generally show lithium-7 below standard Big Bang nucleosynthesis predictions, by roughly a factor-level shortfall depending on sample and corrections.
2. “Everything else fits”: Using the same cosmology and nuclear reaction inputs, the helium-4 mass fraction and the deuterium-to-hydrogen ratio are typically consistent with observations. Adjusting only lithium-7 without damaging those successes is difficult.
3. Three mainstream hurdles:
   • Stellar depletion: Any explanation must account for a widespread, similarly scaled depletion while remaining consistent with indicators like lithium-6 and iron.
   • Updated nuclear rates: Even with refined cross-sections, bringing lithium-7 down alone is hard.
   • Early-time injections of new physics: Models that destroy beryllium-7 via decays or annihilations often require finely tuned spectra, abundances, and lifetimes while avoiding conflicts with deuterium and the cosmic microwave background spectrum.

III. Physical Mechanism (“Dual Corrections”: Tension Rescaling + Background-Noise Injection)

1. Tension rescaling: a gentle retiming of “clocks and windows.”
   • Idea: In a dense early universe—an energetic “sea”—the degree of tension subtly rescales the relative pacing of the microphysical reaction clock and the cooling clock. This is akin to a small, uniform stretch of the time axis. Reaction forms and dimensionless constants remain unchanged.
   • Key windows (two phases):
     1. Second-scale neutron–proton freeze-out: Only a minuscule rescaling is allowed to keep the helium-4 baseline stable.
     2. Hundreds–thousands of seconds, from “deuterium bottleneck opens” to “beryllium-7 formation”: Beryllium-7 is highly sensitive to cooling cadence and overlap time. Slightly advancing or delaying “heat on/off” narrows or misaligns its peak-production window, lowering the net yield.
   • Everyday analogy: Standard Big Bang nucleosynthesis is like a pot of broth cooling on the stove. Tension rescaling is a tiny nudge to the kitchen timer—same recipe, almost the same steps, but an ever-so-slight shift in the ideal mixing moment.
2. Background-noise injection: sparse, brief, selective “finishing touches.”
   • Origin and character: In the high-density early universe, generalized unstable particles appear and vanish rapidly. Their disintegration sheds broadband, low-coherence wavelets. Almost all thermalize immediately and become part of the thermal history. Statistically, however, extremely sparse and well-timed micro-injections can occur.
   • Why it targets beryllium-7: A tiny injection of neutrons or a narrow band of soft photons, introduced during the beryllium-7–dominated phase, preferentially breaks beryllium-7 without disturbing deuterium or helium-4:
     1. Neutron route: Be-7(n,p)Li-7 followed by Li-7(p,α)He-4 lowers the final lithium-7.
     2. Soft-photon route: A narrow, weak, brief spectrum can exploit the more fragile absorption features of Be-7/Li-7, “trimming Be-7” without “overheating” deuterium.
   • Magnitude constraints: Intensity and duration must be small enough to avoid exceeding current bounds on the cosmic microwave background μ/y distortions or light-element budgets—only a selective “touch-up.”
   • Everyday analogy: The stew is essentially done. Just before removing it from the heat, a gentle tap removes the extra puffing in one topping—without changing the base flavor.
3. Synergy: retime first, then apply a light touch.
   • Step one: Tension rescaling narrows or shifts the beryllium-7 production window and lowers the baseline yield.
   • Step two: Background-noise injection, introduced in the adjacent interval, trims the remaining beryllium-7.
   • Net effect: Lithium-7 falls to the observed band while deuterium and helium-4 remain where they should.

IV. Parameters and Boundaries (Protecting What Already Works)

• Helium-4 constraint: Rescaling at the second-scale phase faces a strict upper bound to preserve the helium-4 mass fraction.
• Deuterium constraint: The timing, spectrum, and intensity of background-noise injection must avoid the deuterium-destruction thresholds.
• Cosmic microwave background spectrum: Any allowed injection must sit well below current μ/y distortion limits, leaving only a faint, likely unresolvable trace.
• Isotopic by-products: Watch for small shifts in lithium-6/lithium-7 and helium-3; if present, their amplitudes should match a weak “finishing touch,” not a sweeping overhaul.
• Cosmological consistency: Dimensionless constants and interaction forms remain unchanged. Tension rescaling is only a minor retiming of clocks.

V. Testable Signals and Audit Paths

• Near-zero cosmic microwave background spectral distortions: Future, more sensitive spectrometers should tighten μ/y limits. This mechanism predicts signals below current bounds—very close to zero, but not identically zero.
• Tiny, environment-dependent shifts in the Spite plateau: If tension rescaling is the primary driver, lithium-7 plateaus may show minute, systematic differences across large-scale environments (filaments, nodes, voids), detectable only with large samples.
• Collateral evidence for beryllium-7 destruction: Look for subtle, correlated deviations involving lithium-6/lithium-7 and helium-3, while disentangling any late-stage stellar processing.
• Weak covariance with early activity: If background-noise injection occurred, its statistical strength should weakly correlate with early-universe activity levels, consistent with the diffuse-baseline picture discussed elsewhere in this book.

VI. Relationship to Mainstream Proposals

• A softened take on “new-particle injection”: Traditional models rely on injection as the main effect and thus on fine-tuned spectra, lifetimes, and abundances. Here, the main role goes to tension rescaling (clock retiming), while injection is demoted to a very weak secondary effect—substantially easing parameter pressure.
• A complement—not a substitute—to stellar depletion: Moderate, late-stage surface depletion is not excluded but is not required as the sole explanation. At most, it would lightly adjust the dual-correction baseline.
• Compatible with ongoing nuclear-rate refinements: Continued improvement of reaction rates remains valuable. Given the latest rate compilations, acknowledging modest tension rescaling plus a selective finishing touch can remove the “stubborn excess” of lithium-7 without breaking other successes.

VII. Analogy for Intuition

Baking Timer + Precision Scoring. Tension rescaling nudges the oven timer just a little, shifting the ideal rise window. Background-noise injection is a quick score before serving, flattening only the over-risen peak. The cake itself—helium-4 and deuterium—stays the same; only the surplus lithium-7 “bump” is leveled.

VIII. Summary

• Problem framing: The lithium-7 puzzle calls for small, targeted adjustments to timing and micro-injection, not a wholesale rewrite of the early universe.
• Primary change: Tension rescaling slightly advances or delays the “on/off” cadence of primordial nucleosynthesis, preferentially reducing the beryllium-7 channel that feeds lithium-7.
• Fine finishing: Tensor background noise, introduced briefly and selectively at the right moment, trims beryllium-7 without disturbing deuterium or helium-4.
• Overall coherence: Together, these two corrections preserve the main achievements of standard Big Bang nucleosynthesis while offering concrete, testable avenues. They align with the causal chain that links generalized unstable particles, statistical tensor gravity, and tensor background noise across nearby chapters.