Light Elements without a Hot Big Bang
Standard cosmology fixes the primordial helium, deuterium, and lithium abundances in a hot, dense first three minutes. This framework asserts no cosmic history and has no hot beginning, so big-bang nucleosynthesis does not operate. The chapter treats the light-element abundances as an out-of-scope explanatory gap—a present fact it does not explain—rather than a prediction in conflict.
Three primordial abundances are measured well enough to be decisive. The helium-4 mass fraction, inferred from low-metallicity gas, is Yₚ ≈ 0.247 and is strikingly uniform across the sky. The deuterium-to-hydrogen ratio is about 2.5×10⁻⁵, and lithium-7 is near 1.6×10⁻¹⁰ relative to hydrogen.
Standard cosmology's most quantitative early-universe success is primordial nucleosynthesis: a hot, dense first three minutes that fixes the helium-4 mass fraction at Yₚ≈0.247, the deuterium abundance at D/H≈2.5×10⁻⁵, and lithium-7 at 1.6×10⁻¹⁰. This framework asserts no cosmic history and has no hot dense beginning, so standard big-bang nucleosynthesis does not operate. Because the production of these abundances is inherently an origin question, and this volume adjudicates no cosmic history, the chapter treats the light-element abundances as an out-of-scope explanatory gap—a present fact it does not explain—rather than a prediction in conflict: the framework predicts nothing different, so there is no clash, only an unfilled explanation. We state the target precisely, explain why a naive static route fails for deuterium (so it is not adopted), and record the gap honestly. (The computed badge stays conflicting: the grade vocabulary has no “out-of-scope” token, so it marks the unexplained item while the text carries the status.)The raw facts to be explained
Three primordial abundances are measured well enough to be decisive. The helium-4 mass fraction, inferred from low-metallicity gas, is Yₚ≈0.247 and is strikingly uniform across the sky. The deuterium-to-hydrogen ratio, from high-redshift absorption systems, is D/H≈2.5×10⁻⁵. The lithium-7 abundance is near 1.6×10⁻¹⁰ relative to hydrogen. In the standard account these follow from nuclear reactions frozen out of a hot plasma when the temperature fell through 10⁹K. The challenge for a universe with no such hot phase is to produce the same numbers—above all the 24.7% helium and the fragile deuterium—by present-day or long-timescale processes.
Why this is hard
The difficulty is sharpest for two of the three. The helium fraction is set in the standard model by the neutron-to-proton ratio at freeze-out, n/p≈1/6, which neutron decay reduces to about 1/7 before the neutrons are locked into helium, giving
remarkably close to the observed 0.247. Reproducing this number, and its uniformity, without the freeze-out is the central obstacle. Deuterium is worse: it is so fragile that stars only destroy it, so a static universe that processed its hydrogen through stars would drive D/H down, not up to 2.5×10⁻⁵. Any candidate mechanism must therefore both synthesise a large, uniform helium fraction and create deuterium on net—two requirements that stellar nucleosynthesis alone cannot meet.
Candidate mechanisms (speculative, textsfHYP/textsfSPEC)
We list candidates honestly, none worked out. (i) Long-timescale processing: a static universe is not bounded by 13.8Gyr, so a far longer integrated history of stellar and cosmic-ray nucleosynthesis is available; this can build metals and some helium, but it does not solve the deuterium problem (stars destroy D) and struggles with the helium uniformity. (ii) A lattice-mediated channel: the extreme-density regions near deep vacuum deficits (Chapter 8) or sink cores might host a non-stellar synthesis channel producing light nuclei—purely conjectural, with no rate computed. (iii) Spallation: cosmic-ray spallation is known to make lithium and beryllium and could contribute to the lithium budget, but produces negligible helium and no net deuterium. None of these reaches the precision—especially the 0.247 helium fraction and the positive deuterium abundance—that the hot model reaches.
Simulation: making the target explicit
Rather than claim a mechanism, the simulation makes the target quantitative and the difficulty explicit. Simulation A computes the standard freeze-out helium fraction from Eq. (bbn-yp) to show precisely what must be reproduced, and Simulation B demonstrates that stellar processing of primordial gas drives the deuterium fraction downward, illustrating why the naive static-universe route fails:
# A: standard freeze-out target (what any model must reproduce) n/p at freeze-out = 0.167 -> after decay 0.143 -> Y_p = 0.250 (observed 0.247) # B: stellar processing of primordial gas (naive static-universe route) D/H after N stellar generations: 2.5e-05 -> 1.0e-05 -> 4.0e-06 ... (DESTROYED, wrong way)
The freeze-out calculation returns Yₚ=0.250, fixing the number to beat; the stellar-processing calculation drives deuterium down, confirming that the one naive present-day route fails. The honest verdict follows the framework's own scope discipline. The production of the primordial abundances is inherently an origin question, and this volume makes no claim about cosmic history; it therefore treats the light-element abundances as a present fact it does not explain—an explanatory gap, out of scope—rather than as a prediction in conflict with data. Crucially the framework predicts nothing different here: it is silent on origins, so there is no clash to record, only an unfilled explanation. The deuterium calculation does carry one positive lesson: the obvious static route, long-timescale stellar processing, drives D/H the wrong way, so the framework should not adopt that route—which is why the abundances are left unexplained rather than wrongly explained. What remains, honestly, is the same single open input as the next two chapters: were a fixed early-condition or non-stellar channel ever derived, the abundances would attach to it; absent that, they stand as a bracketed origin question, not a refutation.