Variation of the fundamental constants over the cosmological time: veracity of Dirac’s intriguing hypothesis
Bibliographic record
Abstract
We investigate how the universal constants, including the fine structure constant, have varied since the early universe close to the Planck energy scale (EP ∼ 1019 GeV) and, thus, how they have evolved over the cosmological time related to the temperature of the expanding universe. According to a previous paper (Nassif and Amaro de Faria, Jr. Phys. Rev. D, 86, 027703 (2012). doi:10.1103/PhysRevD.86.027703), we have shown that the speed of light was much higher close to the Planck scale. In the present work, we will go further, first by showing that both the Planck constant and the electron charge were also too large in the early universe. However, we conclude that the fine structure constant (α ≅ 1/137) has remained invariant with the age and temperature of the universe, which is in agreement with laboratory tests and some observational data. Furthermore, we will obtain the divergence of the electron (or proton) mass and also the gravitational constant (G) at the Planck scale. Thus, we will be able to verify the veracity of Dirac’s belief about the existence of “coincidences” between dimensionless ratios of subatomic and cosmological quantities, leading to a variation of G with time, that is, the ratio of the electrostatic to gravitational forces between an electron and a proton (∼1041) is roughly equal to the age of the universe divided by an elementary time constant, so that the strength of gravity, as determined by G, must vary inversely with time in the approximation of lower temperature or for times very far from the early period, to compensate for the time-variation of the Hubble parameter (H ∼ t−1). In short, we will show the validity of Dirac’s hypothesis only for times very far from the early period or T ≪ TP (∼1032 K).
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.010 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".