Generation and annihilation of scalar particles due to a curved expanding and contracting space-time.
Bibliographic record
Abstract
Abstract While a theory calculating a cosmological generation of particles ina case of the expanding space-time is quite developed, we study here a theory of a cosmological generation of particles in a case of a space- time which is expanding and then contracting back. The simplest case of fields studied in this connection is a scalar field. We will show in our paper that the quantum scalar field has delocalized in the conformal time η particle-like modes uⁱⁿ and two localized in the conformal time modes uⁱⁿ and uⁱⁿ for our choosen scale factor C(η). The vacuum for these states | 0, out > defined through massive modes uᵒᵘᵗ and through modes uᵒᵘᵗ and uᵒᵘᵗ is the same as the vacuum | 0, in >. A detector shows that there are no mass particles and no localized states forη → +∞ for non-accelerating case. For η → −∞ a Minkowski space- time is realized, as it is realized also in the out case. The quantum field has delocalized in the conformal time η particle-like modes uᵒᵘᵗ which in the -out region have k-dependent phase shifts with respect to the quantum field delocalized in the conformal time η particle-like modes uⁱⁿ in the -in region. The phase shift of delocalized modes (k-particles) is due to scattering in the gravitational field leading toexpansion and contraction of the space. Thus while in the expansion phase there is present generation of particles, due to nonpresence of particles in η → +∞ conformal time it is clear that in the phase of contraction of the scale factor there is present annihilation of particles from their peak state, where they are occurring from the generationprocess.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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".