Reformulating scalar–tensor field theories as scalar–scalar field theories using a novel geometry
Bibliographic record
Abstract
In this paper, I shall show how the notions of Finsler geometry can be used to construct a similar geometry using a scalar field, f , on the cotangent bundle of a differentiable manifold M . This will enable me to use the second vertical derivatives of f , along with the differential of a scalar field φ on M , to construct a Lorentzian metric on M that depends upon φ . I refer to a field theory based upon a manifold with such a Lorentzian structure as a scalar–scalar field theory. We shall study such a theory when f is chosen so that the resultant metric on M has the form of a Friedmann–Lemaître–Robertson–Walker metric, and the Lagrangian has a particularly simple form. It will be shown that the scalar–scalar theory determined by the Lagrangian can generate self-inflating universes, which can be pieced together to form multiverses with non-Hausdorff topologies, in which the global time function multifurcates at t = 0. Some of the universes in these multiverses begin explosively, and then settle down to a period of much quieter accelerated expansion, which can be followed by a collapse to its original, pre-expansion state. This article is part of the theme issue ‘The future of mathematical cosmology, Volume 1’.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".