Analytical approximations for curved primordial tensor spectra
Bibliographic record
Abstract
We build upon previous analytical treatments of scalar perturbations in curved inflationary universes to obtain analytical templates for the primordial tensor power spectrum in models with non-zero primordial spatial curvature. These templates are derived without assuming a particular inflaton potential, within a background history consisting of an initial kinetically dominated phase followed by an ultra-slow-roll inflationary regime, thereby isolating the universal imprints of curvature on tensor modes. Our results predict characteristic large-scale features -- including low-$\ell$ cut-offs and oscillatory patterns -- that are consistent with numerical solutions and provide a clear physical interpretation of how curvature modifies the underlying dynamics. In particular, we show that curvature effects manifest mathematically as systematic shifts in the dynamically relevant wavevectors, mirroring the behaviour previously identified in the scalar power spectrum. These features translate into distinctive signatures in the large-angle $B$-mode polarisation spectrum, offering a potential discriminant for spatial curvature in forthcoming CMB observations.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".