Self-similar spherically symmetric cosmological models with two scalar fields
Bibliographic record
Abstract
We shall study the qualitative properties of the class of self-similar spherically symmetric models with two non-interacting scalar fields with exponential potentials. Numerous scalar fields, and particularly scalar fields with exponential potentials, are known to arise in a variety of theories of the fundamental interactions. In recent investigations of the cosmological implications of these theories a number of novel features has been obtained, including the important assisted inflationary behaviour. In order to study this inflationary scenario, we shall restrict our study here to the so-called `spatially' self-similar models. We derive the governing system of evolution equations for the model, which is an autonomous five-dimensional system of ordinary differential equations, in terms of appropriately defined bounded variables. A monotonic function is obtained and the local stability of the equilibria is determined, so that global properties of the physical phase space can be deduced. Numerical integrations are also undertaken to complement the qualitative analysis and in order to investigate possible transient behaviour. From our dynamical analysis we find that, depending on the parameters of the models, in general the models begin expanding from a state with two scalar fields which are massless, and subsequently either recollapse and again evolve towards a model with two massless scalar fields or continue expanding towards the assisted inflationary solution. Hence we find that there exists an open set of models that undergo assisted inflation.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".