SciPost Submission Page
The Asymptotic Structure of Cosmological Integrals
by Paolo Benincasa, Francisco Vazão
Submission summary
| Authors (as registered SciPost users): | Francisco Vazao |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2402.06558v2 (pdf) |
| Date submitted: | 2024-09-04 13:51 |
| Submitted by: | Vazao, Francisco |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
We provide a general analysis of the asymptotic behaviour of perturbative contributions to observables in arbitrary power-law FRW cosmologies, indistinctly the Bunch-Davies wavefunction and cosmological correlators. We consider a large class of scalar toy models, including conformally-coupled and massless scalars in arbitrary dimensions, that admits a first principle definition in terms of (generalised/weighted) cosmological polytopes. The perturbative contributions to an observable can be expressed as an integral of the canonical function associated to such polytopes and to weighted graphs. We show how the asymptotic behaviour of these integrals is governed by a special class of nestohedra living in the graph-weight space, both at tree and loop level. As the singularities of a cosmological process described by a graph can be associated to its subgraphs, we provide a realisation of the nestohedra as a sequential truncation of a top-dimensional simplex based on the underlying graph. This allows us to determine all the possible directions -- both in the infrared and in the ultraviolet --, where the integral can diverge as well as their divergence degree. Both of them are associated to the facets of the nestohedra, which are identified by overlapping tubings of the graph: the specific tubing determines the divergent directions while the number of overlapping tubings its degree of divergence. This combinatorial formulation makes straightforward the application of sector decomposition for extracting both leading and subleading divergences from the integral, as the sectors in which the integration domain can be tiled are identified by the collection of compatible facets of the nestohedra, with the latter that can be determined via the graph tubings. Finally, the leading divergence can be interpreted as a restriction of the canonical function of the relevant polytope onto a special hyperplane.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
1 - this paper develops the mathematical technology needed for a systematic understanding of loop corrections for cosmological correlators in FRW spacetimes.
2 - the approach mirrors similar techniques in flat space and thus avoids many of the pitfalls of cosmological loop calculations (namely that they break symmetries, etc).
Weaknesses
1 - this paper is not written for an audience that works on cosmological correlators, except those familiar with these techniques already. There is a high bar of mathematical sophistication that is unique to their approach that is needed to understand the results.
2 - there is very little physics in this paper. The examples are phrases in terms of graphs, not physical processes. This will make it difficult for someone working on loops from a more cosmological perspective to match their intuition with this approach.
Report
This is a very technical paper, but it seems correct and likely to be very useful to a group of researchers working on these kinds of FRW correlators. Benincasa has a long history of writing papers of this kind that are ultimately of high impact but may take others to translate the tools to more physical situations. It is also the case that most progress in direct calculations of cosmological loop corrections have been build on similar mathematical developments and therefore this will surely find use in the community. I recommend publication in the current form.
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)
Strengths
1. This work systematically investigates the UV and IR divergences in the perturbative computation of the Bunch-Davies wavefunction, with the combinatoric perspective of cosmological polytope. The underlying question is about the resummability of subleading IR divergences, which is well-defined and deserves careful consideration.
2. In particular, the authors focused on the cosmological integrals from a power-law FRW background, and examined the presence (and the degree) of divergences for general tree-level and loop-level processes.
3. Certainly this paper made a step forward to tackle the chanllege of loop correlators in cosmology.
Weaknesses
The authors aim for solving universal questions on cosmological correlators and take a combinatiorial perspective toward this goal, but in the end of the analysis the connection with these questions seems a bit weak and less concrete.
Report
The paper contains interesting results and detailed analysis. I think it is well-fitted for publication in SciPost Physics, though some revisions may be needed for further improvement and clarification.
Requested changes
1. One major motivation of the current paper is to understand how the resummation of divergences leads to IR-safe observables in cosmology. This question has been extensively discussed in the context of interacting light scalars in de Sitter spacetime. While the authors here look into a more general setup of power-law FRW universe, it will be very helpful to make the connection with the well-studied dS examples. For instance, can the new method here reproduce the standard results of $\lambda \phi^4$ in dS? There have been several recent works using the Bunch-Davies wavefunction to study these IR effects. Would the combinatorial analysis agree with them at both tree- and loop- levels? If so, what are the new ingredients here? With this part, I think the paper will be more complete and also become beneficial to readers who are less familiar with the polytope language.
2. One confusing point is about the power-law divergences. Unlike the logarithmic divergences, these can be really dangerous instabilities which are not resummable. I understand that they may arise in certain forms of the cosmological integrals, but are they mathematical constructions only, or can be physical contributions to the real parts of wavefunction coefficients? It will be surprising to see any power-law form divergences in realistic scenarios.
3. The authors discussed about the renormalization group structure in the combinatiorial approach, but it is less clear how the current analysis, which is still within perturbation theory, can shed light on the non-perturbative RG. Are there certain advantages of the polytope formalism which cannot be gained in other approaches? This connection (if exist) may need to be further clarified.
Recommendation
Publish (meets expectations and criteria for this Journal)