SciPost Submission Page
Cosmological Infrared Subtractions & Infrared-Safe Computables
by Paolo Benincasa, Francisco Vazão
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Paolo Benincasa · Francisco Vazao |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2405.19979v3 (pdf) |
| Date accepted: | May 28, 2025 |
| Date submitted: | May 20, 2025, 9:16 a.m. |
| Submitted by: | Vazao, Francisco |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
Cosmological observables in perturbation theory turn out to be plagued with infrared divergences, which represents both a conceptual and computational challenge. In this paper we present a proof of concept for a systematic procedure to remove these divergences in a large class of scalar cosmological integrals and consistently define an infrared safe computable in perturbation theory. We provide diagrammatic rules which are based on the nestohedra underlying the asymptotic structure of such integrals.
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
Author comments upon resubmission
We thank the referees for the valuable feedback on our manuscript. Below we answer the comments and concerns of the referees.
Referee 1:
We moved the part where we discuss the flat space example of infrared safe observables from the conclusion to the introduction, we feel this should motivate better why searching for infrared safe quantities can be interesting also in cosmology.
Regarding the question of how many infrared safe quantities there are, we believe this is tied to the previous point. Precisely, despite mathematically one can write many infrared safe quantities, but practically just a handful of them would be physically meaningful. Having a systematic procedure, like ours, that on top of them mimics what happens in flat-space, and whose perturbative expansion is really sourced by an observable which has its own non-perturbative definition (the Wilson loop with Lagrangian insertion). Our procedure points towards understanding the possible existence of an analogous quantity in an expanding universe.
We explicitly discussed conformally coupled scalars only. However, for external massless scalars they directly obtained from conformally coupled from the action of differential operators acting on the external kinematics, and altering the power alpha in the measure, so our thick graphs directly apply.
Regarding the non-trivial examples in eps. 16 and 20 (in the new version), we addressed this by adding the simplest diagrammatic examples in the main body instead of the examples. We altered the discussion around eq. 15 (new version) as well, in hopes this would make the derivation of the rules less dense.
Regarding the section on loops, our procedure only works for removing the secular divergences, associated with the site integration. So in principle it works for all loops. The particular example of the Box in equation 23 (new version) is a particular case, which we did not generalize, It is interesting because in the flat space limit it returns also an infrared finite observable. The generalisation of this example to higher loops is not even settled in flat-space, despite some work like the one by Anastasiou and Sterman that we cite.
Referee 2:
Regarding the worked examples, we feel that putting them fully in the main body would break the flow of the text. Therefore, we decided to put the diagrammatic part of the examples, even adding a new one, in the main body. But we would like to insist in leaving the explicit analytic computations for the appendices
Regarding the reason behind IR divergences, we expanded the second paragraph of the introduction shortly detailing what are these divergences and their physical origin.
Referee 1:
We moved the part where we discuss the flat space example of infrared safe observables from the conclusion to the introduction, we feel this should motivate better why searching for infrared safe quantities can be interesting also in cosmology.
Regarding the question of how many infrared safe quantities there are, we believe this is tied to the previous point. Precisely, despite mathematically one can write many infrared safe quantities, but practically just a handful of them would be physically meaningful. Having a systematic procedure, like ours, that on top of them mimics what happens in flat-space, and whose perturbative expansion is really sourced by an observable which has its own non-perturbative definition (the Wilson loop with Lagrangian insertion). Our procedure points towards understanding the possible existence of an analogous quantity in an expanding universe.
We explicitly discussed conformally coupled scalars only. However, for external massless scalars they directly obtained from conformally coupled from the action of differential operators acting on the external kinematics, and altering the power alpha in the measure, so our thick graphs directly apply.
Regarding the non-trivial examples in eps. 16 and 20 (in the new version), we addressed this by adding the simplest diagrammatic examples in the main body instead of the examples. We altered the discussion around eq. 15 (new version) as well, in hopes this would make the derivation of the rules less dense.
Regarding the section on loops, our procedure only works for removing the secular divergences, associated with the site integration. So in principle it works for all loops. The particular example of the Box in equation 23 (new version) is a particular case, which we did not generalize, It is interesting because in the flat space limit it returns also an infrared finite observable. The generalisation of this example to higher loops is not even settled in flat-space, despite some work like the one by Anastasiou and Sterman that we cite.
Referee 2:
Regarding the worked examples, we feel that putting them fully in the main body would break the flow of the text. Therefore, we decided to put the diagrammatic part of the examples, even adding a new one, in the main body. But we would like to insist in leaving the explicit analytic computations for the appendices
Regarding the reason behind IR divergences, we expanded the second paragraph of the introduction shortly detailing what are these divergences and their physical origin.
Published as SciPost Phys. 18, 176 (2025)