[IPTA-cs] (1) Metastable strings (2) Subgroups

[Kai Schmitz <kai schmitz cern ch>]

Hi All,

A few comments on two topics: (1) Metastable cosmic strings and (2) Forming smaller subgroups. @Paul, @Nihan, please have a look at my question below.

(1) Metastable cosmic strings:

A few of you were reaching out to me after yesterday's call because they are interested in my "metastable cosmic string" proposal. This is great! I indeed think that "metastable strings" are an option that we should explore, because they are (a) well motivated from the particle physics perspective and (b) promise to significantly improve the quality of our fit---if strings happen to decay in the right time window in the early Universe. More precisely, as you can see in our paper https://arxiv.org/abs/2107.04578, the U(1) and GUT symmetry breaking scales that respectively determine the cosmic-string tension and the GUT monopole mass need to be separated by a factor 8 or 9 or so, see the left panel of Fig. 3. This is a somewhat specific value, but there is certainly no strong fine-tuning involved, and values of this order of magnitude are definitely plausible and realistic in concrete GUT models. See, e.g., Eq. (23) in https://arxiv.org/abs/2102.08923, which actually "predicts" a value of 8 in a simple SU(2) x U(1) model.

(2) Subgroups:

We have now reached a good point where we can start thinking about forming smaller subgroups. How about the following three groups as a first proposal:

- Subgroup 1: Implementation into ENTERPRISE (first task: implementation of the look-up table I generated shortly before Christmas)

- Subgroup 2: Metastable cosmic strings (first task: derive a closed analytical _expression_ for the GW spectrum)

- Subgroup 3: Your suggestion (e.g., superstrings, first task in this case: think about going beyond the simple 1/p rescaling, see, e.g., https://arxiv.org/abs/1606.05585)

If I understand correctly, Paul and Nihan would be interested in contributing to subgroup 1, even though they might need some time, because of a few other things keeping them busy at the moment. In addition, it would be great if we could attract more PTA members with ENTERPRISE experience that could help us with the implementation. @Paul, @Nihan, do you think it would make sense to send around a mail on a big IPTA mailing list or something like that, in order to solicit more team members with ENTERPRISE experience?

Another comment is that I will take up a tenure-track assistant professor position at the University of Münster in May. Initially, I will have (at least) two PhD students in my group, and I will definitely suggest to one of them to become a member of our team. If the student should be interested, I would propose to them to spend some time with ENTERPRISE, so that they could help us with the implementation of the signals that we are interested in.

As for the second subgroup, I would suggest that we should have a meeting in two weeks with everyone who's interested in doing some actual analytical pen-on-paper calculations on metastable cosmic strings. If you are interested, please indicate your preferred time slot in the following doodle:

https://doodle.com/poll/q988vifh27xa3g7q?utm_source=poll&utm_medium=link

As a preparation for this meeting, please have a look at https://arxiv.org/abs/2002.01079 and https://arxiv.org/abs/2107.04578 and prepare a list of questions that you want to ask / discuss during the meeting.

Finally, regarding the third subgroup: Please feel free to make suggestions. Cosmic superstrings sound like an interesting possibility to me, especially because they may also allow us to improve the quality of the fit. But most of all, I would like to hear your suggestions.

Talk to you soon and have a great weekend, everyone!

Best regards, Kai.

On 1/27/22 18:21, Kai Schmitz via IPTA-cosmic-strings wrote:

Hi All,

Thanks a lot for the great meeting today. Here are the slides and the recording:

Slides: https://docs.google.com/presentation/d/1t-4FTycO2hWpfv1KzBAkSrgcYif6HWKnKBxkS756Smk/edit?usp=sharing
Recording: https://drive.google.com/file/d/181IPQWW0EIVPHAp2rlX7InPhX9onamgl/view?usp=sharing

The tentative date for the next meeting is Thursday, February 24, 2022 at 15:00 UTC. However, if there should new results from a first Enterprise run at an earlier point, we can as well spontaneously schedule an earlier meeting. In the meantime, let's continue the discussion here on the mailing list.

Speaking of that, let me provide you with a few more details on our analysis of metastable cosmic strings in

[1] https://arxiv.org/abs/2107.04578

which builds upon earlier work by Louis Leblond, Benjamin Shlaer, and Xavier Siemens:

[2] https://arxiv.org/abs/0903.4686

This earlier paper focuses exclusively on gravitational waves from string segments with monopoles on both ends, estimating the GW spectrum based on and extending the following calculation by Xavier Martin and Alexander Vilenkin

[3] https://arxiv.org/abs/gr-qc/9612008

What we now do in our paper from last year is to extend the analysis from segments-only to the full scenario including both types of animals, closed loops and segments. We distinguish in particular between three populations: (a) closed loops that are chopped off from long strings, (b) segments originating from monopole nucleation on long strings, and (c) segments originating from monopole nucleation on closed loops. For closed loops, we assume that GW emission is dominated by cusps (q = 4/3), while for segments we use the Martin-Vilenkin result (q=1, up to some cutoff mode number). Moreover, in order to estimate the number densities of all three populations, we work with transport equations [see Eq. (A.1) in https://arxiv.org/abs/2107.04578], similar to those employed by Leblond, Shlaer, and Siemens. We solve these equations in some cases analytically, in other cases numerically, and make sure that we reproduce the known results for stable strings at early times (i.e., the results of your numerical simulations). The transport equations allow us in particular to describe how one population (e.g., closed strings) can act as the source of another population (e.g., segments originating from monopole nucleation on closed loops).

And again, I invite you to have a closer look at our paper. My impression is that metastable strings could give us a considerably better fit to the data than stable cosmic strings. Plus, they would be well motivated from the perspective of grand unification. (Of course the lifetime would need to fall into a somewhat narrow window, as J.J. was pointing out.)

In a more general sense, my question is whether we should really restrict ourselves to only one benchmark scenario that can parametrized by, say, just one free parameter (log Gmu)? Or whether we want to consider slightly more general scenarios, which may be motivated by different physics arguments (as Ken was emphasizing). We could definitely have a look into cosmic superstrings and see whether they improve the quality of the fit. And we could study Nambu-Goto strings in dependence of two parameters: (a) their tension and (b) their lifetime. In this case, we could present our results in a 2D parameter plot (tension versus lifetime), which would trivially also cover the case of stable cosmic strings (namely, in the parameter region where the lifetime becomes longer and longer). Let me know what you think.

And finally, let me / us know if you have got further questions, ideas, comments? Which other directions would you like to explore? Where and how would you like to contribute to the project? Anything we should change about the style of our meetings? Should we stick to the current format or try something else? Any input or suggestions are welcome.

Thanks again and talk to you soon!

Best regards, Kai.