Running and Running of the Running of the Scalar Spectral Index in Warm Inflation

Round 1

Reviewer 1 Report

In the manuscript “Running and running of the running of the scalar spectral index in warm inflation” the authors study the minimal warm inflation (MWI) scenario in the strong dissipative,  motivated by the hints emerging from the Planck  data  that those parameters characterising the scalar spectral index may be larger than predicted in the standard cold inflation.

 

The authors derive analytical expressions for the running and running of the running scalar spectral index, going beyond the previous numerical approaches. They  obtain persuasive results that warm inflation scenarios may adhere better to the Planck data. 

 

The results seem sound and  are relevant for the subject under consideration. Also the manuscript is both well organised and well written.

 

Therefore I recommend publication of the present work without changes in the journal Universe.

 

Author Response

The referee has not made any specific question and accepted the paper
as it is. We thank very much the referee for the nice comments.

Reviewer 2 Report

Please see the attached file

Comments for author File: Comments.pdf

Author Response

The referee made some specific questions regarding the structure
of the paper and, in special about the hybrid model. We have made our best
to implement them as we explain below.

- Part of the text in section 4 that was common for both models were
moved now to section 2, where we also extended some more on the general
equations for the spectral tilt and runnings.

- We have extended the discussion and results concerning the hybrid
potential model in section 3. We believe that now both sections
3 and 4 are presented in a much more balanced way and on equal
footing.

About the specific questions asked by the referee:

1- The scale M appearing in the dissipation coefficient expression
and in the hybrid potential are not necessarily the same. We have
used now a different symbol for the mass scale in the dissipation
coefficient. We thank the referee for bringing this issue to us.

2- We have now added similar tables for the hybrid model as we had 
for the exponential model and discussed about them in the text.
They are now the tables 1 and 2 in section 3.

3- A footnote as been added to comment on the issue raised by the
referee. Please see footnote 2.

4- Please also see footnote 3 for the issue of topological defects
production in hybrid inflation. 

Please note that the two issues above goes beyond the scope of the
present paper, but nevertheless we agree those are important issues
and we hope the comments added should be enough such that an interested 
reader in those subjects will be aware of them.

On the issues related to both models:

1- Comments about the swampland conjectures concerning the hybrid
model have now been added when we discuss the results shown in table 1.

2- The values for the axion decay constant, considering QCD like parameters
entering the dissipation coefficient of the MWI, have now been given.
The values for f have been added in both tables 1 and 3 and a short
discussion about the results were added to the text following the discussion
about those tables.

3- The temperature at the end of warm inflation is also now given explicitly
in tables 1 and 3. They are also discussed in the text in connection to the
axion decay constant.

We believe that the paper is much improved now after implementing the
the referee's  suggestions. We thank the refereee for such detailed comments which helped improve the quality of the paper.

Reviewer 3 Report

This is a very well-written paper which sheds light on some important cosmic observables in the context of the strong dissipative regime of warm inflation. I think this is an important contribution which should be published.

I just have 2 small suggestions for the authors:

1) There is a small typo "potentail" on Page-2 (line-45) 

2) Perhaps the authors should cite some other contributions in the context of the role of warm inflation in the swampland, namely., 2003.07184 and 1910.10516.

Author Response

The referee accepted the paper pointing out only a smalltypographical error, which we have now corrected and also suggested two references to be cited. Those references have now been cited in the text (see Ref. 17 and 18 of the revised manuscript).

Round 2

Reviewer 2 Report

I would like to thank the authors for their responses to my

queries. From what I can judge their results are sound and

reliable. The fact that the axion decay constant seems to be

compatible with the candidacy of QCD axion for cold dark matter is

interesting and may be the starting point for further

investigations. For these reasons, I recommend publication of the

paper in "Universe".