Starobinsky Inflation with T-Model Kähler Geometries

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this paper, a kind of the so-called Starobinsky Inflation ($R^2$ inflation) is studied in the framework of supergravity. The manuscript is well described in detail. 

1) There have been proposed many similar models of $R^2$ inflation in various context in literature. Compared with the past proposals, the strength of the present model and the new insights of physics including supergravity in the early universe found from the analyses of the present model should explicitly be explained. 

2) It is well known that the ordinary Starobinsky Inflation in general relativity can consistent with the Planck data in terms of the $n_s$-$r$ diagram shown in Figures 1 and 4. If the present model can fit the data better than the traditional Starobinsky Inflation model in general relativity, what physical mechanisms of supergravity can yield any influence?

3) Nowadays, too many inflation models have already been proposed. In such a situation, in addition to examine whether the $n_s$-$r$ diagram is compatible with the Plank result, it would be very important that some arguments of the trans Planckian problem as well as the swampland conjecture are presented. 

This work could be reconsidered for publication if the above points are investigated. 

Author Response

I would like to thank the referee for his/her positive consideration and interesting suggestions. Please find my response to the attached file.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This is a very fine and well written scientific paper. It contains significal new results in a research area with great activity. As usual, when I get such a good paper to review, my report is short. 

My main conclusion is that this paper can be published essentially as it is.

I found two small printing errors:

Line 567: Higgflaton. I guess this should be Higgsflation

Line 581: can employed → can be employed

I think they can be corrected during the publication process.

So in my opinion it is not necessary to ask the author make a revised version of the paper

Author Response

I would like to thank the referee for his/her positive consideration. The typos indicated have been now fixed.

Reviewer 3 Report

Comments and Suggestions for Authors

The paper under consideration explores a novel implementation of Starobinsky-like inflation within the framework of super gravity, employing Kähler potentials parameterizing hyperbolic geometries known from T-model inflation. More precisely, the study introduces superpotentials that are consistent with R and $U(1)_X$ symmetries, with the inflaton field represented by a gauge singlet or non-singlet superfield. An additional key feature is the introduction of a violated shift symmetry, which enables slight variations in Starobinsky inflation predictions. The author's analysis demonstrates that the scalar spectral index has an upper bound close to observational values, while the constant scalar curvature of the inflaton-sector Kähler manifold increases with the tensor-to-scalar ratio. The results indicate that this approach provides a natural embedding of Starobinsky inflation within SUGRA, ensuring a stable inflationary trajectory while maintaining compatibility with cosmological observations.

The paper is overall well written, and the results appear to be correct. The theoretical framework is sound, and the presentation is clear. There are no apparent issues with the analysis or conclusions. I therefore recommend the paper for publication in Universe in its present form.

Author Response

I would like to thank the referee for his/her positive consideration.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The response and revision by the author are appreciated. The revised manuscript could be suitable for publication.