General Slow-Roll Inflation in f(R) Gravity under the Palatini Approach

Round 1

Reviewer 1 Report

The authors consider slow-roll inflation in Palatini f(R) gravity. They show that this can be achieved by including a minimally coupled scalar field χ, which plays the role of the inflaton. By choosing the model f(R) = α Rⁿ  with n=4/5 and assuming a quadratic potential for the inflaton, the authors obtain values for the spectral index and tensor to scalar ratio, and show that these agree well with the Planck constraints. I would like the authors to address the following points:

1. The function Ω is not specified in eq(14).
2. The scalar field χ representing the inflaton as part of the action in (31) is minimally coupled; yet on line (91) the authors write φ ≈ φ(χ) and then conclude that during inflation \dot{φ) << φ. There should be a justification for doing this.
3. I'm not sure how the authors obtained (37) from (33). 
4. It seems to me that the term (U'/U_eff)² should be U'/(U_eff)².
5. The authors do not discuss whether the chosen model is compatible with the evolution of the universe and/or solar system tests. 

Author Response

See attached file.

Author Response File: Author Response.pdf

Reviewer 2 Report

The manuscript consider inflation in Palatini-type of modified gravity. The derivations seem correct though there is not much new, the example models (or, their more realistic variants) have been considered in the literature at much greater depth.

Some care should be paid to minor typos in equations and the use of units. A particular point: before (37), it is stated that $\dot{\phi}<<\phi$, and whether it is meant that $\dot{\phi}<<H\phi$ or $\kappa\dot{\phi}<<\phi$, the argument should be made explicitly, or at least mentioned that this may only be justified in the super-Planckian regime of the field.

Author Response

See attached file.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

See attached file. 

Comments for author File: Comments.pdf

Author Response

See attached file.

Author Response File: Author Response.pdf

Round 3

Reviewer 1 Report

The authors have now made adequate additions to the paper as suggested in my earlier reports. I have one last question. In the first equation of (38), should the term (1/2)V(phi) be corrected to (phi/2)V(phi)? 

Author Response

Dear editor,

we would like to thank again the referee for her/his valuable comments. In the following, we reply to the comment raised in her/his last report: 

Referee: "In the first equation of (38), should the term (1/2)V(phi) be corrected to (phi/2)V(phi)? "

Answer: We think that the referee is talking about the first equation in (39) (reference number from the last version). In the first version of our manuscript there was a typo in the FLRW equations (34), where was written (1/2)V(phi) instead of (1/2phi)V(phi), which might have induced confusion when getting the first equation in (39). This is now corrected.

Yours sincerely,

The authors