Quintom Fields from Chiral K-Essence Cosmology

Round 1

Reviewer 1 Report

The manuscript deals with the application of k-essence formalism to a chiral cosmological model.

The work is relevant.

However, some attention should be drawn to a few remarks which deserve to be better explained, namely:

a) Despite the study of subcases in both classical and quantum formulations, little attention is paid to the differences between the results. Although a very small link is made to other references [66,68,69] in the Conclusions. This could be improved.

b) Some problems arise from Hamiltonians not bounded from below. Would the physical solutions be heavily affected by this in the scenarios studied in the paper?

 

I think that some discussion could be added to the present version of the manuscript so to improve its content. Hence, comments could be introduced to answer the points raised in this report. Until then, I recommend a major revision prior to publication.

Author Response

REVIEWER-1: \\
To my mind, this scenario can be interesting for cosmologists, but it invites some minor criticism.
The authors do not evaluate viability of their solutions (41), (55), (62). In particular, they describe (strongly)
accelerated expansion after the bounce, How this behavior can correspond to available observational data, for instance, $H(z)$ data? \\

RESPONSE TO REVIEWER-1:\\
The viability of our solutions should be taken more in a mathematical context, that is, given a particular set of
yielded parameters from this scenario, the outcome of eqs. (41), (55), (62) describes qualitatively an expanding universe after a bounce.
However, since the barotropic parameter $\omega_{\phi_{1}\,\phi_{2}}$ crosses the ``-1'' boundary, one would expect an instantaneous
phantom scenario that immediately after becomes a quintessence one. Nevertheless, a thorough evaluation with available observational
data is beyond the scope of this paper.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments in the file.

Comments for author File: Comments.pdf

Author Response

REVIEWER-2: \\
Application (3) to $\delta S$ above gives zero identically. It looks strange. \\

RESPONSE TO REVIEWER-2: \\
This equation result from the methodology of the variational principle, and, in fact, this procedure yields the Einstein field equations.
This strategy is usually encountered in any theory that contains gravity. Note that in order to satisfy $\delta S=0$, the expression
within the curly brackets must be identically zero since $\delta g^{\alpha\beta}$ is no null inside the volume. Nevertheless, the
way we presented the procedure is indeed confusing for the reader, therefore we included a better explanation of  our results.

REVIEWER-2: \\
Origin of formula (30) should be clarified. \\

RESPONSE TO REVIEWER-2:  \\
In the manuscript we have omitted the right definition of the parameter $\rm  \Lambda_{12}$; however the equation is now correct.
We also added comments (before equation (30)) to better explain the proper procedure to obtain $m^{12}$.

REVIEWER-2: \\
The authors mentioned the probability density collapse and conclude that the classical scenario is not realized at some parameters.
This point is important and much more intensive discussion is necessary. Does in means that the Universe does not expand? What
is mathematical condition for it?  \\

RESPONSE TO REVIEWER-2: \\
In fact we mentioned that in order to the classical regime take places the probability density must collapse, therefore,
within a framework where the quantum realm persists nothing can be said about an expanding classical universe.
That is the case of equation (74) ($\eta_{1}$ and $\lambda_{1}<\sqrt{6}$), where we could not find any set of
parameters for which the probability density collapses. And interestingly in the classical scheme (Quintessence domination)
the scale factor does not grow given any combinations of the model parameters. However, we insist that if a classical
framework never occurs, within the canonical quantization formalism and the Wheeler-DeWitt equation, we cannot
say that the perseverance of its quantum counterpart is the reason that the universe does not expand.

 

REVIEWER-2: \\
It is known that phantom fields are unstable. Special efforts are necessary when one using them. Can the authors discuss this aspect? \\

RESPONSE TO REVIEWER-2:  \\
Accordingly with a Quintom description, the phantom instability can be avoided given certain potentials. That is the case of our analysis.
Note how the barotropic parameter $\omega_{\phi_{1}\,\phi_{2}}$ crosses the ``-1'' boundary so an instantaneous phantom scenario
 occurs but immediately after becomes a quintessence one. Thus readjusting a probable instability due to the phantom field.

REVIEWER-2: \\
As I see, the authors use the Planck units. If that is true, the figures and conclusions hold in the time interval of the Planck scale,
$t\sim 10^{-43}$s. To make some conclusion, the interval must be many orders of magnitude wider.\\

RESPONSE TO REVIEWER-2:  \\
Here we want to clarify that for this cosmological model we are using a conformal time $dt=N(t)d\tau$, rather that the usual
cosmic time. One of the issues with these type of proposals are that we cannot set $N(t)=1$.

 

Author Response File: Author Response.pdf

Reviewer 3 Report

see attached file

Comments for author File: Comments.pdf

Author Response

I send you a general response for all referee's, because  initially we reply at two of them.

Now, we complete the answer  for all.

j.socorro

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The manuscript deals with the application of k-essence formalism to a chiral cosmological model.

The work is relevant.

However, some attention should be drawn to a few remarks which deserve to be better explained, namely:

a) Despite the study of subcases in both classical and quantum formulations, little attention is paid to the differences between the results. Although a very small link is made to other references [66,68,69] in the Conclusions. This could be improved.

b) Some problems arise from Hamiltonians not bounded from below. Would the physical solutions be heavily affected by this in the scenarios studied in the paper?

 

I think that some discussion could be added to the present version of the manuscript so to improve its content. Hence, comments could be introduced to answer the points raised in this report. Until then, I recommend a major revision prior to publication.

Author Response

We response to reviewer 1 in the attach letter in the first two point.

 

Author Response File: Author Response.pdf

Reviewer 3 Report

Referee report on the paper

"Quintom fields from chiral K-essence cosmology"

The author: José Socorro at all

 It is clear now that system (3) is simply the result of the action minimization (In the previous version it looks like a definition of $G_{\mu\nu}$). 

 For readers, the authors should specify the definition of "probability density collapse". Is this related to the collapse of wave function at the moment of measurment?  

 It seems that the authors argue the cosmological/classical stability of the phantom fields. I kept in mind its instability according to quantum creation of particles. But, OK, let us accept the cosmological stability.

The authors did not answer to my question concerning the units in which time is measured. It is really suitable working with dimensionless units, but final results must be expressed in dimensionful units. I mean Fig. 1 and 2, for example - time must be expressed in seconds, years or the Planck units.

The role of subsection 3.3 remains uncertain. A text should accompany and explain the final formulas.

The paper may be published after minor revision according to my remarks.

Author Response

In the following letter we response to reviewer 3 in all points.

Author Response File: Author Response.pdf

Round 3

Reviewer 1 Report

The authors have answered my points, improving the text with their remarks and comments. I think this version is suitable for publication.