Quantum Fluctuations in Vacuum Energy: Cosmic Inflation as a Dynamical Phase Transition
Round 1
Reviewer 1 Report
In this paper the the author has studied "Quantum Fluctuations in Vacuum Energy -Cosmic Inflation as a Dynamical Phase Transition". My comments regarding the publication of this paper are appended below point-wise:
- The paper is well written and findings are elaborately presented in the draft.
- But the author have not studied anything numerically which can be easily be done for the betterment of the article.
- Also I have found that the author has cited some restricted categorical papers, where the subject demands enormous number of good references which will be helpful for the general readers for future study.
In view of the above mentioned facts stated, I would therefore ask for minor revision. Once the mentioned facts will be addressed in the future revised version, then only will give final decision regarding the publication of this paper at Universe.
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The author introduces and applies an interesting point of view of the dynamics of the inflationary scalar field. The results are presented in a clear manner. Nevertheless a number of points should be clarified before the publication.
1. It is mentioned in lines 90, 132, 243 and 346 that the noise, a variable of the Schwinger-Keldysh formalism, is not really active in harmonic systems due to energy conservation. This is not true, the "noise" represents an environment which renders energy non-conserved, cf. damped harmonic oscillator.
2. It is not clear what kind of divergence the author alludes to in section 2.2. The divergence of this section is driven by a dynamical instability owing to an unbounded potential. This is related to the wrong choice of the ground state, labeled as an IR divergence later in the text. However the latter is reserved in the literature for divergences appearing in the thermodynamical, infinite system limit. In other words, a wrong choice of the vacuum in an infinite system leads to IR divergences. However section 2.2 is about a single degree of freedom where no volume dependence arises. Furthermore it is not clear how the trick of hiding the noise in the functional integral measure and treating it as a formal, non-physical variable changes the traditional use and interpretation of the Schwinger-Keldysh formalism. The dynamical instability and the treatment of a variable of the formalism are unrelated.
3. The author argues at the beginning of section 2.4 that the noise becomes unimportant after the dynamical instability triggers the increase of the order parameter. However the noise, a variable of the formalism, does not disappear and remains a crucial ingredient of the relaxation of the asymmetrical stable vacuum. If the author has a dynamical mechanism in mind which renders the noise less important for a transitional time interval then he should present it with an estimate of the corresponding time scales.
4. There is no ground state for an inverted harmonic oscillator hence the long time dynamics is ill defined. However one assumes in deriving the propagator (42) that the dynamics is well defined for arbitrary long time evolution. This problem appears for instance as a violation of the time translation invariance by G_C in (48). How can one proceed in a perturbative calculation say of the one-loop effective action in this case? In particular, G_C at the end of eq. (91) is not translation invariant.
Furthermore, as soon as the new vacuum is formed the dynamics is stabilized and the fluctuations are restricted to the convex part of the bare potential the propagators obtained for an inverted oscillators are not physical. The equations presented in this work are valid for a finite length of time. How can one estimate this time?
Further minor questions:
- The remark in line 251 about the relation between integrability and random fluctuation is unclear because the noise is present in the Schwinger-Keldysh formalism independently of the integrability.
- The description of the appearance of the order parameter, outlined in the paragraph starting with line 100, is one possible scenario followed in this work and not a necessity.
- Eq. (4) has a typo (exclamation mark?).
- The author states that the parametrization (37) is almost the CTP formalism. Either the difference with the CTP formalism should be explained more clearly or the "almost" should be left out.
- eq. (53): The integration over the three space should not be there in the second line. The source is coupled to x rather than X in the last line.
- The variable X is defined as the expectation value <x> before (52). Hence the average of x introduced in (54) must be vanishing. Is this condition satisfied by (63)?
- It is not clear what the author meant by "legitimate" in the phrase of line 266-267.
- Eq. (61) which contains the leading correction only and the free part of the noise distribution is missing.
- eq. (62) is the saddle point equation because S_{eff} is the bare effective action. The equation of motion of the expectation value X is derived from the Legendre transform (52).
- Eq. (59) holds for vanishing external source rather than in the lowest order in the perturbation. If the author meant the expansion in J then it should clearly be stated.
- What is f(t) in line 324?
- The definition of the normal ordering is missing in eq. (81).
- What attempts the author is alluding to in line 341?
- What is the functional integral measure introduced in eq. (89)?
- The phrases in lines 389-390 and in lines 437-439 should be corrected.
- line 404: Why is the dynamical instability related to secular divergences?
- What is the relation between the loss of perturbative approach and determinism, mentioned in line 442? How can the determinism be expected in a quantum dynamics?
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
I accept the author's response to my questions. There are only two remaining points to correct:
- The main message could be presented in a simpler manner. While the researchers have the natural right to express their finding in their own words I suggest to think over the presentation and make it easier to read. For instance it seems to me that the frequent reference to squeezed state is misleading and it would be more illuminating to use simply an adiabatic ground state (lowest lying state of a Hamiltonian with slow time-dependence). The difference between the SK noise and the "dry noise" is important and the term "noise" seems to be wrongly chosen in a closed system.
- The issue of the IR divergences is nor properly summarized in point 5. on pg. 18. An essential difference between the UV and the IR divergences is that the former reflects our ignorance about the short distance physics and can be removed by an appropriate redefinition of the parameters of the action which are nonlocal at the scale of the cutoff. The IR divergences indicates our wrong, unstable description of the vacuum and can not be cured by the renormalization group method because that would imply strongly nonlocal operators. These divergences should simply be absent when the (adiabatic) ground state is well approximated. This is actually what the author is doing.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
