Here are some comments about the article. TAM: My responses to these comments appear in italics.
I really like the historical part and appreciate the part on the physics of the cosmological constant. However, I find that there are some imprecisions, gaps, and parts that are not completely clear in the rest of the text. Here is a list:
- after eq. (13), I do not understand the meaning of the sentence: "In an homogeneous universe there are no pressure gradients, so a positive pressure does no work and has no expanding effect.".
> TAM: I have now elaborated with: "For pressure to do work there needs to be a pressure gradient - a relatively high pressure region next to a relatively low pressure region - that will then cause movement from high pressure to low. In a homogeneous universe there are no pressure gradients, so a positive pressure does no work and has no expanding effect (there are no low-pressure regions for it to push matter into)."
- also the sentence "By combining CMB measurements of the large scale structure" is not very clear.
> TAM: I have also elaborated on this to try to make it clearer: "Using measurements of temperature fluctuations in the cosmic microwave background radiation (CMB) from when the universe was ~380,000 years old one can conclude that the Universe is spatially flat to within a few percent. By combining these data with accurate \(H_0\) measurements and/or measurements of the matter density of the universe, it becomes clear that the matter in the Universe only contributes approximately 23% to the critical density."
- The author write: "The cosmological constant problem arises because quantum field theory predicts a value of the vacuum energy far in excess of the cosmological constant value measured in cosmology.". QFT cannot "predict" any value for the cosmological constant. More correctly, using naive naturalness arguments in QFT one cannot explain why the observed cosmological constant is so small. See for instance S. Weinberg, Rev. Mod. Phys. 61 (1989) 1 (http://rmp.aps.org/abstract/RMP/v61/i1/p1_1) or a more recent discussion in the introduction of http://arXiv.org/pdf/1004.1782.
> TAM: Fair enough. I have replaced my sentence with the referee's suggested wording and added the reference to Weinberg.
- The author writes: "which have a time-varying value of dark energy that traces the energy density and thus naturally solves the coincidence problem." This sentence is not really true. In all models of dynamical dark energy there is a dimensional parameter (a mass) that needs to be unnaturally tuned to explain the coincidence. See for instance a discussion in http://arxiv.org/abs/astro-ph/0005265.
> TAM: I've now discussed this in the Dark energy or cosmological constant section and added the reference.
- It is not possible to forget a very important explanation for the cosmological constant value, i.e. the anthropic argument in the context of the string landscape. Whether one likes it or not, this is today one of the dominant arguments in the scientific debate. See for instance http://arxiv.org/abs/hep-th/0603249 for a small review.
> TAM: I've now added a section on the anthropic arguments.
- I would suggest to add in the references the important reviews of Weinberg (The Cosmological Constant Problem. Steven Weinberg, Rev.Mod.Phys.61:1-23,1989) and of Padmanabhan (Cosmological constant: The Weight of the vacuum, Phys.Rept.380:235-320,2003).
> TAM: Done
- in two different places: "in an homogeneous" -> "in a homogeneous"
- "G is the gravitational constant" should be put after eq. (1) and not before eq. (8).
- between eqs. (9) and (10): "as a forms of energy density" -> " as forms of energy density"
> TAM: Done
- after eq. (13) "does no work" -> "does not work"
> TAM: No, I meant that it does not do any work, i.e. does no work.