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2014-05-27

Christian Corda5

This is a very good paper which deserved publication in ScienceOpen.

Average rating: | Rated 5 of 5. |

Level of importance: | Rated 5 of 5. |

Level of validity: | Rated 5 of 5. |

Level of completeness: | Rated 5 of 5. |

Level of comprehensibility: | Rated 4 of 5. |

Competing interests: | The reviewer and the author of this article have co-authored four publications between 2009-2013. |

- Record: found
- Abstract: found
- Article: found

Lorenzo Iorio (2014)

10.14293/S2199-1006.1.SOR-ASTRO.AWXWIL.v1.RKXGOE

This work has been published open access under Creative Commons Attribution License **CC BY 4.0**, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at **www.scienceopen.com**.

In this paper the author computes the long-term orbital variations of a test particle orbiting a central body acted upon by an incident monochromatic plane gravitational wave under the assumption that the wave is “frozen” with respect to the astrophysical observations. This assumption is justified from a phenomenological point of view because if one applies the author's results to the solar system it will be possible, in principle, to put constraints over a part of the ultra-low frequency spectrum of gravitational waves for which neither ground-based nor space-based dedicated experimental devices are available. This is a very important observation which, even if taken alone, justifies the importance of this paper.

More in general, the paper is well written and looks mathematically consistent. I stress also the importance of the presented results in cosmology because the resulting bounds can be considered independent tests on relic gravitational waves that the BICEP2 collaboration claimed to have recently detected. The author also recalls other different approaches to study the same problem discussed in the present paper. I have no doubts that this is a very good paper which deserved publication in ScienceOpen. I have only a minor suggestion in order to clarify a issue that could be, in principle, misleaded. Page 2, the sentence below eq. (3) “The fact that both^{7} h_{00} and h_{0i}, i=1,2,3 vanish in the transverse traceless (TT) gauge [76], which is tacitly assumed here^{8}” can mislead and must be modified. In fact, the (TT) coordinates are slightly different from the local inertial Fermi coordinates. The coordinate transform can be indeed found in D. Baskaran and L. P. Grishchuk, Class. Quant. Grav. 21 4041 (2004) and its generalization to scalar waves in C. Corda, Phys. Rev. D83, 062002 (2011). Thus, I suggest to re-write the sentence in a way similar to the following: “As the linarized Rienmann tensor is gauge-invariant [76], one can compute h_{00} and h_{0i}, i=1,2,3 directly in the transverse traceless (TT)^{7} gauge [76] finding that they vanish”. The author should also remove note ^{8} accordingly.

More in general, the paper is well written and looks mathematically consistent. I stress also the importance of the presented results in cosmology because the resulting bounds can be considered independent tests on relic gravitational waves that the BICEP2 collaboration claimed to have recently detected. The author also recalls other different approaches to study the same problem discussed in the present paper. I have no doubts that this is a very good paper which deserved publication in ScienceOpen. I have only a minor suggestion in order to clarify a issue that could be, in principle, misleaded. Page 2, the sentence below eq. (3) “The fact that both^{7} h_{00} and h_{0i}, i=1,2,3 vanish in the transverse traceless (TT) gauge [76], which is tacitly assumed here^{8}” can mislead and must be modified. In fact, the (TT) coordinates are slightly different from the local inertial Fermi coordinates. The coordinate transform can be indeed found in D. Baskaran and L. P. Grishchuk, Class. Quant. Grav. 21 4041 (2004) and its generalization to scalar waves in C. Corda, Phys. Rev. D83, 062002 (2011). Thus, I suggest to re-write the sentence in a way similar to the following: “As the linarized Rienmann tensor is gauge-invariant [76], one can compute h_{00} and h_{0i}, i=1,2,3 directly in the transverse traceless (TT)^{7} gauge [76] finding that they vanish”. The author should also remove note ^{8} accordingly.