Anthropic Principle and the Hubble-Lemaître Constant
Round 1
Reviewer 1 Report
The paper cannot be accepted because it suffers from critical
weaknesses and shortcomings in the contents, mathematical
formulations, the way of expressing the ideas, and style of
writing. I cannot go into full detail because this would
require considering all the sentences and formulas one by one,
which is not possible to do. Let me just give two examples
concerning the claims mentioned in the third and fourth lines of the abstract that are ambiguous. There is no authentic mathematical reason behind this. For me, these details are sufficient to reject the
given submission in the most definite form. It is difficult
to imagine that the given authors can do something reasonable
with this level of attention to what they do.
Author Response
Dear Editors,
First of all we would like to thank each reviewer for his/her very valuable comments. We tried to follow all suggestions proposed by the reviewers. All changes are indicated by yellow color.
In our survey paper we present a number of astrobiological, astronomical, geophysical, geochronometrical, heliophysical, climatological, paleontological, and OBSERVATIONAL arguments showing that the Solar system slowly expands by a speed comparable to the Hubble-Lemaitre constant, see e.g. (4), (5), (6), (7), (9), (10). These arguments are independent. This guarantees that the Earth received almost constant solar flux during the last 3.5 Gyr when life on Earth continually existed, since the luminosity of the Sun increases (see new Theorem 1 in Section 2). This fact significantly contributed to the existence of humankind and thus supports the Anthropic Principle.
Reviewer 2 Report
For the authors:
Figure 1 should not be placed here in this cosmological context; it does not have relevance for the main context of the paper.
Figure 2 must have been taken from somewhere else. It must be clarified by the authors what are the assumptions on which these curves are based. The authors should understand that cosmological Hubble parameters are connected with a symmetrization or homogenisation of the cosmic matter distribution such that a Robertson-Walker geometry can be adopted. Then one can start working with the two Friedman equations and obtain solutions for H=H(t).
See e.g. :
H. Goenner: Einfuehrung in die Spez. und Allgemeine. Relativitätstheorie, Spektrum Akadem. Verlag, Heidelberg, !996
or;
Peacock, J.A.: Cosmological Physics, Cambridge University Press. 1999
But it turns out that H(t) in any way is connected with the given type of gravitating matter, i.e. baryons, pressurized or cold, photons, or Lambda etc. Best fitting solutions are presented e.g. by
Fahr and Heyl: Adv.Theor.& Comput. Phys., 4(3), 253-258, 2021.
Your Figure 2?, for what kind of cosmic matter is it valid???
What concerns the influence of the Hubble expansion on cosmic matter structures like e.g. the Solar System there exists a long list of publications starting with Einstein-Strauss and their "vacuole". More recently this has been evaluated for the Solar System by Fahr and Siewert; Imprints from the global cosmological expansion to the local space-time dynamics, NATURWISSENSCHAFTEN, 95, 413-425, 2008 (DOI10.1007/s00114-007-340-1) ; The Pioneer anomaly problem.
Literature with concern to local cosmology:
Einstein, A. and Straus, E.G.: The influence of the expansion of space on the gravitation fields surrounding individual stars, Rev.Mod.Phys., 17(2), 120-124, 1945
Einstein, A. and Straus, E.G.: Corrections and additional remarks to our paper on the influence of the expansion of space on the gravitation fields surrounding individual stars, Rev.Mod.Phys., 18(1), 148-149, 1946
Carrera, M. and Guilini, D.: On the influence of the global cosmological expansion on the local dynamics of the solar system, WWW.arxiv.org//abs/gr-qc/0602098, 2006
Cooperstock, F.I., Faraoni, V. and Vollick, D.N.: The influence of the cosmological expansion on local systems, Astrophys.J ., 501, 61-66, 1999
Fahr, H.J. and Siewert. M.: Imprints from the global cosmological expansion to the local space-time dynamics, NATURWISSENSCHAFTEN, 95, 413-425, 2008 : DOI 10.1007/ s 00114-007-0340-1
The Hubble migration, if taking place like the authors assume, should have restructured the solar system with its planets: What about perturbation forces and stabilizing forces of the planet Jupiter???
Good luck in improving your paper.
Author Response
Dear Editors,
First of all we would like to thank each reviewer for his/her very valuable comments. We tried to follow all suggestions proposed by the reviewers. All changes are indicated by yellow color.
For the authors: Figure 1 should not be placed here in this cosmological context; it does not have relevance for the main context of the paper.
Answer: Figure 1 was removed.
Figure 2 must have been taken from somewhere else. It must be clarified by the authors what are the assumptions on which these curves are based. The authors should understand that cosmological Hubble parameters are connected with a symmetrization or homogenisation of the cosmic matter distribution such that a Robertson-Walker geometry can be adopted. Then one can start working with the two Friedman equations and obtain solutions for H=H(t). See e.g. : H. Goenner: Einfuehrung in die Spez. und Allgemeine. Relativitätstheorie, Spektrum Akadem. Verlag, Heidelberg, !996 or; Peacock, J.A.: Cosmological Physics, Cambridge University Press. 1999
Answer: This book was added to References and is cited in Section 3. The function H=H(t) was calculated from the classical Friedmann equation for ΩM = 0.3 and ΩLambda = 0.7. This first order ordinary differential equation describes the behavior of the expansion function (scaling parameter). We only needed to illustrate that H=H(t) was almost constant during the last 3.5 Gyr. It remains almost constant also for slightly different values of cosmological parameters.
But it turns out that H(t) in any way is connected with the given type of gravitating matter, i.e. baryons, pressurized or cold, photons, or Lambda etc. Best fitting solutions are presented e.g. by Fahr and Heyl: Adv.Theor.& Comput. Phys., 4(3), 253-258, 2021.
Answer: We cite this paper in Section 1.
Your Figure 2?, for what kind of cosmic matter is it valid??? What concerns the influence of the Hubble expansion on cosmic matter structures like e.g. the Solar System there exists a long list of publications starting with Einstein-Strauss and their "vacuole". More recently this has been evaluated for the Solar System by Fahr and Siewert; Imprints from the global cosmological expansion to the local space-time dynamics, NATURWISSENSCHAFTEN, 95, 413-425, 2008 (DOI10.1007/s00114-007-340-1) ;
Answer: We added the papers by Einstein & Straus and Fahr & Siewert to References. Einstein & Straus try to connect smoothly the classical Schwarzschild metric with global time-dependent Robertson-Walker metric. However, their approach has several drawbacks, since Einstein’s equations are not satisfied in a region, where one metric changes into another. Such a composite solution would require that the second derivatives of the metric tensor are continuous.
The Pioneer anomaly problem.
Answer: The Pioneer anomaly problem was not included, since:
1) it can be explained by radiation of an asymmetric position of internal heat sources;
2) the corresponding time interval is too short compared to cosmological time;
3) the additional acceleration has the opposite sign than the local Hubble expansion.
Literature with concern to local cosmology: Einstein, A. and Straus, E.G.: The influence of the expansion of space on the gravitation fields surrounding individual stars, Rev.Mod.Phys., 17(2), 120-124, 1945 Einstein, A. and Straus, E.G.: Corrections and additional remarks to our paper on the influence of the expansion of space on the gravitation fields surrounding individual stars, Rev.Mod.Phys., 18(1), 148-149, 1946
Answer: This is discussed in Section 3.
Carrera, M. and Guilini, D.: On the influence of the global cosmological expansion on the local dynamics of the solar system, WWW.arxiv.org//abs/gr-qc/0602098, 2006
Answer: This paper is similar to the article Carrera, M., Giulini, D.:
Influence of global cosmological expansion on local dynamics and kinematics,
Rev. Mod. Phys. 82 (2010), 169-208, which was cited in the previous version of our manuscript. So we did not include the old version by Carrera and Giulini from 2006.
Cooperstock, F.I., Faraoni, V. and Vollick, D.N.: The influence of the cosmological expansion on local systems, Astrophys.J ., 501, 61-66, 1999
Answer: We already cited this paper in the previous version of our manuscript with vol. 503 (1998).
Fahr, H.J. and Siewert. M.: Imprints from the global cosmological expansion to the local space-time dynamics, NATURWISSENSCHAFTEN, 95, 413-425, 2008 : DOI 10.1007/ s 00114-007-0340-1
The Hubble migration, if taking place like the authors assume, should have restructured the solar system with its planets: What about perturbation forces and stabilizing forces of the planet Jupiter??? Good luck in improving your paper.
Answer: The paper Fahr & Siewert (2008) was added to References and cited in Section 3. Concerning Jupiter, if Mars were substantially closer to the Sun 4.5 Gyr ago, then Jupiter was closer as well, since otherwise Mars would have larger dimensions. This is, of course, only a speculation, so we did not add this argument.
Reviewer 3 Report
Dear Editor,
This paper summarizes past studies on effects of the expansion of the universe on small-scale phenomena in the solar system, and examines the relationship between the increased solar luminosity over time and the evolution of life. The paper is generally well written, and it is scientifically worth pointing out that small-scale phenomena that have not been clearly elucidated may be related to the expansion of the universe. Before I recommend the publication of the paper, a few points summarized below need quantitative descriptions or clarifications. It would be great if the authors reflect these.
First, since it is possible to calculate the variation in the Earth's equilibrium temperature due to the increase in the solar luminosity and the expansion of space, it is necessary for the authors to present the result quantitatively as a figure or numerical table, allowing the reader to agree with the main findings of this paper.
Second, the authors interpret a specific local phenomenon as a phenomenon caused by the local Hubble expansion, but the original authors who actually reported the phenomenon suggested a different interpretation. In this case, I think the authors need to say that there are different opinions in this issue. For example, the authors interpreted the phenomenon presented in Reference 33 as the expansion of space, but the original authors of the Reference interpreted this phenomenon as the growth of the galactic disk. Besides, contrary to the authors’ idea on ​​the faint sun paradox, there are various opinions such as the green house effect, the variation of planetary albedo, and other astrophysical influences.
Third, the authors seem to confuse the expansion of the universe with the anti-gravity effect. The existence of dark energy can cause an anti-gravity effect. However, since the universe filled only with matter can expand, it is inappropriate to express the expansion of space as an anti-gravity effect.
Author Response
Dear Editors,
First of all we would like to thank each reviewer for his/her very valuable comments. We tried to follow all suggestions proposed by the reviewers. All changes are indicated by yellow color.
This paper summarizes past studies on effects of the expansion of the universe on small-scale phenomena in the solar system, and examines the relationship between the increased solar luminosity over time and the evolution of life. The paper is generally well written, and it is scientifically worth pointing out that small-scale phenomena that have not been clearly elucidated may be related to the expansion of the universe. Before I recommend the publication of the paper, a few points summarized below need quantitative descriptions or clarifications. It would be great if the authors reflect these.
First, since it is possible to calculate the variation in the Earth's equilibrium temperature due to the increase in the solar luminosity and the expansion of space, it is necessary for the authors to present the result quantitatively as a figure or numerical table, allowing the reader to agree with the main findings of this paper.
Answer: Figure 2 illustrates an idealized increase of the relative luminosity of the Sun. The main finding is now stated in Theorem 1 (see Section 2).
Second, the authors interpret a specific local phenomenon as a phenomenon caused by the local Hubble expansion, but the original authors who actually reported the phenomenon suggested a different interpretation. In this case, I think the authors need to say that there are different opinions in this issue. For example, the authors interpreted the phenomenon presented in Reference 33 as the expansion of space, but the original authors of the Reference interpreted this phenomenon as the growth of the galactic disk. Besides, contrary to the authors’ idea on the faint sun paradox, there are various opinions such as the green house effect, the variation of planetary albedo, and other astrophysical influences.
Answer: We added three more references [Buitrago et al., Rudnick et al., Trujillo et al.] to show that also galaxies themselves expand with rate similar to the Hubble-Lemaitre constant. In other words, galaxies themselves were much denser for high redshifts. These three new references are cited in Introduction before formula (4).
Concerning opinions about the Faint Young Sun Paradox, they are mentioned after formula (8) in Section 2. We also added reference [Lang], where a detailed analysis can be found.
Third, the authors seem to confuse the expansion of the universe with the anti-gravity effect. The existence of dark energy can cause an anti-gravity effect. However, since the universe filled only with matter can expand, it is inappropriate to express the expansion of space as an anti-gravity effect.
Answer: The term “antigravity” was systematically removed from the whole paper.
Round 2
Reviewer 1 Report
Accept.
Author Response
Dear Reviewer,
We corrected several typos. Thank you very much.
With best wishes Michal Krizek
Reviewer 3 Report
Dear Editor,
The authors revised their manuscript to reflect all of my requests and responded appropriately. Therefore, I recommend the publication of this paper.
*There is a typographical error on page 4 line 5, where ‘70% of dark matter’ should be corrected as ‘70% of dark energy.’
Author Response
Dear Reviewer,
Thank you very much for finding this important typo.
Best regards
Michal Krizek
