Fitting Type Ia Supernova Data to a Cosmological Model Based on Einstein–Newcomb–De Sitter Space

Round 1

Reviewer 1 Report

see attached file

Comments for author File: Comments.pdf

Author Response

(Point 1) ... the fact that the considered model explains the redshift-distance relation is not a solid argument against
an expanding universe as the author seems to suggest.

(Response-1): In Section 2.1, the R2-version of my manuscript I mention that the model under discussion is not against an expanding universe concept.  In fact, the discussed ENdS space admits the FLRW time-dependent scaling factor. But this variant is not discussed in the current manuscript. In the R3-revised manuscript, I have added a comment that the mixed version of ENdS space is a work in progress (Section 4.2) and that this would allow the exploitation of the existing structure-formation and light-element-synthesis formalisms that are in the current use for the FLRW expanding-universe models.  

(Point-2) It should be emphasized that the standard (expanding) cosmological model is supported by different pillars others than the distance-redshift relation as the synthesis of light elements like helium, deuterium and lithium (primordial
nucleosynthesis), the angular two-point temperature correlation of the cosmic microwave background and the power-spectrum of matter, which is retrieved from the two-point galaxy-galaxy correlation.

(Response-2): This suggestion is reflected in the R3-version of my manuscript in the form of a new subsection 4.2 "Experimental challenges of static and dynamic cosmological models". This subsection deals with all the questions posed by the Reviewer. Mainly, I am redirecting these questions to the previous works of prominent physicists who solved them in the past. But I am also referring to the recent observational puzzles which apparently annihilate the foundational pillar of the standard model - the geometrical structure of expanding-space.  

(Point-3): Notice that the temperature fluctuations present in the cosmic microwave background are supposed to be the consequence of quantum fluctuations of the inflation field, the feature included "by hand" in the standard cosmological model.

(Response-3): In this manuscript, I avoid entities, which are unobservable or unknown to physics, like inflaton fields, quintessence,  repulsive gravity, or quantization of space and/or time. Quantum fluctuations of the inflation field are of his exact nature: the field is unknown to physics, hence its quantum fluctuations are unknown as well. What is known from laboratory experiments is vacuum energy. By contrast, dark energy was never observed, and the discrepancy between the physically observed and unobserved entities is of the order of 10^120. That is what I had to mention in this manuscript, although I believe that the specific design of this paper does not allow much space for discussions about pros and contras of expanding and static universe models. There is already a broad discussion of these themes going on elsewhere. There is no need to convert a classical scheme of discussing a newly proposed model
(model's description > model's test against observations > model's predictions for future observations) into something belonging to another class of publications (discussion reviews or books). That is why, following the reviewer's suggestion, I have limited subsection 4.2 to just a few arguments in favour of static-universe models and a few arguments against the standard cosmological model.

(Point-4): Other tests can be found in one of the references cited by the author (Lopes-Corredoira, 2017), who also states in his conclusion that alternative theories are not at present as competitive as the standard model in terms of giving better explanations (to these tests)".  

(Response-4): Lopez-Corredoira has published many works,  arguing in favour of  Zwicky's tired-light cosmological model and using carefully calibrated arguments criticising the standard cosmological model. Five or six years ago these careful arguments were relevant. But  nowadays, after the crucial observational evidence obtained from the JWST, these arguments became less important. Therefore, I have removed the reference to Lopez-Corredoira's work without any harm to my text.    

(Point-5) The author also mentions the paper by LaViolette (2021) who emphasizes the difficulty of the standard model to explain the redshift-distance relation for gamma-ray bursts and QSO's or the ... "redshift quantisation"! These are not well-founded arguments: gamma-ray bursts and QSOs are not standard candles. and the "redshift quantization" is probably a consequence of observational bias known for more than 40 years (see, for instance,  D. Basu, Astron & Astrophys. 77, 255, 1979).

(Response-5): I agree with the reviewer that gamma-ray bursts and QSOs cannot be used as standard candles. However, since, at this moment,  there are no standard candles available for redshifts 3 or 4, I needed to use, at least, something that would provide a glimpse of what would be found in the future at  these redshifts. I have added a new paragraph to Section 4.1, explaining why QSO's are not appropriate to be "proxies" to the standard candles (adding appropriate citations). By contrast, GRBs can be regarded as a sort of "proxies" to the standard candles. That is why I believe that using GRB distance moduli for this purpose is appropriate in this context.  As for "redshift quantization", I have not mentioned this notion at all in my text. The cited LaViolette's  work is of no great importance for my manuscript, so I have removed it.

 

Reviewer 2 Report

This manuscript is novel, interesting and very well written. It shines a light on high redshift supernovae and the performance of the Lambda-CDM model against the ENdS model introduced in the paper. The author provides a hint that the distance modulus may be LARGER than LCDM expectations at higher redshifts. While this may be true, there are a number of observables pointing to SMALLER values of the distance modulus at high redshifts. Please see arXiv:2206.11447 and references therein. In particular, that quasars prefer smaller values of \mu(z) has been documented since Risaliti & Lusso (2019). While the community do not trust QSOs on their own, if both QSOs and SN show similar behaviours, as outlined in 2206.11447, then it becomes more difficult to question QSOs. QSOs have overlap with GRBs, but the samples are much larger, so the statistics are better. I would be grateful if the author could highlight these observations that appear to be at odds with speculation in the paper. Finally, I would be grateful if the author could provide more detail on the fitting procedures used. In particular, how are the errors estimated at the start of section 3? Is the author making use of Markov Chain Monte Carlo? There also seems to be sizable difference in the Omega_{M} parameter with Pantheon+, which warrants a better explanation that the one currently given. Once these minor improvements are made, I think the paper is suitable for publication. 

Author Response

(Point-1): The author provides a hint that the distance modulus may be LARGER than LCDM expectations at higher redshifts. While this may be true, there are a number of observables pointing to SMALLER values of the distance modulus 
at high redshifts. Please see arXiv:2206.11447 and references therein. In particular, that quasars prefer smaller values of \mu(z) has been documented since Risaliti & Lusso (2019). While the community does not trust QSOs on their own,  if both QSOs and SN show similar behaviours, as outlined in 2206.11447, then it becomes more difficult to  question QSOs. QSOs have overlap with GRBs, but the samples are much larger, so the statistics are better.  I would be grateful if the author could highlight these observations that appear to be at odds with speculation in the paper.

(Response-1): In response to this request, I have added a new paragraph at the end of Section 4.1, explaining the reasons  for not using a large QSO sample for validating my model. The problem is that QSO observations exhibit a strong 
observational selection effect for redshifts z > 3,as I found in 2022 (I have added the corresponding reference,  as well as two other references demonstrating that QSOs cannot be used for testing cosmological models).
 
(Point-2): I would be grateful if the author could provide more detail on the fitting procedures used. In particular, how are the errors estimated at the start of section 3? Is the author making use of Markov Chain Monte Carlo? T

(Response-2):  Section 3 is re-written in the version R3 of the manuscript. I have provided the details concerning  the calculating the chi-square statistics and the corresponding references to the explanations of using the chi-square statistic in different circumstances.

{Point-3): Here also seems to be sizable difference in the Omega_{M} parameter with Pantheon+, which warrants a better explanation that the one currently given. Once these minor improvements are made, I think the paper is suitable for publication.

(Response-3):
Indeed, there is a difference with respect to the Pantheon+ published parameter Omega_M. The parameter H0 is also different. This follows from using a simplified formula for computing the chi-squared statistic, Eq. (13) in the revised manuscript, which is different from the formula, Eq. (11) used in the Pantheon+ work. The explanation is given after presenting the estimated Omega_m and H0 parameters, Eq. (14), as well as around Eq. (13). This discrepancy is expected, as I am using  the uncertainties in distance moduli based on the diagonal terms of the covariance matrix, Eq. (13). An estimation based on Eq. (11), which takes into 
account the full covariance matrix, would provide the LCDM parameters in agreement with the Pantheon+ publication. The purpose of this manuscript is not to provide exact LCDM parameters but rather to intercompare two different models via their goodness of fit values. So, there is no problem in obtaining here slightly different cosmological parameter values.

 

Round 2

Reviewer 1 Report

see attached file

Comments for author File: Comments.pdf

Author Response

(Point-1)
In this paper the author has only shown that the considered static model can reproduce the distance-redshift relation as well as the SM. This is not enough to state (see line 180) that both models compete on…’’equal footing’’. As I mentioned in my previous report, there are other tests to satisfy.

Response-1:
It is true, although, in principle, all other tests can be satisfied. But there is no much room for detailed discussion of each particular cosmological test in a concise description of a new cosmological model. Many other available publications have already demonstrated that static cosmological models can compete with expanding-Universe models, and I provide corresponding references. Moreover, the model based on the ENdS space is not static. Its static version is just a first step in its description. Its dynamic version (based on McVittie metric) will embrace all the cosmological probes currently used for testing expanding-Universe models. This is also mentioned in Sections 2.1 and 4.2. Since the presented manuscripts deals mainly with geometry and distance measurements, I have modified the phrase in line-180, Section 4.1, by adding " when it comes down to predicting distance moduli" after "equal footing" (although this was clear from the context and the paragraph following this phrase).

(Point-2)
Concerning primordial nucleosynthesis, the author claims that stars could be the source of helium and other light elements (Burbidge & Hoyle 1998). However, stars cannot produce enough deuterium in order to explain observations of absorption features at high redshift in quasar spectra as well as the lithium ‘’plateau’’ in old stars, first observed by François and Monique Spite. Can a static model and stellar yields explain these observations?

Response-2:
There are other elements (e.g. beryllium and boron) that cannot be produced in stars in sufficient quantities to explain their existence. The solution to this problem is known: cosmic ray spallation and fusion reactions [Reeves, Fowler, Hoyle, 1970, Nature, 226, 727). In exactly the same way one can devise the production of other light elements [e.g. S.M. Austin, The creation of the light elements - cosmic rays and cosmology, Progr. Part. Nucl. Phys. 1981, 7, 1-46]. Since the energies of cosmic rays can be as high as 10^19 eV, they can be used not only for solving the lithium problem, but also the production of deuterium  without invoking the big bang nucleosynthesis. So, in this regard, static-universe models are not incompatible.

(Point-3)
Concerning the CMB, the author mentions old estimates by Eddington (1926), Nernst (1937) who predicted a thermalized background with temperature around 3 K. However, in an expanding background the temperature increases with redshift as the well-known relation T proportional to (1+z). Observational data that agree with such a dependence (see, for instance, Arjona arXiv:2002.12700). Can the author show that the ENdS model can do the same?

Response-3:
I am grateful  for mentioning this point, as I have forgotten to discuss the (1+z) CMB-temperature-redshift relation by assuming that this relation goes without saying when a model reproduces the (1+z) factor in the redshift-distance relationship. Then the thermalised photon background temperature dependence on redshift is also scaled with the same factor (1+z). Of course, in static-universe models this is valid only for a remote cosmic background, which I have highlighted by adding a new paragraph with comments on the (1+z) CMB temperature-redshift relation - after line 239 of the manuscript's version R3 or lines 232-242 of the version R4

(Point-4)
The author raises the ‘’Hubble tension problem’’ as another difficulty with the SM. This ‘’problem” exists since the late seventies when de Vaucouleurs’s team claim for Ho = 100 km/s/Mpc and Sandage’s group argue for Ho = 50 km/s/Mpc. In fact, these differences are due probably to systematic errors in the calibration of standard ‘’candles’’ and not to ‘’some new physics’’ as some theoreticians like to claim. Some recent investigations revisited Cepheid data
(see, for instance, Perivolaropoulos & Skara, arXiV:2109.04406) and indicate no discrepancies with CMB data.

Response-4:
It this point, I must completely disagree with the reviewer. Unfortunately, the cited paper by Perivolaropoulos & Skara, arXiV:2109.04406, is invalidated by the authors of this paper themselves because they interpret their result as evidence of "the presence of a fundamental physics transition taking place at a time
more recent than 100 Myrs ago". This result does not help to solve the Hubble constant tension because the authors trust an abstract mathematical/statistical model selection criterion instead of using physics. They have simply replaced one problem (the H0 tension) with another, calling it a transition to new physics at a critical distance D_c from the observer. Does this mean that another observer located at 100 Mpc from us would find that transition to new physics occurs
at yet another 100 Mpc away from us? Etc. etc. How many "new physics" domains the Universe would contain then?

The situation resembles the solution proposed by Di Valentino et al. [Class. Quantum Grav. 38 (2021) 153001] in the form of a slight change of the Universe's curvature. But, at least, this proposal was global, applied to the whole of the Universe.  Di Valentino and her co-authors made an exquisitely thorough
review of the H0-tension problem, and they found that this problem is different from being "just another difficulty" due to possible systematic errors. They have proved that this is not a problem but "the problem", and they correctly arrived at the conclusion that it means a crisis in cosmology.  

The paper by Perivolaropoulos & Skara is based on the bad practice of ignoring physics and blindly trusting statistical analysis. That is why it is not worth while citing. Although it was cited by Di Valentino in her more recent publication [Gariazzo, Di Valentino, Mena, Nunes, Phys. Rev. 2022, D 106, 023530], but it was cited in the context of the H0-tension problem becoming stronger,  more significant. So, Di Valentino and her co-authors have ignored Perivolaropoulos & Skara's result. And rightly so.

(Point-5)
In conclusion, the main contribution of this paper concerns the modeling of the distance-redshift relation resulting from a static space-time, whose data fit has a quality comparable to that of the SM. In this sense I can recommend the publication of the manuscript but not as an indication of a viable alternative to the SM, unless the author is able to demonstrate that the ENdS model can do equally well on the other pillars of the SM.

Response-5:
Where we claim that LCDM and ENdS compete on an equal footing (page 7,
line 180), we have now added the phrase "with respect to the prediction
of distance moduli", to show that we do not claim the models are equal
with respect to the other pillars of the SM.

In the concluding section, I mention that the models compete only within the redshift range 0 < z < 2.3. The prediction of the ENdS model for higher redshifts will undoubtedly be tested soon by JWST observations. Then one would be able to properly judge as to the validity of the discussed model

.