An Accelerating Universe without Lambda: Delta Gravity Using Monte Carlo^†

Round  1

Reviewer 1 Report

Report on the paper

Delta gravity: A new phantom menace

by J. Alfaro, M. San Martín, and J. Sureda


The authors use their alternative theory of gravity, called delta gravity, to see whether the cosmic expansion derived from observations of type-Ia supernovae can be reproduced in this theory under appropriate symmetry assumptions. This is in principle an interesting question. However, it would seem to me that the paper leaves several important questions unanswered. In my view, the main issues are:

– Delta gravity is introduced in Sect. 2, but it remains unexplained what the variation \tilde\delta is supposed to mean and how it gives rise to additional fields. Of course, this information can be collected from earlier work, but the present paper should at least be self-contained enough to enable the reader to follow the main ideas. Several other symbols crucial for a detailed understanding are not defined or introduced either, for example the function F_a appearing in (24).

– The largest fraction of the paper duplicates results already presented in the preprints gr-qc:1704.02888 and gr-qc:1811.05828. Some parts even re-appear literally, including the typographical errors. There is no need for this repetition. In fact, the present paper is largely identical to gr-qc:1811.05828, which has, however, a different title. It needs to be clarified what the intended relation is between the present paper and gr-qc:1811.05828, in particular as to where gr-qc:1811.05828 has been submitted for publication. Obviously, since the authors quote gr-qc:1811.05828 in the present paper, it should be considered as an independent publication, which it clearly is not.

– With the main equations and results of the paper already presented elsewhere, the question remains what the new results of the present paper could be. Even if one would be willing to accept the fit to the type-Ia supernova data as new (which it is not, in my view), the source for one of the main results claimed by the paper, namely the value of the Hubble constant H_0, remains unclear. Since the type-Ia supernova data themselves do not allow to independently determine H_0, which piece of information should allow this inference?

Given these arguments, I conclude with the recommendation that this paper should not be accepted for publication.

Author Response

– Delta gravity is introduced in Sect. 2, but it remains unexplained what the variation \tilde\delta is supposed to mean and how it gives rise to

additional fields. Of course, this information can be collected from earlier work, but the present paper should at least be self-contained enough to

enable the reader to follow the main ideas. Several other symbols crucial for a detailed understanding are not defined or introduced either, for

example the function F_a appearing in (24).

Answer:

F_a:

The F_a appearing in (24) is a arbitrary function that is introduced to generalize a the new Tilde Metric. Why? We have the standard FLRW metric, and

we need to determine the Tilde Metric. This metric must be isotropic and homogeneous (Cosmological principle). Furthermore, the effective metric for

the Universe is a linear combination between Metric and Tilde Metric. Then, it's possible to generalize the Tilde Metric using and arbitrary function

in the space component, and other in the time component of the metric. Obviously, we have to impose isotropy and homogeneity. This functions must be

only time dependent. Furthermore, we can fix the dependence between this two new functions (one on the space component and the other on the time

component), fixing a gauge. Fixing the extended harmonic gauge we obtain the equation (29) where F is an arbitrary function that must be  determined  
solving the differential equations(10).

We added a little comment in the document: lines 143-145

\Tilde \Delta:

With respect to the Tilde Delta variation or symmetry: we add an explanation in the document: lines 84-97

We think anything else about the mathematical formalism and the extended treatment about the delta tilde on every term of the action can be found in  the references (Delta Gravity, Jorge Alfaro) named in the References of the paper, where the idea about DG was born.

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– The largest fraction of the paper duplicates results already presented in the preprints gr-qc:1704.02888 and gr-qc:1811.05828. Some parts even re-appear literally, including the typographical errors. There is no need for this repetition. In fact, the present paper is largely identical to gr-qc:1811.05828, which has, however, a different title. It needs to be clarified what the intended relation is between the present paper and gr-qc:1811.05828, in particular as to where gr-qc:1811.05828 has been submitted for publication. Obviously, since the authors quote gr-qc:1811.05828  in the present paper, it should be considered as an independent publication, which it clearly is not.

Answer:

This is not a new paper. The paper is a review submitted to  the proceedings of the conference "7th International Conference on New Frontiers in Physics(ICNFP2018)"

In any case, the actual review it's NOT about Delta Gravity. It's about the MCMC analysis using SN to find cosmological parameters and study the accelerating Universe in DG:

This idea can be found literally in the abstract:

"A gravitational field model based on two symmetric tensors,gμν and ̃gμν, is studied, using a Markov Chain Monte Carlo (MCMC) analysis with the most  updated catalog of SN-Ia."

In the previous publications the fitting was based on Least Squares Fitting that was clearly much less  efficient as MCMC. MCMC let us analyze if the fitting method is clearly convergent, if there is anything dependent on the seeds of the parameters to fit, and furthermore we can evaluate a multi
parameter fitting. In this specific case, the function to fit was numerically hard to analyze, because the upper limit of the integral have free parameters that can be found using numerical methods. Then, MCMC is really more efficient and robust than Least squares fitting.

In any case, the full analysis of the fitting using MCMC is in a reference: [46]  Alfaro,J;San Martín, M & Sureda,J, "An accelerating Universe without Λ in concordance with the last H0 measured value", e-Print: arXiv:1811.05828 [astro-ph.CO

Another difference between the previous work (any work before  2018) is that this work is based on the most updated SN Ia Catalog, that includes (lines 238-239) 1048 SN Ia spectroscopically confirmed (year 2018, Scolnic and Jones) vs 585 SN Ia (year 2010, Supernova Cosmology Proyect) These data can be found at: http://supernova.lbl.gov/Union/

We also added on lines 370 - 375 some comments about the interpretation of Delta Gravity as a phantom model which is addressed only on this work.

Summarizing: New data, better fitting process, better statistical analysis of the errors (MCMC) and analysis of the cosmological parameters like H0 and q0. Furthermore, we found a very interesting relation between L2 and the acceleration. This is totally new.

Note: this is a review presented at a conference, not a fully original paper.
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– With the main equations and results of the paper already presented elsewhere, the question remains what the new results of the present paper could be. Even if one would be willing to accept the fit to the type-Ia supernova data as new (which it is not, in my view), the source for one of the main results claimed by the paper, namely the value of the Hubble constant H_0, remains unclear. Since the type-Ia supernova data themselves do not allow to independently determine H_0, which piece of information should allow this inference?

Answer:

Our analysis has been built based on the distance ladder built starting from Cepheids up to SN in low redshift galaxies. We are aware of the dependance of H_0 on the absolute magnitude for SN, however during the construction of this distance ladder this value (M) can be determined in a
model independent way. This is written explicitly on Riess (2016) (Ref 51). Then the determination of H_0 is model independent and we do not need any information more than the redshift and the apparent magnitude for each SN.

We added some comments on this in lines 212 - 227

We also mention that we have explored the possibility of leaving  M free during the MCMC analysis finding a dependence between M and L_2.
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WE WANT TO THANK THE REFEREE FOR ITS COMMENTS. WE THINK THAT THEY HAVE CLARIFIED IMPORTANT POINTS IN THE PRESENTATION OF THE PAPER.

Reviewer 2 Report

I think authors do a minor mistake calling their approach “modification of GR”.

Section 2 defines Delta gravity which exactly coincides with GR plus perturbations. It was somewhat unexpected for me that it is sufficient retaining only the first order perturbation terms in the action to get complete set of equations of motion for the background and perturbations. The linear term admits both signs and therefore it may look both like a phantom field and the normal field as well.

In general relativity however the negative energy related to perturbations cannot be an arbitrary big.

It cannot eat more than all the value related to the background energy. This gives a very strong restriction which does not allow the acceleration of the present Universe without Lambda term (or dark energy).

It seems if we weaken the above requirement (the above restriction imposed on the value of negative energy), we get indeed some modification of GR. However this kind of modification may reflect quantum corrections (as it is inspired by previous works of authors). It gives at least a good phenomenological model and gives analogous predictions as some of the so-called f(R) theories.

I think authors know that general true terms describing quantum corrections have a non-local character. In this sense all local modified theories may pretend only to be phenomenological models.

I think this paper should be published as it is.

Minor misprint – line 146  (6) à(5) check

Author Response

Comments and Suggestions for Authors
I think authors do a minor mistake calling their approach “modification of GR”.

Section 2 defines Delta gravity which exactly coincides with GR plus perturbations. It was somewhat unexpected for me that it is sufficient
retaining only the first order perturbation terms in the action to get complete set of equations of motion for the background and perturbations.
The linear term admits both signs and therefore it may look both like a phantom field and the normal field as well.

In general relativity however the negative energy related to perturbations cannot be an arbitrary big.

It cannot eat more than all the value related to the background energy. This gives a very strong restriction which does not allow the acceleration
of the present Universe without Lambda term (or dark energy).

It seems if we weaken the above requirement (the above restriction imposed on the value of negative energy), we get indeed some modification of GR.
However this kind of modification may reflect quantum corrections (as it is inspired by previous works of authors). It gives at least a good
phenomenological model and gives analogous predictions as some of the so-called f(R) theories.

I think authors know that general true terms describing quantum corrections have a non-local character. In this sense all local modified theories
may pretend only to be phenomenological models.

WE AGREE.

I think this paper should be published as it is.

Minor misprint – line 146  (6) à(5) check WE HAVE CORRECTED THIS.

Submission Date 29 November 2018
Date of this review 08 Dec 2018 11:29:36

WE THANK THE REFEREE FOR HIS DEEP OBSERVATIONS ON THE NATURE OF THE MODEL.

Reviewer 3 Report

Dear editor,

in this manuscript, the authors study supernova Ia and H_0 measurements
in order to constrain Delta Gravity, a gravitational model based on two
different tensor fields. I have read carefully the work and I think the
analysis can be published in the present form.

Yours sincerely,

Author Response

Comments and Suggestions for Authors Dear editor,

in this manuscript, the authors study supernova Ia and H_0 measurements
in order to constrain Delta Gravity, a gravitational model based on two
different tensor fields. I have read carefully the work and I think the
analysis can be published in the present form.

Yours sincerely,
Submission Date 29 November 2018
Date of this review 15 Dec 2018 20:58:26

WE WANT TO THANK THE REFEREE FOR HIS REPORT.

Round  2

Reviewer 1 Report

(see attached report)

Comments for author File: Comments.pdf

Author Response

Please see attached.

Author Response File: Author Response.pdf

Round  3

Reviewer 1 Report

As I wrote in my earlier reports, I would not see any convincing reason to publish this paper in addition to the very similar paper gr-qc:1811.05828 on ArXiv. I now understand that the authors do not wish to publish that and the present paper separately, but rather develop gr-qc:1811.05828 into a paper for Universe. Assuming that the published version will then contain the more recent data analysis based on Monte-Carlo Markov Chains, I am happy to support following this procedure.