This is a summary of the rough road to publication of the paper entitled ``Imitating accelerated expansion of the Universe by matter inhomogeneities -- corrections of some misunderstandings''

In the following ``we'' means Andrzej Krasiński, Charles Hellaby, Krzysztof Bolejko and Marie-Noëlle Célérier

We came upon the first misunderstanding while preparing our book (``Structures in the Universe by exact methods -- formation, evolution, interactions'', Cambridge University Press 2009). We wondered why certain authors claimed there was a ``weak singularity'' in the centre of some Lemaitre -- Tolman cosmological models that, by our own accounting, were perfectly regular except at the Big Bang. The origin of this terminology turned out to be the paper (in the following referred to as ``VFW''):

R. A. Vanderveld, E. E. Flanagan, I. Wasserman, ``Mimicking dark energy with Lemaitre--Tolman--Bondi models: weak central singularities and critical points", Phys. Rev. {\bf D74}, 023506 (2006); also http://arxiv.org/abs/astro-ph/0602476.

The authors claimed that a singularity was occurring wherever the d'Alembertian of the scalar curvature was infinite. Physically, this meant that the supposed singularity was caused by a discontinuity of the second derivative of the mass density by the radial coordinate. The particularly offending statement in the paper was:



The singularity is weak according to the classification scheme of the literature on general relativity [28]


Ref. [28] in this quotation is F. Tipler, Phys. Lett. 64A, 8 (1977). In it, the author proposed a definition of a strong singularity, and did not even mention any ``classification scheme''. Moreover, the ``weak singularity'' as defined by VFW is not a singularity in any accepted sense in the relativity theory.

We began to suspect that some foul play was at work here. Clearly, VFW quoted Tipler without knowing what the paper actually said, just to add weight to their own invention. The real aim of their paper was to discredit the Lemaitre -- Tolman (L--T) solution as a cosmological model. To some cosmologists it is an offense to consider the possibility that our Universe might be more complicated than the Friedmann -- Lemaitre -- Robertson -- Walker (FLRW) models indicate. (Funny thing -- Lemaitre himself was perfectly aware, already in 1933, that the real Universe is much more complicated.) Specifically, VFW and a few other authors (most notably C. M. Hirata and U. Seljak, Phys. Rev. D72 , 083501 (2005), abbreviated as HS) could not bring themselves to accept the result that the ``accelerated expansion of the Universe'' is just an artifact of using the oversimplified FLRW models, and not a real phenomenon. When one adapts the arbitrary functions of the L--T model to the observed luminosity distance -- redshift relation for the SNIa supernovae, accelerated expansion goes away. The ``weak singularity'' was meant to brand those L--T models that do this trick as ``singular'', and thus unphysical.

Moreover, VFW completely misunderstood the law of propagation of light in an expanding Universe and mistook the re-convergence of the observers' past light cones toward the Big Bang for some ``pathology'' (their word) of the L--T model -- even though the same ``pathology'' had long been known in the Friedmann model. We thus decided to write a paper that would set the record straight (now available from arxiv: http://arxiv.org/abs/0903.4070v1), and submitted it to Phys. Rev. D, where the VFW paper and some other misguided critiques of the L--T model had been published before. The submission date was March 25, 2009.

The referee report (received April 21, 2009) ran like this (I comment on the coloured bits below the table, on each in its respective colour):



We did respond to these criticisms, and the response we sent to Phys. Rev. D is copied further below in the present text. However, I first offer shorter and less technical comments, using the extra insight that we gained into this subject during the year that passed between the first attempt at publishing and the final publication.



We have to confess to one more weakness of the first version of our paper. We tried to get our result cheaply and did not verify the calculations of HS or VFW, we just pointed out the contradictions between their claims and what is known in relativity -- in the hope that we would provoke them to verify their reasoning. We failed with this plan and eventually had to follow VFW and HS into some details of their calculations, to pinpoint the errors.

VFW responded to our paper (published at that time only in the arxiv) by a note in arxiv, to which we refer here out of loyalty:

http://arxiv.org/PS_cache/arxiv/pdf/0904/0904.4319v2.pdf

In this note, VFW give further arguments in defense of their results. However, we decided not to enter a discussion with this text and did not refer to it in our second version. We think such a discussion would only complicate matters and would make our point less clear.

Note how well-acquainted the first referee was with the contents and intentions of the VFW paper. We suspect he/she was one of the VFW authors. The circumstances described above motivated us to ask the PRD editors to send our paper to a second, independent referee. A copy of the letter that we sent to PRD, on May 7, 2009, together with our detailed replies to the first referee report can be found here .

PRD did fulfil our request and sent the paper to a second referee. However, we doubt he/she was really independent. The response (received May 12, 2009 -- note how quickly) was rather arrogant:



Dear Editor, I think that the Referee’s report is right on the money. This Krasinski et al. article is based on several critical misunderstanding/ misinterpretation of prior work, and the attacks on prior work are entirely unwarranted. It is not suitable for publication in PRD.


We could not stop at that. In the PRD web page, Krzysztof traced an instruction how to lodge a formal appeal against the decision of the editor. He composed the appeal that we next sent to the editor of PRD (on May 28, 2009). It says in long diplomatic expressions that we do not accept the verdict of the first referees and that we question their objectiveness. A copy of our letter is accessible here .

Three weeks later, on June 19, 2009, we received the reply from Misao Sasaki. It was half-favourable in that it gave us one more chance -- to re-submit a modified version of our paper. While we are grateful to him for the extra chance we got, I am sorry to say that most of the comments in his long letter tend to obscure the core of the disagreement. His judgements are evasive, as if he wished to satisfy everyone, avoid hurting anyone, and also avoid going too deeply into the subject (probably by saying so I am being impolite again...) However, I do not wish to make this long text even longer, so I will not comment on his statements. Sasaki's reply is quoted here .

To this, we responded in a letter to the editor of PRD, sent on June 24, 2009, in which we agreed to revise and resubmit the paper taking Sasaki's suggestions into account. We promised to have the new version ready in a few weeks.

But we were too optimistic -- it had taken us half a year to prepare the new version. The reason was that we decided, instead of just pointing out the erroneous claims of VFW or HS, to go after their reasoning and put our fingers on the exact spots where errors were made. This required careful re-reading of their papers, verifying the calculations and making sure that all four of us understand the results of the calculations in the same way. All this we had to do in parallel with our several other duties... On January 19, 2010, we sent to PRD a completely revised version of our paper, very similar to the one that was finally accepted for publication (later changes are explained below). This was accompanied by the following letter to Prof. Sasaki:



A reply from PRD to this letter came on February 10, 2010, and it ran like this:



Dear Dr. Krasinski: The revised version of the manuscript ``Imitating accelerated expansion of the Universe by matter inhomogeneities: Corrections of some misunderstandings'' (DC10766) by Andrzej Krasinski et al. was sent to Professor Sasaki for further review. Professor Sasaki informed us that he is unable to review the paper because of time constraints and suggested another referee. We then sent the paper and entire file of correspondence to a new referee. Comments from the report of this referee are enclosed. We regret that in view of these comments we cannot accept the paper for publication as a regular article in Physical Review D. The referee has instead suggested publication in the Comments section. We cannot publish your paper in its current form as a Comment since a Comment must be a critique of just one paper previously published in our journal and must not exceed our length restriction of four journal pages. We would therefore be willing to consider a revision of your work that is split into two separate Comments, one on the paper cited in your Ref. [1] and one on Ref. [2], with each Comment of no more than four journal pages in length. Sincerely, Dennis Nordstrom Editor Physical Review D ------------------------------------------------------------------------------- Report of Referee D ------------------------------------------------------------------------------- After reading the paper carefully, the previous referees' reports, the authors' replies, and the report of an Editorial Member, I think that the authors have made an effort to soften the tone of the paper, compared with the first version in the arXiv, although one can still find a somewhat unnecessary use of incriminatory language both in the abstract and in the titles of some sections. In my opinion scientific progress does not need to follow these rough paths. Nevertheless, I find the paper useful as a source of discussion on inhomogeneous models. Although it does not contain sufficiently new and scientifically relevant elements to be worth publishing as a regular article in Physical Review D, I suggest that the paper is published in the Comments section of Physical Review D, thus giving an opportunity to the authors of Refs. [1] and [2] to write a Reply.




At this point, we decided to just give up on Phys. Rev., and instead to submit our paper to a journal where we could count on being evaluated by real experts in relativity. We chose General Relativity and Gravitation, and the reasons of our decision are explained in the letter that we sent to the Editor of GRG, copied below. While preparing our paper for the GRG journal, we made an extra pass through the text in order to locate and remove the bits of ``incriminatory language'' mentioned by the last referee, and this was the only modification. Here is a copy of the letter, sent on February 25, 2010:



Dear Professor Ellis, This is a covering letter to our paper "Imitating accelerated expansion of the Universe by matter inhomogeneities -- corrections of some misunderstandings" that we are about to submit for publication in the GRG journal. Please forward it to the paper's referees. In our paper we point out and, wherever possible, correct several errors in three papers by other authors, all published in Phys. Rev. D in 2005 and 2006. It would thus be natural to publish our text also in Phys. Rev. D, and this is what we had initially tried. Unfortunately, we encountered a stiff unfriendly attitude of all the parties involved who were clearly unhappy about having to deal with scientific misconceptions in published papers, and even accused us of attacking the original authors. After a lengthy to and fro with the referees and editors we have finally received the answer enclosed below. In it, the editor, following a 3rd referee's advice, proposed that we split our paper into two 4-page notes, each one to be published in the comments section of Phys. Rev. D as a separate comment on one of the papers that we criticise. This is after we had extensively revised our paper in accordance with the comments of referees 1 and 2. We feel we cannot accept this offer for the following reasons: 1. The papers we criticise are so closely intertwined that answering to them separately would be artificial, and it would be rather difficult to confine each comment to addressing just one paper. 2. Each of the separate comments would have to contain introductory explanations, almost the same for both, thus additionally robbing us of space. 3. Our text is something more than just a list of errors and corrections. The points that we criticise are not any simple mistakes of the authors, but rather are light-hearted abuses of scientific rules of conduct, committed, perhaps in good faith, in order to give support to pre-assumed views. The abuses are as follows: (a) The original authors, Hirata and Seljak (HS) hid from the readers the fact that their basic equation (38) is approximate rather than exact, and did not discuss the approximation involved in it. Then, treating that equation as if it were exact, they used it to "determine" the sign of the angle-averaged deceleration parameter q4 - which is a basic logical and mathematical error (an approximate equation cannot determine the sign of anything). (b) HS failed to notice that the averaging over directions involved in the definition of q4 is ill-defined and gives self-contradictory results at the centre of symmetry of the Lemaitre - Tolman (L-T) model. Moreover, such averaging is not used in observational determination of the deceleration parameter, so q4 does not represent any observational quantity. (c) The other authors, Vanderveld, Flanagan and Wasserman (VFW) then argued that the L-T models that have q4 < 0, thus contradicting HS's claim, contain what they called "weak singularity" at the centre, and so should be rejected as unphysical. We show that this "weak singularity" is not any singularity, and that VFW used a well-known singularity reference that actually has nothing to do with the phenomenon they consider. (d) Finally, the infinity encountered by VFW while trying to solve the "inverse problem" in an L-T model is no "pathology". Rather, a well-understood feature of the apparent horizon causes a 0/0 in the DEs of the inverse problem in ALL models, FLRW or LT, and Hellaby, Lu and McClure have already shown how to handle it properly. For the reasons listed above, we believe our text has to be published as a single self-standing paper in a visible section of a journal. The erroneous claims of HS and VFW have already propagated into the literature and misled several other authors into believing that they are proven truths. The true facts need to be clearly and coherently laid out. Two short notes hidden in the comments section of Phys. Rev. D would have no possibility to achieve that. Since we have been denied a fair chance to publish our critique in Phys. Rev. D, we kindly ask you to give us this chance in Gen. Rel. Grav. As referees of our paper we propose the following persons: [list deleted from this copy] Yours sincerely Andrzej Krasinski, Charles Hellaby, Krzysztof Bolejko, Marie-Noelle Celerier




We were not disappointed. This time the referee was an expert indeed. On April 12, 2010, we obtained the following report:



Just for completeness, our reply to this, sent together with our corrections, is copied here .

With these corrections, the paper was accepted for publication and finally appeared in print.

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Happy ending? Yes, in a practical sense. But...

General relativity used to be a Temple of Rigour. Whatever one said, had to be backed by logically clean proofs done with mathematical perfection. Attempts to demonstrate pre-assumed theses by sloppy means, mathematical errors, perturbations upon perturbations to obtain a result that can be arrived at exactly, failure to ensure covariance -- are elements of profanity that have been, until recently, very much unwelcome in relativity publications. An old-fashioned relativist would instantly feel that an equation involving a factor like 7/15 cannot be correct. Not so in astrophysics, where, as J. A. Wheeler might have said, `mathematics without mathematics' has reigned supreme. Which tendency will prevail?



The ill-founded statements that imitating acceleration in a decelerating inhomogeneous model is impossible were named, with excessive anticipation, ``no-go theorems''. Our result says the opposite -- therefore I propose to name it a ``go-go'' theorem.