## A small journey in the Bogdanoff universe

Since it is possible that some of the readers of this page (Note from this site : this article has been originaly posted on the Talk Page of the Wikipedia article Bogdanov Affair) may be interested in knowing a cosmologist's point of view about the Bogdanoff stuff, maybe my humble contribution could be useful. Those interested in my records may find them here.

Stating that the Bogdanoff work has to do with (scientific) cosmology is a bit like stating that the Bible also has. The Bogdanoff do talk about the early universe, but lack more or less all the basis that should be required for their "work" to be considered in the field of science. I shall give below a number of example which I hope will show pretty clearly their ignorance about physics in general. In order that everybody can judge what I say, I will mostly stick to documents written by the Bogdanoff brothers that are freely available. i.e. Grishka's and Igor's PhD manuscripts (for some reason, Igor's manuscript does not seem to be available from French National Reaserch Agency (CNRS) PhD server, so the link points to my copy of it). Igor's manuscript includes four of the six papers written by him and/or his brother. The two missing one are essentially identical to some of those included. The rest is written in French. The Classical and Quantum Gravity (CQG) article, or in fact a preprint version of it is starts at page 56 of Igor's thesis.

• The first point I would like to raise is that the Bogdanoff brothers do not know anything about cosmology. The begining of the CQG article is very clear about that. It says, in its first sentence One of the limits of the standard space-time model remains its inability to provide a description of the singular origin of space-time. So they take for granted that the universe emerged from a space-time singularity. At present, this question is unanswered, and it is not even clear that it will be possible to address it one day. One of the reason is that in order to explain the homogeneity and isotropy of the universe on the largest observable scales, one has to call upon some process involving some yet undetermined new physical processes, the presently most popular of which being cosmic inflation, which predicts that the "initial state" of the universe (understand here the state of the universe at the beginning of inflation) has been washed away by the inflationary process. So, if these ideas are true, there is just no hope to explore the preinflationary era of the universe. Morevover, there is nothing that guarantees that the preinflationary era started from a singularity. For example, in the spirit of what is called chaotic inflation, the universe might well be an eternal "self-reproducing" thing with inflationary eras starting every time in various distant regions. The pre Big Bang model by G. Veneziano or the ekpyrotic universe are other (less popular) models where there is not initial singularity of space-time. All these models are more or less compatible with observations but start from very, very, very different states: chaotic inflation starts from an ever expanding eternal universe, pre Big Bang starts from an empty contracting universe followed by a bounce and the ekpyrotic model is based from brane cosmology.
• So, not only making the assumption that the universe started from an initial singularity is very strange (the authors should at least have stated that it was an as yet untestable hypothesis), but also there is no discussion about the observability of their "model". Actually, it is very hard to imagine that anything from Planck era could be observable today (see below), so that from very general grounds, it is very difficult to consider their work as being part of science.
• Now, if one wants to enter into the details, it is hard not to reach the conclusion that in fact the Bogdanoff know almost nothing in physics except some of the jargon. But mastering the jargon does not mean having an understanding of the underlying concepts.
1. For example, the motivation for considering an initial singularity of space-time comes from a serious misunderstanding of the Hawking-Penrose singularity theorems which they obviously think (this is explicitely stated on Sec. 5.2 p. 69 of Grichka's thesis) proves that the universe emerged from a singularity. Actually, these theorems state under which conditions the universe might have emerged form a singularity, and there is absolutely nothing which guarantees that all these hypotheses are valid in the early universe. All the above mentioned models violate at least one of the hypothesis of these theorems (namely, the strong energy condition), so that it is completely irrelevant to mention the Hawking Penrose theorems when studying the early universe.
2. Actually it is of no use to deal with sophisticated stuff to realize the Bogdanoff's ignorance. The most enlightening part of their "work" is I think Grichka's thesis p. 47 and 48, at the beginning of chapter 4 (note that the PDF page number does not correspond to the printed page number, I mention the printed page numbers here, which correspond to pages 59 and 60 of the PDF). So, below Conjecture 4.1.2 is written a number of sentences whose aim is to justify that the universe is in thermal equilibrium at the Planck era. All the material here is merely a copy followed by a stupid translation of a book written by Peter Coles and Francesco Lucchin. One of the authors has allowed me to put online a copy of the corresponding pages, so I will put them online in the next days so that everybody can compare Grichka's thesis and this part of the book. The point here is not plagiarism issue, of course, but to show at what extent the Bogdanoff could copy a meaningful thing but without understanding it, so that in the end, the results is completely meaningless. So, they begin by their equation (4.1), which is a copy of part of equation (7.1.4) of Coles and Lucchin (CL) book. Is it really the same ? No. The Bogdanoff equation is $\rho (T) = g^*(T) \frac{\sigma T^4}{2}$, where CL's is $\rho (T) c^2 = g^*(T) \frac{\sigma_r T^4}{2}$. CL follow the unusual convention to note the mass density instead of the energy density with ρ, hence their extra factor c2. But this formula, which gives the energy density of a radiation fluid as a function of the temperature involves the radiation constant, which CL notes σr, but the Bogdanoff used something (which they do not define) they note σ. The standard thing that is noted σ is not the radiation constant, but the Stefan-Boltzmann constant, which differs from the former by a factor c / 4... Now, the interesting thing lies in the next equation (4.2), where the Bogdanoff now give the particle number density of a radiation gas as a function of temperature. This is equation (7.1.5) in CL. It reads $n_B = \frac{4}{3} n_F = \frac{\zeta(3)}{\pi^2} \left(\frac{k_B T}{\hbar c} \right)^3$. The expression in fact depends wether the particles one considers follow the Fermi-Dirac statistics or the Bose-Einstein statistics. This is why the nB and nF (respectively for bosons and fermions) appear. In their equation (4.2), the Bogdanoff use nG, which is logical since they deal with a graviton gas. Now, the point obviously missed by the Bogdanoff is that in the right handside of the equation, a kB appears, but the subscript B has nothing to do with Bose-Einstein or bosons! It just stands for Boltzmann, since kB is the Boltzmann constant. Since after equation (4.2) they always note kG instead of kB, it is pretty clear that they had not recognized the Boltzmann constant and more generally that they had absolutely no idea of what they were copying (it is very hard to imagine that any physicist could make such a mistake).
3. Of course, this is not the end of the story, because there are actually many, many terms which have been incorrectly translated by the Bogdanoff, which also show without doubt that they did not know the things they were writing. For example, they perform a litteral translation of number density into nombre densité. But this term does not exist in French! (the term is just densité or densité de particules if any confusion either with mass density or with energy density can arise). Page 48, they also make the funny litteral translation of cross section into section droite. The term section droite exists in French, but it is used in geometry, not in physics (see the cross section disambiguation page). So, again, it is unthinkable that any physicist could make such a confusion and/or and incorrect translation. Even more unthinkable is the confusion the Bogdanoff made a bit further page 48. They state Ce temps doit être comparé avec le taux d'expansion $\tau_h = \frac{a}{\dot a}$. Here, they just follow CL book, which compare the collision time (noted τcoll) with the expansion timescale (i.e., the Hubble time, the inverse of the Hubble constant, noted τH) in order to check whether it is possible that thermal equilibrium can be achieved. The point here is that expansion rate (= the Hubble constant) is translated in French as taux d'expansion. The x of taux is not pronounced, so that taux and the Greek letter τ are pronounced exactly the same. So this led them to make the confusion between the expansion rate (taux d'expansion) and what is noted τH, which corresponds to the expansion timescale, that is the inverse of the former. Actually, this expression is more often stated using collision rate Γ and expansion rate H, so that one has $\Gamma \gg H$ as a necessary (but not sufficient) condition for thermal equilibrium. Page 15 of Igor's thesis, it is $\frac{\Gamma}{H} \ll 1$, which is (incorrectly) stated. This is also the case on page 109 and 122. But strangely it is the opposite correct $\frac{\Gamma}{H} \gg 1$ which appears on page 79... I have no time to list of the errors that appear on pages 47-48, their total number is above 20.
4. Actually, such a game could continue for long. For example, in Grichka's thesis, what is below Conjecture 7.1.2 is just a copy of this article, page 21-22 (whose reference is given in the thesis, so that it is, again, not a plagiarism issue here). Again, it is interesting to note that none of the technical terms are translated. Both worldsheet and target space appear untranslated in the thesis. Although this is not an uncommon practice in French, the fact that the sentence so that the winding modes in Y are responsible for the elimination of flat connections with non trivial holonomy is missing is much more annoying, since it is important in this context. Also, the discussion page 67-68 of Grichka's thesis is a copy of a paper by Teyssandier. It is interesting to note that the (correct) expression (60) of Teyssandier's article was incorrectly copied by the Bogdanoff on Eq. (5.7) (a copy of part of Teyssandier's article can be found here for those who do not have an online access to the journal). I had asked Igor some time ago whether he could confirm the exactness of his equation (5.7), and he had replied that it was... It can also be noted that Grichka's conjecture 5.1.4 is completely meaningless. It says that the linearized approximation of the Schwarzschild metric can be considered as a local exact solution of some extended gravity theory they are considering. This is beyond stupidity as there are plenty of gravitational effects which are routinely measured and that would not exist is the "linearized approximation of the Schwarzschild matric" existed in Nature. In particular, there would be no Tests_of_general_relativity#Classical_tests relativistic precession of planets perihelion...
5. More generally the number of incorrect statements that can be found in the theses is incredible. As an example, on can mention the statement that the Dirac operator is a supergravity hamiltonian (G's thesis, p. 49, 54, I's thesis, p. 34, 60, 142). One can also mention that the terms Lagrangian and action, are used improperly instead of Lagrangian density.
• Those who are more interested in gravity and mechanics will probably find interesting to have a look at the paper Topological origin of inertia published in the almost unknown Czechoslowak Journal of Physics (page 133-162 of I's thesis). The very first equation is apparently supposed to give some estimate of the potential energy of a given point in the universe. Actually, this concept is not defined in general relativity and in Newtonian mechanics it diverges for an infinite universe. So this very first equation is stupid, as is stupid the statement that the origin of inertia is an unsolved problem in physics. Most of the stuff of this article can be skipped till Eq. (34) which makes the stupid claim that the gravitational force between two bodies goes as 1/r. For what is said after, it seems that the total mass of the universe is finite (even if the universe is infinite...). Equation (37), although containing only very basic terms is completely meaningless, as well as Eq. (38) which obviously state that the Gaussian curvature of some surface is a dimensionless number (equal to 1 here, don't ask me why). The presence of the qed at the bottom of page 150 is not understood in this context.
• To come back to their "model", their point is to say that the space-time metric is subject to signature fluctuations. One incredible thing here is that this core concept (signature fluctuation) is never defined in their work. It is mentioned (but not defined) in the introduction and then first appears on page 2, still without definition. It can be noted that there is a huge number of incorrect stuff since the very first chapter of G's thesis. One of them is for example the claim that there is a bijection between a fundamental group of some object and its universal cover (p. 8, above (1.8)).
• The only part of their work which shows some meaning is their work on quantum groups (chapter 3 of G's thesis). However, no exaggerated importance should be given to this work. Although it shows some knowledge of the subject (which is sufficiently rare with the Bogdanoff to be emphasized), this is a rather trivial corollary of some work by S. Majid. One can easily check that part of this work was put by the Bogdanov on the preprint server here, but that at present it has not been cited once (click on the "CiteBase" link to check). Moreover, there are no connection between chapter 3 of G's thesis and the rest of his work. The only place where the results of chapter 3 are mentioned in the next parts of the thesis is on page 70 where it is stated (bottom of page) that their cocycle bicrossproduct suggests that metric fluctuations are possible... Actually the verb suggérer (to suggest) is used 95 throughout G's thesis, much more often than the verbs to show, to demonstrate, to deduce, etc.
• Among the things which are not done in science but which were done by the Bogdanoff (there are so many...), one can mention the fact that identical articles were submitted (and accepted!) in different journals. It is obvious by comparing the papers published in Chinese Jounal of Physics (pp. 119-132 of I's thesis) and the one published in Annals of Physics (pp. 106-118 of I's thesis). The titles, abstracts are different, as well as the authors (Igor & G for one, Igor alone for the other). Then, only the beginning of the first section differ (just because of some trivial rephrasing), but all what follows is identical, up to the typos in the reference list (in particular in their Ref 18). Actually, one the the tiny difference in the two preprint is that the 24th and last reference has number 25 in one paper and 26 in the other. Needless to say, I have also checked on the published versions of these papers (as well as the Nuovo Cimento paper) which are identical to the two others and their preprints except some trivial rephrasing.
• Something that could also be noted is the distortion between the actual content of their work and the way they present it. In various French popular articles, they present their work as solving the mystery of the origin of the universe. They also claim that they have proved that a mysterious "cosmological code" determines the evolution of the universe from the very beginning. There is also a very large number of nonsensical claims in their popular book "Avant le Big Bang", the most famous of which being the fact that the golden ratio is a transcendental number and that the size of the solar system was sensitive to the expansion of the universe. They claimed this many times.
• They show a systematic tendancy to present their stuff as something important and to claim they have done (much) more in science than what they indeed did. Without being exhaustive (this is just impossible), one can cite this interview where they claim they have redone the analysis of the WMAP data (page 13, right column). It is by the way interesting to note that they claim to have proven that is universe was not flat on the (hypothetical!) basis that the central value of the density of the universe is (according to them!) 1.023 times its critical density with an error bar of 0.02, which is (according to them!) due to the fact that 1.023 - 0.02 = 1.003 > 1. Needless to say, these error bars (published by the WMAP team) are at one sigma, so that whether the central value is 1.02 or 1.023 does not change anything to the facts that present data do not imply that the universe is closed. Just to make sure: it is pretty clear that they did not analyze WMAP data since they ignore what an error bar is. So they lied when claiming the performed the analysis. One can also mention the interesting claim in the same interview that the Poincaré dodecahedral space has the same topology that a 3-sphere (p. 13, in the middle), which again is stupid since the latter if the universal cover of the former.

It should be noted that the use of the Bogdanoff stuff by the scientific community is non existent, which can be easily check with the SPIRES database here. No one should be surprised of this. If one really wants to check the details, it is easy to see that the three papers which cite the Bogdanoff do not use anything they made, but just mention the existence of their papers.

Actually, stating (as in the present form of the Wikipedia article) that there was a controversy about the value of the Bogdanoff stuff is incorrect. There was never such a controversy, neither in France nor elsewhere (the Bogdanoff already had a bad reputation after a first successful book full of silly errors published in the early 90's). The only open question was (but only at the time the affair started) whether it was a deliberate hoax or just a bad work. The fact that people thought that it was done on purpose reflects nothing but the fact that people considered at some time the bogdanoff as (much) more brilliant than what they actually are.

The above is alas by no mean exhaustive. As was already stated by Eli Hawkins long ago, It would take up too much space to enumerate all the mistakes: indeed it is difficult to say where one error ends and the next begins. This is the most compact and most accurate way to describe their "work". Considering the possibility that any serious scientist might disagree with the above is in my opinion a matter of superstition or religious belief. Everybody is free to check some of these facts with people who work in the field.

Alain Riazuelo 13:44, 26 September 2005 (UTC)