Subject: The algebraic approach, arXiv:0907.0416v1 [gr-qc], p. 8
Date: Fri, 3 Jul 2009 13:44:43 +0300
From: Dimi Chakalov <>
To: Robert M Wald <>
Cc: Stefan Hollands <>


I provided link to your recent arXiv:0907.0416v1 [gr-qc] at

If you and your colleague wish to "simultaneously consider all states arising in all Hilbert space constructions of the theory without having to make a particular choice of representation at the outset" (p. 8), recall KS Theorem,

Have a nice summer.

Every new member in a hierarchical organization climbs the hierarchy until he reaches his level of maximum incompetence

Laurence J. Peter


Subject: General Relativity, by Robert M Wald, 2008?
Date: Fri, 18 Jan 2008 18:05:30 +0200
From: Dimi Chakalov <>
To: Robert M Wald <>


If you plan to upgrade your 1984 textbook, check out



Subject: QFT in curved spacetime vs updated GR
Date: Fri, 14 Mar 2008 03:33:39 +0200
From: Dimi Chakalov <>

Dear Dr. Holland,

I spotted two interesting statements in your latest arXiv:0803.2003v1 [gr-qc]:

"there will not, in general, even be an asymptotic notion of particle states", and

"the only "background structure" that should occur in the theory is the spacetime manifold".

If you are interested in the subject of this email, see


D. Chakalov



From: Dimi Chakalov <>
To: Robert M Wald <>
Cc: Karel Kuchar <>,
M Gromov <>,
Jorge Pullin <>,
Bob Reroch <>,
Frank Wilczek <>,
Chris Isham <>
Subject: How to "unlearn" the fundamental falsehoods about the nature of space and time?
Date: Tue, 15 Nov 2005 05:36:58 +0200

Dear Professor Wald,

I wonder where and how you would introduce the notion of "dark energy" in GR. It is roughly 18 times more than the normal stuff you use to teach your students [Ref. 1]. It springs from "empty space", and I cannot see in your textbooks any possibility to EMBED it in GR from the outset.

What kind of "additional structure present beyond that of a manifold" [Ref. 1] do we need to introduce the possibility for "dark energy" from the outset?

We have to do something. I believe it isn't fair to direct kids to a dead end. Please advise. The opinion of your colleagues will be greatly appreciated, too.

My efforts can be read at


D. Chakalov

[Ref. 1] Robert M. Wald, Teaching General Relativity, gr-qc/0511073 v1, 14 Nov 2005

"A much better idea is to work infinitesimally, using the idea that, on
sufficiently small scales, a curved geometry looks very nearly flat. These departures from flatness can then be described via differential calculus.
"First, one needs a mathematically precise notion of the "set of points" that constitute spacetime (or that constitute a surface in ordinary geometry). The appropriate notion is that of a manifold, which is a set that locally "looks like" R^n with respect to differentiability properties, but has no metrical or other structure. The points of an n-dimensional manifold can thereby be labeled locally by coordinates (x1, ..., xn), but these coordinate labels are arbitrary and could equally well be replaced by any other coordinate labels (x'1, ..., x'n) that are related to (x1, ..., xn) in a smooth, nonsingular manner.
"The next key step is to formulate a notion of differentiation of tensor fields. The notion of differentiation of tensor fields is nontrivial because on a manifold M, there is no natural way of identifying the tangent space at a point p with the tangent space at a different point q, so one cannot simply take the difference between the tensors at p and q and then take the limit as q approaches p. In fact, if we had no additional structure present beyond that of a manifold, there would be no unique notion of differentiation; rather
there would be a whole class of possible ways of defining the derivative of tensor fields."


Note: See the discussion of the dynamic dark energy (coincidence problem) on p. 16 and p. 6 from gw.pdf. The idea of embedding this "dark" stuff is also explained with the ladder metaphor here. Recall also that the cosmological constant was introduced 'by hand', as stressed by Albert Einstein. It is totally alien to GR. Es explained eloquently by Larry Kraus, the dynamic dark energy "does not depend on position or time -- hence the name "cosmological constant". The force caused by the constant operates even in the complete absence of matter and radiation. Therefore, the source must be a curious energy that resides in empty space."

So, how would you tackle a dark stuff that is 18 times more than the "normal" stuff [Ref. 1], has its own dynamics, and resides in empty space? Also, how can the Hubble parameter "vary" in its own time [Ref. 2]?

The so-called empty space is nothing but the quantum-gravitational potential reality; see the second footnote on p. 16 from gw.pdf. Put it differently, the dynamic dark energy is embedded within the 'infinitesimal displacement' in the smooth, nonsingular transport [Ref. 1].

If you choose to ignore the global mode of spacetime, the hypothetical source of quantum-gravitational potential reality, you also face the problem of the cosmological time arrow; see my comments on Bob Wald's "The Arrow of Time and the Initial Conditions of the Universe", gr-qc/0507094 v1. Moreover, we need a generic patch to the non-linearity of Einstein equations, as explained here.

Briefly, the decomposition of spacetime into 3-D space and 1-D time, along the lines of Dirac-ADM, is deadly wrong and utterly misleading, since it cannot reveal the true dynamics of GR [Ref. 3]. I tried to explain this to my 12-yeard old daughter here; more here. (Can you exclude on purely theoretical grounds a past sudden singularity and a past "big rip" [Ref. 3]? If you can't, your theory is wrong, since it predicts catastrophes which have never happened.)

Our students are kids, and kids have the right to know everything we know. We must never give them directions to a dead-end. I wonder if Bob Wald agrees.

The dead-end in question is the 'question mark' area in Fig. 1 from the recent book by Slava Mukhanov [Ref. 2]. The only possible -- we don't have multiple choice here -- resolution is to introduce a new degree of freedom, called 'global mode of spacetime', for both the graceful exit and the physical presentation of The Beginning [John 1:1]. We need a new parameter to allow for the variation of the Hubble parameter, since it cannot vary in its own "time" from the Hamiltonian formulation of GR (the coincidence problem). Hence the only possible solution is to include that same 'question mark' area in each and every elementary step of the cosmological time arrow: just place it in the global mode of spacetime. Once created, the universe cannot reach The Beginning from the local mode; it can only tend asymptotically toward it (see the 'vacuum cleaner paradox' here). This 'question mark' area [Ref. 2] is again the case of 'numerically finite but physically unattainable boundaries of the physical world'. Once created, the universe has a dual age: finite in the local mode, and infinite (or rather indecisive) in the global mode. Have your "inflation" cake and eat it!

God is, and has always been, inside the instant 'now'. Physically, this is a very special state of the whole universe as ONE. There is no way we could physically trace it back along the local mode of spacetime: we would need an exposed privileged reference frame, but then Bob Wald wouldn't be able to teach GR [Ref. 1] and Slava Mukhanov wouldn't write his book [Ref. 2]. They teach their students, but do they tell these kids everything they know? Do they really care about their students?

This is a very sensitive issue to me. Back in 1972, when I was a 20-year old kid, I was specifically instructed by the Bulgarian colleagues of Bob Wald to forget about "upgrading" Einstein's GR, and subsequently lost many years in exploring different solutions to the mind-brain problem. Now, see my comments on Bob Wald's "The Arrow of Time and the Initial Conditions of the Universe", gr-qc/0507094 v1, below. He still hasn't acknowledged my email from Tue, 26 Jul 2005 03:41:01 +0300, and probably never will. Needless to say, I haven't heard from Slava Mukhanov either. What can you expect from American and Russian professors who live in total socialism?

Anyway. I believe it is agonizingly clear that in cosmology we need a fundamental time asymmetry. But this same fundamental time asymmetry must be totally hidden in the local mode of spacetime: if we "look" in the past, we should see a time-reversible snapshot that has already been created in the cosmological time arrow. Again, the only possible way to solve this highly non-trivial task is to introduce a new degree of freedom, called here 'global mode of spacetime'. It makes the local mode a perfect continuum, since its "duration" there is strictly zero. The only way to solve the problem of The Beginning [Ref. 2] is to embed it in the cosmological time arrow, in each and every elementary step. Otherwise we cannot solve the most difficult paradox of cosmology. Back in April 1986, the late Yakov Zel'dovich explained it in the following manner: "Long time ago, there was a period of time during which there was still no time at all." Any time you look at your wristwatch, you've already passed through the "dark gap" of the global mode of spacetime.

All this is very old. I am terribly tired of repeating what I've written on August 15, 1999. Will quote just this: "Should a discussion prompted by this paper confirms the custom-made interpretation of the cause (or 'diagnosis') for the problem of time, I would be greatly encouraged to make the next step of suggesting concrete ideas potentially applicable for a background-free quantum gravity endowed with some 'universal time arrow' matching the psychological time arrow."

All I got so far was a dark and somber silence. It just makes me wonder how many students of Bob Wald, Slava Mukhanov, etc., have graduated since August 1999, and how many of them will choose to teach GR.

D. Chakalov
November 15, 2005
Last update: November 22, 2005

[Ref. 2] V. Mukhanov, Inflation: Homogeneous Limit. Sample chapter from "Physical Foundations of Cosmology" published by Cambridge University Press (2005). November 18, 2005, astro-ph/0511570 v1.

Sec. 3, How can gravity become "repulsive"?

"To have a graceful exit from inflation we must allow the Hubble parameter to vary in time."

"Inflation is a stage of accelerated expansion of the universe when gravity acts as a repulsive force."

[Ref. 3] Vasileios Paschalidis, Alexei Khokhlov, and Igor Novikov, Well-posed constrained evolution of 3+1 formulations of General Relativity, gr-qc/0511075 v2. (None available - D.C.)

Miguel Alcubierre et al., Towards an understanding of the stability properties of the 3+1 evolution equations in general relativity, gr-qc/9908079 v2.

"One might argue that present day computational resources are still insufficient to carry out high enough resolution 3D simulations. However, the difficulty is likely to be more fundamental than that. There is no theorem guaranteeing the well-posedness of the initial boundary value problem for the full ADM system. In particular, one must consider the possibility that free evolutions using the ADM system might be unstable, e.g., against constraint violations in 3D. There are also well-known complications due to the gauge (coordinate) degrees of freedom in the theory. This is one of the major open problems in numerical relativity."

Celine Cattoen and Matt Visser, Necessary and sufficient conditions for big bangs, bounces, crunches, rips, sudden singularities and extremality events, gr-qc/0508045 v2, Class. Quantum Grav. 22 (2005) 4913-4930.

"Big rips: A "big rip" is said to occur if a(t) --> 0 at finite time [7, 8]. We can distinguish a "future rip" from a "past rip", where the literature to date has solely considered future rips (as a past rip would be a most unusual and unexpected beginning to the history of the universe).
"Sudden singularities: Past or future sudden singularities are a recent addition to the collection of cosmological milestones, and are defined by some time derivative of the scale factor diverging at finite time, while the scale factor itself remains finite [11, 12, 13]. Again, almost all attention has been confined to future sudden singularities (as a past sudden singularity would be a most unusual and disturbing beginning to the history of the universe)."


Subject: Re: Kozma Prutkov on cosmology
Date: Mon, 21 Nov 2005 16:03:06 +0200
From: Dimi Chakalov <>

P.S. I quoted from your sample chapter, astro-ph/0511570 v1, at


On Tue, 12 Apr 2005 18:21:13 +0300, Dimi Chakalov wrote:
> Many things are incomprehensible to us not because our comprehension
> is weak, but because those things (sii veshti) are not within the frames
> of our comprehension.
> Kozma Prutkov,


Subject: arXiv:0802.2068v1 [astro-ph]
Date: Mon, 18 Feb 2008 05:55:00 +0200
From: Dimi Chakalov <>
To: Slava Mukhanov <>
Cc: Alexey Golovnev <>,
Vitaly Vanchurin <>,
Andrei Linde <>,
Claus Kiefer <>

Slava i ego komanda napisali: "All successful inflationary scenarios are based on the use of scalar field condensate."

Eh ti, staruha Izergil', who brought you in Munich, I wonder.

There are no successful inflationary scenarios whatsoever, simply because you can't embed the "dark energy" of [you-name-it] into GR, for reasons explained at

I will be happy to elaborate, if only you and/or any your colleagues gets professional.

You also wrote: "To Andrei Linde on the occasion of his 60th birthday."

I think he absolutely deserves it.



From: Dimi Chakalov <>
To: Yurii V Dumin <>
Cc: <>,
Subject: Scale-dependent DDE & CDM effects
Date: Fri, 25 Nov 2005 14:40:34 +0200

Dear Dr. Dumin,

I read with great interest your "Testing the "Dark-Energy"-Dominated Cosmology via the Solar-System Experiments", astro-ph/0507381 v2. I wonder if you or some of your colleagues can elaborate on the effects of dynamic "dark" energy (DDE) and cold dark matter (CDM). It seems to me -- please correct me if I'm wrong -- that these "dark" phenomena are (i) scale-dependent, (ii) produce rotational patter of the observable matter, and (iii) run in opposite "directions": expansion for DDE and contraction for CDM.

Regarding (ii), I believe the rotational pattern of Milky Way is firmly
confirmed, but I'm not aware of any data about similar CDM effect, on much larger scale, produced from the dark galaxy VIRGOHI 21,

At cosmological scale, the rotation pattern from DDE shows up as 'cosmic

Can VIRGOHI 21 swirl the near-by galaxies? I'm not aware of any such data.

As to the task of understanding (iii), I believe we need to incorporate these two "opposite" effects in GR from the outset,

A penny for your thoughts!


Dimi Chakalov


From: Dimi Chakalov <>
To: Alexander Burinskii <>,
Emilio Elizalde <>,
Sergi Rafael Hildebrandt <>,
Giulio Magli <>
Cc: Jerzy Kijowski <>,
John Friedman <>,
Yurii V Dumin <>,
Jim Isenberg <>
Subject: Narrow beams from naked rotating "dark matter" sources?
Date: Mon, 28 Nov 2005 13:34:25 +0200

Dear colleagues,

I read with great pleasure your recent paper on "half dressed" sources [Ref. 1], and wonder if you would go so far as to consider a generalized model of dark matter-dark energy sources. What if the narrow jet is produced by "dark energy"? It seems to me that we have to introduce all that "dark" stuff in GR from the outset,

I wonder if you can elaborate on the mysterious jet [Ref. 1]: what keeps it
"narrow"? How come it doesn't tear apart the whole "event horizon"? I am not aware of *any* stable event horizon; see the time-like naked singularity at

Looks like we have yet another catastrophe, which too hasn't happened in the past 13.7 billion years.

Your feedback will be greatly appreciated.


Dimi Chakalov

[Ref. 1] Alexander Burinskii, Emilio Elizalde, Sergi R. Hildebrandt, Giulio
Magli, Rotating "Black Holes" with Holes in the Horizon, Thu, 24 Nov 2005
10:24:39 GMT, gr-qc/0511131 v1.

"We show that axial singularities "break up" the Kerr black hole, forming a
hole in the horizon which connects the internal with the external regions. As a result, although a "horizon" is still present, it does not isolate any more the Kerr singularity from the exterior, and it turns out to be "half dressed". We conjecture here that the formation of the axial singularities may result in the production of jets [4], thus providing a model for important astrophysical phenomena and dramatically extending the scope of Einstein's theory.

"These "black holes with holes in the horizon" have thus "preferred
directions" in which the causal structure differs from that of "true black
holes". Their singularity is naked, but the nakedness is of a very peculiar
type, since it manifests itself in specific directions only. A similar
situation occurs with others non-spherical exact solutions, like e.g. the so
called Gamma metric [10].

"5. Astrophysical applications.

"Two main questions appear in confronting astrophysical applications of these solutions: (i) which consequences will follow from the origin of the holes in the black hole horizon? (ii) which kind of mechanism could lead to the appearance of the axial singularity and corresponding holes in the horizon?

"In real situations, axial singularities cannot be stable and they will
presumably correspond to some type of jet or burst, hence it is natural to
conjecture that the related holes in the horizon will also be at the origin of
jet formation.

"It is known, that the Kerr solution has a repulsive gravitational force
acting on the axis of symmetry for r < a.


"From the analysis above, we conclude that the aligned excitations of the
rotating black hole (or naked rotating source) lead, unavoidably, to the
appearance of axial singularities accompanied by outgoing traveling waves and also to the formation of holes in the horizon, which on its turn can lead to the production of astrophysical jets [4].

"As it was mentioned too, multiparticle Kerr-Schild solutions of Einstein's
equations suggest that axial singularities are to be oriented along the line
connecting the interacting particles. Thus, it will be interesting to analyze
in further detail the observed jets in order to check the conjecture that they may be indeed triggered by radiation coming from remote active objects.

"Finally, one may suspect this effect to be related to the known phenomenon of superradiance, although the usual treatment of this last does not take into account the condition (2) which specifically leads to the formation of narrow beams."


Subject: Re: Are Gravitational Waves Directly Observable?
Date: Tue, 26 Jul 2005 03:41:01 +0300
From: Dimi Chakalov <>
To: Robert M Wald <>

Dear Professor Wald,

Sorry for my bulk email from yesterday; it was the last one indeed.

I wrote: "Would you endorse the submission of paper.doc, from 25 July 2005 (cf. above), to the gr-qc section of e-print archive?

"If you agree, please write me back.

"Should you find 1 (one) error in paper.doc, please write me back as

I will be happy to hear from you and from your colleagues. Please feel free to download the paper in DOC and PDF formats, whichever you prefer, from

May I comment on your recent "The Arrow of Time and the Initial
Conditions of the Universe", gr-qc/0507094 v1. You wrote:

"However, our ignorance of the probabilities of various cosmological occurrences is truly dwarfed by our (nearly) total ignorance of the probability of the existence of observers, since we know virtually nothing about what is really required to produce conscious life."

I believe have tried in my web site to elaborate on the proposition due to Pauli and Jung, which goes back to Leibnitz. Physically, it boils down to the idea of 'quantum-gravitational potential reality'; please see Secs. 3 and 4 in my paper. BTW I believe the very notion of 'isolated system', such as 'the whole universe', needs to be specified by answering the question 'with respect to what?' Well, I dare to suggest that the only truly isolated system is "isolated" w.r.t. the 'quantum-gravitational potential reality'.

You also wrote: "It seems to me to be far more plausible that the answer to the above question (why the observable universe is in the state we find it to be in? - D.C.) as to why the very early universe was in a very low entropy state is that it came into existence in a very special state. Of course, this answer begs the question, since one would then want to know why it came into existence in a very special state, i.e., what principle or law governed its creation. I definitely do not have an answer to this question. But I believe that it will be more fruitful to seek an answer to this question than to attempt to pursue dynamical explanations."

I believe we can 'have our cake and eat it', that is, both pursue dynamical explanations and maintain a very special "dark" state of 'the whole universe', such as the putative 'quantum-gravitational potential reality'. Again, please see Secs. 3 and 4 of the paper, particularly my NB argument on p. 12.

Kindest regards,

Dimi Chakalov


Subject: CQG Special Issue
Date: Thu, 11 Aug 2005 02:36:54 +0300
From: Dimi Chakalov <>

RE: Proceedings of the 9th Gravitational Wave Data Analysis Workshop, Annecy, France, 15-18 December 2004; CQG Special Issue, expected online publication September 2005,

Dear Professor Wald,

I wonder if there is at least *one* article from the forthcoming CQG
Special Issue, which deals with the possibility that Gravitational Waves (GWs) may not be directly observable *in principle*.

If none of your colleagues have done that, would you allow me to balance their efforts by publishing my viewpoint in your Journal?

I will be happy if you personally agree to review my article, entitled:
"Are Gravitational Waves Directly Observable?"

Please look at the outline intended to my 12-year old daughter at

My manuscript is ready to land on your desk.

Looking forward to hearing from you,

Dimi Chakalov


Subject: Re: CQG Special Issue
Date: Fri, 12 Aug 2005 00:36:52 +0300
From: Dimi Chakalov <>
To: robert manuel wald <>
CC:, Bernard F Schutz <>

On Thu, 11 Aug 2005 10:25:28 -0500 (CDT), robert manuel wald wrote:
> > If none of your colleagues have done that, would you allow me
> > to balance their efforts by publishing my viewpoint in your
> > Journal?
> Please consult
> and the other linked pages for instructions on how to prepare and
> submit an article to Classical and Quantum Gravity.
>                 Robert Wald

Dear Professor Wald,

I've done my homework, opened an account, now I'm waiting to hear from Dr. B. Schutz (cf. below). I hope to submit my manuscript very soon.


Dimi Chakalov

Message-ID: <>
Date: Mon, 01 Aug 2005 13:08:59 +0300
From: Dimi Chakalov <>
To: Bernard F Schutz <>
Subject: Request for reproducing published material
X-Priority: 2 (High)
References: <>

Dear Dr. Schutz,

In line with IOP Guidelines for reproducing published material, I am
respectfully requesting your permission to reproduce Fig. 24.3 from
[Ref. 1, p. 349] and Fig. 1 from [Ref. 2].

I will argue [Ref. 3] that the strain of GWs may not be observable *in principle*, and hence need to elaborate extensively on your viewpoint, which, in turns, requires reproducing your two figures, as requested above.

Looking forward to hearing from you,

Yours sincerely,

Dimi Chakalov

[Ref. 1] Bernard Schutz, GRAVITY from the Ground Up: An Introductory Guide to Gravity and General Relativity, Cambridge University Press, Cambridge, 2003.

[Ref. 2] Bernard F. Schutz, Gravitational Radiation, AEI-2000-020,
gr-qc/0003069 v1; Accepted by Encyclopedia of Astronomy and
Astrophysics, 2000.

[Ref. 3] D. Chakalov, Are Gravitational Waves Directly Observable?
Manuscript, August 2005.


Subject: Re: CQG Special Issue
Date: Thu, 13 Oct 2005 12:31:00 +0100
From: Dimi Chakalov <>
To: Robert Manuel Wald <>
CC: Bernard F Schutz <>,,,,,,,,,,,,,,
     LIGO Scientific Collaboration Spokesperson Peter Saulson
BCC: [snip]

Dear Professor Wald,

Regarding my email message from Thu, 11 Aug 2005 02:36:54 +0300: I regret to report that I still haven't received any response from Dr. B. Schutz to my request from Mon, 01 Aug 2005 13:08:59 +0300 for reproducing published material.

I need to reproduce some crucial text and images from B. Schutz' papers, but cannot of course break IOP Guidelines for reproducing published material. Thus, I am still unable to submit my manuscript to CQG. If some day Dr. B. Schutz allows me to quote from his published papers, I will send you my manuscript ASAP.

Meanwhile, I invite you and all your colleagues to read an outline at

Should you and/or any of your colleagues have questions, please don't hesitate. I will be more than happy to elaborate.

Thank you for your time.

Sincerely yours,

Dimi Chakalov
35 Sutherland St
London SW1V 4JU, UK


Subject: What is deflation time?
Date: Thu, 13 Jun 2002 12:00:52 +0300
From: "Dimiter G. Chakalov" <>
To: Robert Wald <>
CC: Stefan Hollands <>,,,,,,,,,,, Steven.Weinstein@Dartmouth.EDU,,,,,

Dear Professor Wald,

Regarding your article "An Alternative to Inflation", gr-qc/0205058 [Ref. 1], and the reaction to it [Ref. 2], may I ask you to help me understand your interpretation of 'deflation time'.

The hypothesis of inflation/deflation has always puzzled me: how can you link the Beginning (we know nothing about it) to the fast-roll inflation, and "then" link the latter to the slow-roll inflation up to the present moment of time, as read with you wristwatch?

I can't see how some *physical clock*, as defined in GR, could possibly survive if you run it back to the inflation stage, if any.

The situation becomes even more puzzling if you consider the paradox of energy (non)conservation [Ref. 3] and other 'dark' issues, as explained to the general audience [Refs. 4 and 5].

Perhaps the crux of the matter is in the absence of some time parameter suitable for any dynamical evolution, as advocated by Baez and Geroch,

If this is the case, how is the time measured with your wristwatch different than the "time" of inflation/deflation?

I will be happy to learn the opinion of your colleagues as well.

Thank you very much for your time, as read with your watch.

Sincerely yours,

Dimiter G. Chakalov


[Ref. 1] Stefan Hollands, Robert M. Wald. An Alternative to Inflation. Fri, 31 May 2002 19:04:48 GMT,

Footnote 1: "It also should be noted that for a self-gravitating system such as our universe, dynamical evolution will normally tend to make the system become more inhomogeneous with time ("Jeans' instability"). Thus, the isotropy of the microwave background radiation on large scales would truly be a puzzle if it did have time to equilibrate on these scales.

In other words, it seems overwhelmingly improbable that a collapsing universe would undergo an era of "deflation" just before the "big crunch".

Footnote 7: "In other words, we suggest that it makes sense to talk about phenomena "emerging out of the spacetime foam" at length scales greater than l_0, and that *some* sort of semiclassical description of such phenomena may be possible even in an era that would correspond to t << t_p in the naive extrapolation of a semiclassical solution of Einstein's equations to early times. Note however that we do *not* suggest that an accurate semiclassical description should be given by such a naive extrapolation of the classical spacetime metric to time earlier than t_p . Instead, the "correct" semiclassical description that we have in mind would presumably be obtained by some suitable "coarse graining" of the degrees of freedom of quantum gravity over length scales < l_0.

"In summary, we have argued that inflation does not satisfactorily "solve" the homogeneity/isotropy and flatness "problems" -- nor is any other dynamical mechanism likely to give a satisfactory explanation of the homogeneity/isotropy and spatial flatness of our universe. Rather, a much deeper understanding of the nature of the birth of our universe undoubtedly will be required."

[Ref. 2] Lev Kofman, Andrei Linde, V. Mukhanov. Inflationary Theory and Alternative Cosmology. Tue, 11 Jun 2002 19:53:58 GMT,

"Paradoxically, evaluation of the "alternative to inflation" proposed in [6] provides an additional argument in favour of inflation.

"Indeed, in inflationary cosmology the total energy of the scalar field and particles created by its decay is not conserved. (...) The absence of adiabaticity is a key feature of all inflationary models because inflation removes all particles that could be present before inflation; all 10^88 particles that we see now within our cosmological horizon were created by the decaying scalar field.

"Decay of the scalar field and particle production are irreversible processes, and therefore, quite independently of the issue of probabilities, time reversal of inflationary evolution *can never produce the same initial conditions the universe started with*. The scalar field that decayed at the end of inflation is not going to re-appear again if one reverses the time evolution. The number of particles produced by this field, just as the inhomogeneities produced during inflation, will only grow on the way back to the singularity.

"Thus, inflationary evolution is irreversible, and the 'obvious' requirement of measure preserving evolution is not satisfied in inflationary cosmology."

[Ref. 3] Carlos Barcelo, Matt Visser. Twilight for the energy conditions? Thu, 16 May 2002 03:05:41 GMT,

"The fact that the ANEC can be violated by classical scalar fields is significant and important (even with the trans-Planckian caveat). The ANEC is the weakest of the energy conditions in current use, and violating the ANEC short circuits all the standard singularity/positive mass/censorship theorems. This observation piqued our interest and we decided to see just how weird the physics could get once you admit scalar fields into your models.

"In summary: The conflict between quantum physics and gravity is now becoming acute. Problems are no longer confined to Planck scale physics but are leaking down to arbitrarily low energies and even into the classical realm. These problems appear to be insensitive to and independent of high energy phenomena and so it is not at all clear that a high energy cutoff (string theory, quantum geometry, lattice gravity, etc...) would do anything to ameliorate them. The situation is both puzzling and exciting."

[Ref. 4] James E. Kloeppel, "Dark Matter: Science Doesn't Know What, Where Or How",

[Ref. 5] Steve Bradt, "Planets, Stars And Gases Make Up Only 5% Of Universe",


Subject: Re: What is deflation time?
Date: Sun, 29 Sep 2002 13:51:07 +0300
From: Dimi Chakalov <>
To: Robert Wald <>

Dear Professor Wald,

I have not yet received a reply to my email from Thu, 13 Jun 2002 12:00:52 +0300,

In your recent contribution to MOG [Ref. 6], you wrote that "(...) theories that are renormalizable in Minkowski spacetime will also be renormalizable in curved spacetime, although additional "counterterms" corresponding to couplings of the quantum field to curvature will arise."

Sure will. Why waste time with mixing apples with oranges? Let me quote John Wheeler (courtesy by Christopher Fuchs): "We must make as many mistakes as we can, as fast as we can, or we'll never have a hope of gaining a true understanding!" That was 30 years ago, I'm afraid.


To cut the long story short, I've compiled a CD-ROM and if you or any of your colleagues agree for a brief and informal review, I will be happy to send it. More info at

Thank you for your time, as read with your watch. I'm afraid it won't help you nor Prof. Geroch [Ref. 7] to attach gravity to quantum fields and explain the deflation time. What you're looking for may not be there,

Again, I will be happy to mail you and your colleagues my CD-ROM for a brief review.


Dimi Chakalov
The hardest thing of all is to find a black cat in a dark room, especially if there is no cat.


[Ref. 6] Quantum field theory on curved spacetime at the Erwin Schrödinger Institute by Robert Wald <>

"A program on "Quantum field theory on curved space times" was held at the Erwin Schroedinger Institute in Vienna, Austria from July 1 through August 31, 2002. The main goal of this program was to bring together researchers with expertise in general relativity and researchers with expertise in mathematical aspects of quantum field theory, in order to address some problems of mutual interest in quantum field theory in curved spacetime. Approximately 25 researchers in quantum field theory in curved spacetime and related areas participated in the program. The following is a brief summary of some of the main topics and results discussed during the program.

"The upshot is that perturbative renormalization theory for quantum fields in curved spacetime is now on as sound a footing as in Minkowski spacetime. Furthermore, theories that are renormalizable in Minkowski spacetime will also be renormalizable in curved spacetime, although additional "counterterms" corresponding to couplings of the quantum field to curvature will arise."

Source: MATTERS OF GRAVITY, No. 20, Fall 2002,

[Ref. 7] R. Geroch (Monday, July 29, 2002). Diffeomorphism Freedom. 50 years of the Cauchy problem in General Relativity. Cargèse, Corsica, France, July 29 - August 10, 2002.

[Working draft]


"A fundamental feature of Einstein's equation is that it manifests gauge freedom associated with diffeomorphisms, and that, up to this freedom, it has a well-posed initial-value formulation.  The diffeomorphism freedom, for example, plays a central role in discussions of energy in general relativity (ref) and of gravitational radiation and asymptotic structure (ref). The initial-value formulation underlies virtually every topic in the theory.  For instance, "stability" of an astrophysical system refers to the character of the evolution of a small perturbation in initial conditions, i.e., requires, in order to be sensible, an initial-value formulation.

"It would be some interest, given the crucial role this feature plays in the structure of the theory, to understand better how it works. One method of doing this would be to formulate a general, practical characterization of having "gauge freedom associated with diffeomorphisms, and, up to this freedom, a well-posed initial-value formulation".