**(c) Robert Neil Boyd**

[R. N. Boyd]:

I like Linde's views, based as they are on quantum physics, because they show that each universe has a unique set of physical laws, which is true to fact.

Although I understand the mechanism of inflation described by Linde et al, I am not convinced it is true to fact, however mathematically correct. My question is, what requires that the universes and dimensions must have had a beginning point?

Is it not possible for all of these universes and dimensions to have pre-existed, so that we are simply examining the given when we explore the universes? Like mathematical results, the structure of Reality and Nature, seem simply inevitable...

I am convinced that the universe in which we live, is not expanding, and as you know, I am of the view that there was never a "big bang". My view resembles a "steady state" universe of continuous creation. I don't see that creation had some "beginning", then the process of creation stopped after that instant. The requirement for superluminal expansion in inflationary scenarios is a difficulty.

(Superluminal processes of any sort, mean that energy is not conserved at infinity. This seems sufficient to power the universe as we observe it.)

It appears that the description of Steinhardt, et al, of "...a collision between two 4-dimensional membranes in a 5 dimensional subspace of the 11-dimensional space of a superstring M-theory", require mechanisms involving manifestations of forces which have never been directly observed in Nature. How can there be a "collision" of these 4D "membranes", and secondly, why must such "collision" result in the production of energy sufficient to make an infinite volume 3D universe? It seems to me just as likely that the 4D volumes would intersect without any large-scale interactions, or perhaps with no interactions at all.

They say:

"...Furthermore, as we shall show, the brane gains kinetic energy due to its coupling to moduli fields. Upon impact, the bulk brane is absorbed by the visible brane in a so-called small-instanton phase transition (see Sec. II for details). This transition can change the gauge group on the visible brane."

"...This model, discussed by Randall and Sundrum, (9) consists of a five dimensional bulk described by Einstein gravity with a negative cosmological constant , bounded by a pair of branes with tension + or - (a)."

Based on Finkelstein's work, involving "mass infinitesimals" which are, by definition, smaller than the Plank length and "time infinitesimals", which are by definition, smaller than the Plank time, gravitation is not quantizable. Therefore, all theories which depend on quantization of gravity must fail at the lower limit. Even though Steinhardt talks here about an Einsteinian gravity, he relies on the quantization of gravity, later in his paper.

Although I like the implications of activities of topological forces, these descriptions of brane "tension" are not sufficiently well derived, and the entirety of the development of the thesis depends on this derivation.

[Tony Smith]:

The web page you mentioned, http://feynman.princeton.edu/~steinh/npr/ describes in general terms the physics of a paper at http://xxx.lanl.gov/abs/hep-th/0103239 by Steinhardt, Khoury, Ovrut, and Turok entitled The Ekpyrotic Universe: Colliding Branes and the Origin of the Hot Big Bang and, as I understand it, it proposes to replace the standard cosmological picture of a big bang followed by inflation with a collision between two 4-dimensional membranes in a 5 dimensional subspace of the 11-dimensional space of a superstring M-theory,

Since I like inflation, and I don't like the supersymmetry part of superstrings, I don't agree with the Ekpyrotic Universe model of Steinhardt et al.

Even if you like superstrings and their 11-dim M-theory, there may be serious problems with the Ekpyrotic Universe of Steinhardt et al as an alternative to inflation, as pointed out by Linde, Kallosh, and Kofman at http://xxx.lanl.gov/abs/hep-th/0104073 where they say:

"... Khoury, Ovrut, Steinhardt and Turok ... suggest a ... cosmological model and argued that it may resolve all major cosmological problems without any use of inflation. Their model was called the ekpyrotic universe, from the Greek-derived word ekpyrosis.

...

... inflation removes all previously existing inhomogeneities, whereas in the ekpyrotic scenario even very small initial inhomogeneities become exponentially large. Therefore instead of resolving the homogeneity problem, it makes this problem much worse. This demonstrates once again how difficult it is to construct a consistent cosmological theory without using inflation. ...".The details of how Linde et al got to their conclusion is given in their paper on the xxx e-print archives at http://xxx.lanl.gov/abs/hep-th/0104073

Steinhardt et al replied to the criticism of Linde et al in http://xxx.lanl.gov/abs/hep-th/0105212 saying that the criticism of Linde et al "... rests on examples of Horava-Witten models in the literature rather than on mathematical analysis. ...". However, as Steinhardt et al say, "... The ekpyrotic model ... is built on the principle that the initial state is quasi-static with properties dictated by symmetry, particularly supersymmetry. ...".

Since the supersymmetry to which they refer is doubtless the naive 1-1 boson-fermion supersymmetry of superstring theory, and since such naive 1-1 supersymmetry has NEVER been observed in decades of high-energy physics experiments, I think that the Ekpyrotic Universe is based on a defective foundation and is therefore itself defective.

In summary, I think that the Ekpyrotic Universe is very good press agentry (good in the capability/skill sense, not in the moral sense) and very bad (in all senses) physics.

Tony 3 June 2001