**Table of Contents**

*.......The Elegant Universe*

**THE ELEGANT UNIVERSE,****Brian Greene,**1999, 2003

```(annotated and with added

**bold highlights by Epsilon=One**)

**Chapter 14 - Reflections on Cosmology**

In the Beginning There Was a Planck-Sized Nugget

In the late 1980s, Robert Brandenberger and Cumrun Vafa made the first important strides toward understanding how the application of these string theoretic features modifies the conclusions of the standard cosmological framework. They came to two important realizations. First, as we run the clock backward in time toward the beginning, the temperature continues to rise until the size of the universe is about the Planck length in all directions. But then, the temperature hits a

This led Brandenberger and Vafa to the following cosmological picture. In the beginning, all of the spatial dimensions of string theory are tightly curled up to their smallest possible extent, which is roughly the Planck length. The temperature and energy are high, but not infinite, since

*maximum*and begins to*decrease.*The intuitive reason behind this is not hard to come by. Imagine for simplicity (as Brandenberger and Vafa did) that all of the space dimensions of the universe are circular. As we run the clock backward and the radius of each of these circles shrinks,**the temperature of the universe increases.****(Epsilon=One: No! The**But as each of the radii collapses toward and then through the Planck length, we know that, within string theory, this is physically identical to the radii shrinking to the Planck length and then bouncing back toward increasing size. Since temperature goes down as the universe expands, we would expect that the futile attempt to squeeze the universe to sub-Planck size means that the temperature stops rising, hits a maximum, and then begins to decrease. Through detailed calculations, Brandenberger and Vafa explicitly verified that indeed this is the case.*overall*temperature of the Universe remains constant. The locus of the Universe, the duality of*Infinity,*is invariable. The Universe's locus is congruent with*Infinity*; thus, it can be said that the Universe is . . . the Singularity. Such an understanding quickly dissipates many enigmas, conundrums, myths, questions, and superstitions of mankind through all of anthropic history.)This led Brandenberger and Vafa to the following cosmological picture. In the beginning, all of the spatial dimensions of string theory are tightly curled up to their smallest possible extent, which is roughly the Planck length. The temperature and energy are high, but not infinite, since

**string theory has avoided the conundrums of an infinitely compressed zero-size starting point. At this beginning moment of the universe**, all the spatial dimensions of string theory are on completely equal footing—they are completely symmetric—all curled up into**a multidimensional, Planck-sized nugget.****(Epsilon=One: The "Planck-sized nugget" is analogous to a Pulsoid; and, "multidimensional" is analogous to the various oscillations that create, and are within, the Pulsoid, such as slide, swing, vibration, rotation, spin, et cetera.)**Then, according to Brandenberger and Vafa, the universe goes through its first stage of symmetry reduction when, at about the Planck time, three of the spatial dimensions are singled out for expansion, while all others retain their initial Planck-scale size. These three space dimensions are then identified with those in the inflationary cosmological scenario, the post-Planck-time evolution summarized in Figure 14.1 takes over, and these three dimensions expand to their currently observed form.