# Mathematics of cyclic cosmology: The universe that existed before the Big Bang was arranged like a basket of sunflowers

# The 2020 Nobel Prize in Physics was awarded to Oxford professor Roger Penrose "for his discovery that general relativity reliably predicts the birth of black holes." Considering it necessary to mark this event, we will briefly describe, perhaps, the most revolutionary theory of this outstanding mathematical physicist and equally outstanding popularizer of the exact sciences.

Penrose, together with the Armenian theoretical physicist from Yerevan Vahagn Gurzadyan, proposed a model of the Universe that did not start with the Big Bang. According to the conformal cyclic cosmology proposed by these physicists, the universe did not begin with the Big Bang, but goes through an endless sequence of cycles, called eons by Penrose. Each aeon ends with a Big Bang, in which space "temporarily" disappears, after which the next aeon begins.

In the transition from one aeon to another, space - and with it the distinction between huge and small - disappears. Only corners are saved. Such a transformation in mathematics is called conformal. The Penrose-Gurzadyan theory is based on an analysis of the CMB radiation map that emerged during the Big Bang, in which, in their opinion, circles of different sizes are signals from the Universe that existed in the previous eon.

Conformal transformations are part of the course of functions of a complex variable studied at universities. Today, such transformations can be built using computers by writing a function without touching a pencil and paper.

The theory of conformal cyclic cosmology differs from today's standard model of the universe, according to which there was no universe before the Big Bang. And also from the theory of multiple universes, according to which, in order to explain the established fact that matter, and even more so life, can exist only with an extremely unlikely set of values \u200b\u200bof the constants of physics, it is assumed that there are a great many universes. For the latter, in addition to somehow explaining the possibility of the existence of chemical elements, planets, stars and life, at present there are no experimental grounds.

Let's pay attention to another, unexpected side of the formal connection between Penrose's conformal universe and what happens in the living world. Namely ... with a basket of sunflower seeds.

From the point of view of mathematics, the seeds in a sunflower are ordered as a result of a conformal transformation of a square grid. The segments forming the sunflower flower are curved while maintaining right angles between adjacent seeds. At the same time, they are curved in such a way that there is symmetry between the spiral-shaped visible figures directed clockwise and counterclockwise.

The seeds forming a conformal transformation in the sunflower basket diverge from the central point, which, if the head of the sunflower were a strictly mathematical conformal transformation, would be a singularity. Similar - but wrapped in three dimensions - the structure of filling a cedar cone with its constituent parts (nuts, seeds). In this case, spirals arise - right and left - having a similar structure, but located in a sunflower in two, and in a cone - in three dimensions.

So why do corn seeds and nuts in a pine cone grow so exquisitely? What is the evolutionary advantage of the arrangement of seeds obtained as a result of the transformation used in the theory of functions of a complex variable, in comparison with a rectangular grid? The idea that such a pretentious structure was created by someone deliberately, for their own aesthetic pleasure, which, apart from it, can only be appreciated by the human eye, the atheistic mind will reject as unscientific. But if not this, then what? Why is the conformal transformation in biology and, according to Penrose, in cosmology, as important as the double helix? Questions that, even without getting an answer to them, fascinate.

Such is the rather unexpected analogy between the theory of the conformal universe, created by this year's physics prize winner, and the structures that arise in vivo. What kind of conformal transformation is implemented in the sunflower? Defining this function is a good task for a thesis of a student majoring in mathematical biology. How the sunflower genome encodes a conformal transformation that arranges the arrangement of seeds is a much more fundamental question, it can become a topic for obtaining a degree in any university.

The analogy between the structure of the Universe, in which the conformal transformation makes cosmology cyclic, has more general grounds in the living world than a particular case of a sunflower. Namely, bone growth. They grow with the preservation of shapes, and hence angles, including a smooth change in curvature, from infancy to adulthood. This, in particular, is the growth of bones of the endoskeleton of Homo sapiens. How the conformal transformation of bones is encoded in the genome while maintaining their shape is an absolutely fundamental problem. The solution of this problem is extremely important and worthy of the highest scientific awards, including the Nobel Prize.

*NY*

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