Within the universe, the singularities Cosmic anomalies of space-time appear. Examples are black holes or the big bang, points where current models of physics collapse and reality becomes an intriguing puzzle. According to mathematical predictions of theorems stated by Roger Penrose in the 1960s and recognized with the Nobel Prize in 2020, its existence is expected. However, little is known about its dynamics, i.e. its path through space. The period behaves close to singularity.
Modern cosmology holds that a good approximation of the present universe is, to a large extent, given by Alexander Friedman’s 1922 solution to the equations of Albert Einstein’s theory of relativity. According to Friedman’s solution, space does not exist still, but rather expands with time – this was experimentally confirmed by Edwin Hubble in 1929. From the expansion of the universe, the existence of a singularity is known: if we turn back the clock and travel back in time, space will shrink to a point (the Big Bang).
In his determination, Friedman assumed that space is homogeneous – that is, behaves the same at all points – and isotropic – has the same behavior in all directions. However, this may not be true at the Big Bang, so Friedman’s solutions do not help explain what happens near this singularity.
Measurements Cosmic background radiation After the Big Bang, it implies that the universe expanded almost equally in all spatial directions. But still A small asymmetry in isotropy can produce different behavior near singularity implied by Friedman’s solutions. In particular, unlike what happens in these, spatial dimensions may have different roles in the structure of our destiny.
To answer these questions, in the 1970s, Vladimir Belinsky, Isaac Galatnikov, and Evgeny Lifshitz speculated that after the explosive birth of the universe, it went through a chaotic growth phase. Chaos, in this cosmic context, represents a fascinating problem rather than disorder. According to this hypothesis – called P.K.L-, chaotic fluctuations yield chaotic patterns and complex mathematical structures that ultimately shape our present universe. More than 50 years later, this mathematical question remains unanswered.
The BKL conjecture states, for the most part, that singularities have three properties. First, they are local, that is, particles Unpaired One from the other and each evolves towards uniqueness. Hence, Einstein’s equations become Ordinary differential equations.
Second, the singularities are dominated by the vacuum, meaning that for most types of matter their effect on the dynamics of the spacetime geometry is negligible near the singularity. In John Wheeler’s words, “the substance is not important” near a singularity.
Finally, singularities are oscillating and confusing. At the same time, Charles Miesner proposed a model to analyze these chaotic oscillations, from which the term was coined. Mix Master – refers to an electric kitchen mixer for making dough. This model describes a Cosmological Dance, each spatial direction alternates between expansion and contraction, the same way pizza dough is made: dough is kneaded, stretched, and folded over and over again, changing direction slightly each time this process is repeated. In cosmology and pizza making, a small change in initial conditions can lead to more complex and complicated results.
There are more Many unanswered questions In this cosmic story about the birth of the universe. Obtaining experimental data and verifying theories of gravity is very difficult, especially in the region of extreme gravitational fields. Thus, in the absence of direct observations, sound mathematical structures become important guides toward plausible and meaningful theories. The Penrose Singularity Theorems and the BKL Conjecture reveal a rich panorama of cosmic evolution that continues to inspire wonder and scientific interest, providing a unique view of the complex dynamics of the universe past, present, and future.
Philipo Lapici He is a Marie Curie Research Fellow (Una4Career). Complutense University of Madrid
Coffee and principles A section dedicated to mathematics and the environment in which it is created, coordinated by the Institute of Mathematical Sciences (ICMAT), in which researchers and members of the center describe the latest developments in the field, sharing meeting points between mathematics and other communities. and remember how cultural expressions and their development signifiers and coffee can be transformed into theorems. The name evokes the Hungarian mathematician Alfred Reny’s definition: “A mathematician is a machine that turns coffee into theorems.”
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