Controlling Chaos through Compactification in Cosmological Models with a Collapsing Phase

We consider the effect of compactification of extra dimensions on the onset of classical chaotic "Mixmaster" behavior during cosmic contraction. Assuming a universe that is well-approximated as a four-dimensional Friedmann-Robertson--Walker model (with negligible Kaluza-Klein excitations) when the contraction phase begins, we identify compactifications that allow a smooth contraction and delay the onset of chaos until arbitrarily close the big crunch. These compactifications are defined by the de Rham cohomology (Betti numbers) and Killing vectors of the compactification manifold. We find compactifications that control chaos in vacuum Einstein gravity, as well as in string theories with N = 1 supersymmetry and M-theory. In models where chaos is controlled in this way, the universe can remain homogeneous and flat until it enters the quantum gravity regime. At this point, the classical equations leading to chaotic behavior can no longer be trusted, and quantum effects may allow a smooth approach to the big crunch and transition into a subsequent expanding phase. Our results may be useful for constructing cosmological models with contracting phases, such as the ekpyrotic/cyclic and pre-big bang models.Comment: 1 figure. v2/v3: minor typos correcte

Exponential thinking for early understanding of the scale of the universe

In the last century, science has given us knowledge of the smallest things in the universe through to the vast distances of the visible universe. Science also gives us the ways to see the scale, with the modern technologies on which our lives depend. Education should respond to these revolutionary changes in human perception. However, for many people big and small numbers are just words with very little meaning (Resnick et al., 2017).  A good way to help us gain meaning is to find a simple way to operate with huge and tiny numbers using the powers of ten as a notational tool. There is some evidence, that young children have an intrinsic logarithmic ability (Opfer et al., 2010). To exploit these abilities, we present on results of a program that introduces large number concepts through engaging activities. We aim to make the mathematics needed for describing physical reality more intuitive, more relevant and less dependent on rote learning. This work is part of a broader project called Einstein-First that aims to introduce Einsteinian concepts throughout school education (https://www.einsteinianphysics.com). We use powers of two as a stepping stone to develop language and concepts for powers of ten.  The Powers of two program has been tested with year 3-4 students and Powers of ten with year 5-6 students. Lessons in the 8 hours programs are built around activities following four general principles: a) learning from group activities, b) using models and games to explore concepts, c) using Google searches for data gathering where appropriate, and d) learning through play-acting. We present some of the activities. One successful activity was the Powers of the Universe book, created by students. Each page is a power of ten. Numbers that describe all the known physical quantities in the Universe can be fitted in this 120-page logarithmic book, in which all quantities are expressed in SI units. The program demonstrated significant outcomes regarding understanding scale of the Universe, estimation of big and small numbers, using powers of ten as a tool for calculation and reasoning about numbers. The results of pilot trials from pre-test and post-test comparisons indicate that nearly 100% of students were able to use powers of two for describing numbers in processes such as bacteria splitting or numbers of ancestors. 78% of students preferred to use powers of ten notation over multiple zeros for big and small numbers. 98% of students widened their knowledge about the scale of the Universe. Evidence from teacher and student interviews indicates student enjoyment and appreciation of the relevance and capacity of students to extend their understanding. REFERENCES Opfer. J. E., Thompson, C. A., & Furlong, E. E. (2010). Early development of spatial-numeric associations: evidence from spatial and quantitative performance of preschooler. Developmental Science, 5, 761-771. Resnick, I., Newcombe, N., & Shipley, T. (2017). Dealing with big numbers: Representation and understanding of magnitudes Outside of Human experience. Cognitive science, 41, 1020-1041

Big Bang Nucleosynthesis with Independent Neutrino Distribution Functions

We have performed new Big Bang Nucleosynthesis calculations which employ arbitrarily-specified, time-dependent neutrino and antineutrino distribution functions for each of up to four neutrino flavors. We self-consistently couple these distributions to the thermodynamics, the expansion rate and scale factor-time/temperature relationship, as well as to all relevant weak, electromagnetic, and strong nuclear reaction processes in the early universe. With this approach, we can treat any scenario in which neutrino or antineutrino spectral distortion might arise. These scenarios might include, for example, decaying particles, active-sterile neutrino oscillations, and active-active neutrino oscillations in the presence of significant lepton numbers. Our calculations allow lepton numbers and sterile neutrinos to be constrained with observationally-determined primordial helium and deuterium abundances. We have modified a standard BBN code to perform these calculations and have made it available to the community.Comment: 9 pages, 5 figure

Población, progreso técnico y economía

Economists are learning the truth as old as the Bible that population growth is good for progress. This article discusses how the growth of population stimulates technical progress while stagnation limits the numbers born of creative persons who are the real motors of growth. The Universe still has many secrets to reveal so it is a big mistake to penalize fiscally and culturally large families. The Welfare State gives misleading answers as to what should be done in the face of the ageing of society

Joining General Relativity to Particles Physics through Complex Numbers and Autism

The cognitive impairment of autistics and the Tau Identity in the plane of complex numbers suggest that if the accelerating expansion of our universe and the anti-universe succeeded a coasting expansion 8.8 billion years after the Big Bang, an accelerating contraction will start in 3.8 billion years. Mirroring the expansion phase, a coasting contraction of the two universes will come up in 12.6 billion years. The end of the fourth section of 8.8 billion years will host two Big Crunches, two White Holes, and a new Big Bounce. The z-plane and autism can also help us a) solve the “cosmological constant problem”; b) join general relativity to particle physics; c) cross science with the arts and religion; d) retain the search for truth, beauty, and goodness by our descendants; and e) seize the message of progress hidden in the Ark of the Covenant, the Great Pyramid, and Giza’s Sphinx: Any selfish brain hides a selfless heart

The Prime Numbers

A prime number is a natural number that has Just two divisors: one and itself. From antiquity until our time, scientists are researching mathematical reasoning to understand the prime numbers; eminent scholars had worked on this field before it is abandoned. Mathematicians considered the prime numbers like « building blocs in building natural numbers » and the field of mathematics the most difficult. Everything is about numbers, everything is about measure, The understanding of the natural numbers and more general the understanding of the numbers depend on the understanding of the prime numbers. This understanding of the prime will gives us greater ease to understand the other sciences. The prime numbers play a very important role for securing information technology hence promotion of the NTIC, Every year, there is a price for persons who will discover the biggest prime “it‟s the hunt for the big prime” This first part of this article about the prime numbers has taken a weight off the scientists „s shoulders by highlighting the universe of the prime numbers and has bring the problem of the prime numbers to an end. The mathematical formulas set out in this article allow us to determine all the biggest prime numbers compared to the capacity of our machines

SERIES " H154M " AS A UNIT AREA OF THE REGION BETWEEN THE LINES AND CURVES

This world events consciously or not realize everything has a pattern, until the events of the universe according to the Big Bang theory of the solar system which makes so regular in the rotation . The author would like to create a results curve area between the quadratic function y = kx2 and line y = ka2 using GeoGebra application version 4.2 . This paper can provide a series that is no less interesting with Fourier series , so that will add new material about the series can be calculated with sigma notation . In addition, the ranks of the unique natural numbers of extensive changes in established areas. Finally, this paper provides analytical and geometric proof of the vast area in between the lines and curves that give the area is formed by y = ka dan kurva y = kx2 , x-axis , line x = dan x = - make a series of numbers for k = 1 and a original numbers. The author calls the series “H154M