The book "The End of Everything - Astrophysically Speaking" (2020) is written by the American astrophysicist Katie Mack who holds the Hawking Chair in Cosmology and Science Communication at the Perimeter Institute in Ontario, Canada. In her book, Mack describes five very dark scenarios for the end of the universe's existence. They are called Big Crunch, Big Freeze or Heat Death, Big Rip or Big Tear, Big Slurp or Vacuum Decay, and Big Bounce. While the first two have been discussed by several generations of astrophysicists, the latter three are all developed after the millennium shift and relate to dark energy interpretations. However, a less dark Phase Shift scenario could have been added. It is hardly more speculative than the described scenarios or more difficult to grasp for people in general. In the fall of the International Astronomy Year 2009, a description was published by me in a Swedish journal for mathematicians.

Katie Mack says that she was inspired already at school age by the disabled cosmologist Stephen Hawking's ability to arouse interest in cosmology. As for myself, his funeral in 2018 motivated me to write a tribute.* Hawking actually turned fifty years older than doctors thought possible and talked often about the goal of his life - to understand why the universe behaves as it does and what lies behind its existence. Like Albert Einstein, he spent time on questions where the answers are most difficult to find. With the privilege of age (four years older than Hawking became), I will here make an attempt to answer the above questions before describing my Phase Shift scenario for the end of the universe.

What all physical phenomena in the universe have in common is that they can be described with the language of mathematics and simulated with the help of mathematical machines which are also known to be able to simulate each other. It is therefore possible to develop explanatory models for the behavior of the universe from knowledge about the functioning of mathematical machines in general and of quantum computing in particular.

The reality behind the existence of the universe is, in my humble opinion, the infinite lifetime per se of an elementary particle of gravitation having a rest mass and being a counterpart to the electron, the elementary particle of electromagnetism. A common wave nature of the two particles is a possibility which has motivated me to propose a wave theory of time, WTT. One outcome is the Phase Shift scenario for the end of the universe. In a mathematical model of time itself, a number in the order of twenty powers of ten results for a wave period measured in seconds and linked to the elementary particle of gravitation as well as for a wave frequency measured in periods per second and linked to the electron (originally proposed by Louis de Broglie).

For the existence of the universe as regards just the present half period in an endless succession of generations where history is repeated to a varying degree, WTT predicts an end within 62 billion years and a cosmic expansion peak within 24 billion years. No errors have been found in my calculation of these numbers even though challenges were made by me and published by the Swedish Mathematical Society in follow-ups to the above-mentioned article published in the fall of the International Year of Astronomy 2009.**

Nobel laureate Roger Penrose wrote to me during the work on his book "Cycles of Time" that he lacked time to discuss my proposal about "Waves of Time" and also reasons to take his time, which in retrospect was not difficult to understand. About the content of his book, it can be mentioned that the end of the universe will, according to him, be very protracted with a probable resurrection in a future random process. The well-known cosmologist Andrei Linde also lacked time to discuss my proposal. However, it is of interest to note that he and his wife Renata Kallosh have published a study on such a quick end to the expansion of the universe as calculated by me without their dark energy assumptions.***

The Phase Shift scenario for the end of the universe is mathematically elegant. As compared to the known scenarios, it is hardly more speculative to discuss a continuous-wave model linking gravitation to a sinusoidally varying measure of time changing direction in the phase shift between subsequent half periods. Applying the very same continuous-wave model to the electron and the positron, they are assigned intrinsic time arrows that are in opposite phases with each other. The strength ratio between the electromagnetic force and the gravitational force follows from the ratio between their wave frequencies.  

*   http://www.swe-math-soc.se/pdf/SMSbull1805.pdf (8)
 **  http://www.swe-math-soc.se/pdf/utskick0910.pdf (69-73)
 *** https://arxiv.org/abs/astro-ph/0301087