After the universe changes from expansion to contraction, all matter will eventually squeeze together, commonly known as the “big squeeze”, which is equivalent to the reverse big bang. But in the conformal cycle universe, the big squeeze does not happen. On the contrary, the history of the universe will gradually diminish and matter will become thinner and thinner. Next, we need to explain what is conformal. With conformal, we can cross from the end of eternity where matter becomes extremely thin to the beginning of the next eternity.

Conformal scaling refers to contraction or expansion while keeping all relative angles unchanged. Using conformal scaling, you can convert things with infinite volume into finite volume.

Take a simple example. Suppose there is an infinite two-dimensional plane and a hemisphere. Draw a line from every point on this infinite plane and connect it with the center of the ball. Then project the intersection point of each line and the sphere onto the lower disc. In this way, you project every point on the infinite plane onto the disk below the sphere.

In Penrose’s hypothesis, scaling is not only space, but space-time. Time and space experience scaling together, and the end of one universe connects with the beginning of the next. From a mathematical point of view, this can be done. But why do we need this scaling? What does this have to do with physics?

Penrose is trying to solve a big unsolved mystery in contemporary universe theory, that is, the second law of thermodynamics - entropy increase. We all know that entropy will increase, but since it will increase, it means that the entropy in the past is smaller than that in the present. Indeed, the entropy of the universe must have been very small at the beginning, otherwise we can’t explain the phenomenon we see now. The “low entropy of the early universe” is generally called the “past hypothesis”, which was put forward by the philosopher David Alberta.

The current theory matches the “past hypothesis” very well. But it would be better if this is not a hypothesis, but a conclusion that can be deduced directly from a theory.

In order to solve this problem, Penrose first found a method to quantify the entropy in the gravitational field. As early as the 1970s, he proposed that entropy is hidden in Weill curvature tensor. In short, Weill curvature tensor is a part of all spatiotemporal curvature tensors. Penrose pointed out that the will curvature tensor should be very small in the universe at first. In this way, the entropy at the beginning of the universe will be very small, and the “past hypothesis” makes sense. He called this “will curvature hypothesis”.

Therefore, compared with the vague and general “past hypothesis”, we now have a more mathematically accurate “will curvature hypothesis”. Like entropy, Weill curvature is small at first, and then increases gradually with the age of the universe, which is synchronized with the formation of large celestial structures such as stars and galaxies.

There is another question: how to make the will curvature smaller. This is when conformal scaling comes into play. At the end of a universe, the will curvature must be large, which needs to be reduced by scaling in order to be ready for the beginning of the new universe.

This answers the question “why zoom”. Next, we need to find out the role of physics in it. Scaling works mathematically because there is no point in discussing time in a conformal universe. It’s like discussing whether the Koch snowflake is big or small. The fractal will repeat indefinitely, so it’s impossible to judge its size. In a conformal cyclic universe, time is the same at the end of each universe.

However, only when the universe is about to end can conformal invariance be achieved, can expansion and contraction and head to tail connection be realized. However, this is not certain. The universe contains many massive particles, which do not have conformal invariance, because particles are also waves. Massive particles are waves with specific wavelengths, whose wavelengths are called Compton wavelengths, which are inversely proportional to mass. These particles have a special scale, so they will not remain conformal when scaling the scale of the universe.

However, the mass of elementary particles comes from the Higgs field. So if we can manage to get rid of the Higgs field at the end of the universe, these particles can obtain conformal invariance and everything can be established. Or there are other ways to remove these massive particles. However, since we don’t know what will happen at the end of the universe, it’s uncertain that there will be a way to the front of the mountain. These tangles will be solved by then.

But we can’t verify what will happen in 100 billion years, so how can we verify Penrose’s cyclic cosmology? Interestingly, this conformal scaling does not erase all the details of the previous “eternity”. Gravitational waves can be preserved because their scale is different from Weill curvature. The gravitational wave of the previous immortality will affect the movement mode of matter after the next immortality big bang, thus forming the cosmic microwave background radiation, leaving a very special “pattern”.

Penrose first suggested that we should look for circular patterns. These ring patterns come from the collision of supermassive black holes in the last eternal world, and the collision of supermassive black holes is the most intense event we can imagine, so it should be able to produce a large number of gravitational waves. However, the search for these signals has still yielded nothing.

He later found a better basis for observation, called “Hawking point”. The supermassive black hole in the last immortality will gradually evaporate, leaving a mass of Hawking radiation that will gradually expand throughout the universe. But at the end of this immortality, these Hawking radiation can be reunited into a ball by scaling, and then continue to the next immortality. It becomes a small point in the cosmic microwave background, surrounded by several rings.

These Hawking points do exist. In addition to Penrose and colleagues, others have also found their presence in the cosmic microwave background. However, some cosmologists have suggested that the Hawking point also exists in the most popular early universe model, the inflation model. Therefore, although this prediction is not wrong, it can not be regarded as the uniqueness of Penrose’s model different from other models.

Penrose also pointed out that in order to achieve conformal contraction, a new field needs to be introduced to produce a new particle. He called this particle “erebon”, which was taken from the name of the dark god “erebos”. The particle may form dark matter. Its mass is almost the same as Planck’s mass, which is higher than that of celestial objects