Two-Universe Model

The Premises

Historically, as almost always in physics, everything has revolved around symmetry. By the middle of the last century, the situation with it had become utterly confused. First, cosmologists came to realize the baryon imbalance, one of the main enigmas of our universe [1]. For some reason, at its birth, particles and antiparticles did not annihilate each other: matter persists — in the form, for example, of stars, planets, and us humans — but antimatter simply disappeared somewhere. While deeply perplexing, it was, in fact, the first overt clue.

Then came the second one: scientists discovered the asymmetry of processes that were believed to occur in exactly the same way in matter and antimatter. It was the transformation of quarks within heavy particles: ‘ordinary’ quarks did this a little faster than antiquarks [2]. The phenomenon was given the name “CP violation”, where C stands for “charge conjugation,” which reverses all internal charges such as electric charge, baryon number, lepton number, and strangeness, and P is “parity,” a quantum number that characterizes the conservation of properties under mirror reflection. As an example of a mirror transformation, imagine particles with a different spin — that is, ‘rotating’ in the opposite direction. The mechanism of CP violation was studied in great detail, but its cause remained a complete mystery.

And the third hint lies in a global puzzle that was formulated long ago, back in the late 19th century: the improbably low entropy of our universe. Unlike baryon asymmetry, this subject is hardly ever presented to the general public, though it is no less astonishing. The question is, why, after fourteen billion years of its existence, is the universe still developing somewhere, and we speak so confidently about its arrow of time? In other words, why is the current entropy of our universe small enough to grow and grow further? Mainstream science says: this is because in the beginning, entropy was even smaller — much, much smaller. Well, it’s an elegant piece of reasoning — a less critical reader might believe it and feel reassured. But one can do a calculation – to estimate the value of entropy in the early stages of our universe when it was about four hundred thousand years old. We can capture photons today that were released from the darkness of those times and sent off on their flight — even using an ordinary television antenna – that is the so-called cosmic background radiation. Its distribution indisputably indicates that early entropy — taking into account gravity, of course — was so small that it is simply impossible to imagine. The probability of the emergence of a universe like that is expressed as a fraction with so many zeros after the decimal point that if they were written down on paper, they would fill our Solar System, and there would still be some left over! [3]

Of course, it is not comforting to know that everything has arisen as the result of a miracle. Scientists have tried to find an explanation — the most widely accepted is the so-called anthropic principle: we observe this universe because the emergence of life would have been impossible in a world with a higher initial entropy — it would have been dominated by black holes instead of clusters of stars, the generators of the chemical elements... In other words, many universes are presumably born, but most of them are not suitable for life. Only a minority are, and ours is one of them — otherwise, there would simply be no one to be concerned with this issue.

The reasoning seems logical, but it does not work: some skeptics have calculated the likelihood of a universe like ours emerging among all universes in which life is possible. And this calculation, once again, provides us with a probability represented by a fraction with an unimaginable number of zeros — albeit fewer than the first time, but still sufficient for this miracle to remain the miracle of miracles, compared to which, walking on water and turning it into wine look like perfectly probable events. But forget wine – if we take the enormous number of particles in the Solar System and calculate the probability that they will randomly assemble into this same system with all its planets, this probability will still be far greater than that of observing a universe with such a low initial entropy, taken from all universes suitable for life. In short, we can confidently say that official science has no worthy explanation for this paradox! [4]

Andrei Sakharov's Idea

In the second half of the last century, the distinguished Soviet physicist Andrei Sakharov published a series of papers proposing fundamentally new solutions: the ‘broken’ CP symmetry is only a part of a more global symmetry, and our universe is a part of a larger world. This implies the existence of a ‘twin sister’ universe, composed of its own distinct matter, which has properties different from ours. In particular, its parity and charge are opposite in sign, and its time flows in the other direction. The CP symmetry that has ‘disappeared’ is restored when time is reversed, as full CPT symmetry — where T represents ‘time’. And the baryon imbalance is explained by the fact that the missing part of the matter is contained within the ‘sister’ universe [1,6,7,8]. It is still appropriate to apply the prefix ‘anti’ to this matter, but this is not the antimatter that we get in our laboratories and colliders. It is closer to the concept described by another outstanding physicist, Feynman — he actively developed the idea of antiparticles with opposite parity that move in the opposite direction in time [9].

Janus: Jean-Pierre Petit's Model

Sakharov’s hypothesis solved the problem of the global symmetry of known physical processes and showed where the antipodal matter, which arose simultaneously with ours, went. But it did not reflect the gravitational influence of one matter on the other. This was the view of a nuclear physicist regarding the world of isolated elementary particles — his two universes, having arisen from some common fluctuation, never interacted again and did not ‘know’ anything about each other. The next major advance in the development of the two-universe theory was made by the French physicist Jean-Pierre Petit. The culmination of his forty years of research is the Janus Cosmological Model [10,11,12], which unites Sakharov's concept with Einstein's General Relativity.

Petit placed two Sakharov universes in one space, giving them two distinct ‘sectors’ with different geometric properties. Essentially, they were transformed into a single universe with two components, simultaneously and interdependently deforming spacetime. It can be imagined as follows: if the entire universe system is like a sheet of paper, then the two paired components — ours and its anti-twin — are the two sides on the front and back of it. Together, they ‘push against’ the flexible sheet, forming its curvature — while their matter and energy have different properties, and their time flows in opposite directions. In my book "Cogito Man," a fundamental concept is articulated: the sheet, representing the unified space of two universes, intrinsically contains both its past and its future – from the perspective of an observer situated on either side. Note: this does not mean all the events of our past are repeated in the future of the twin universe – no, it operates under its own physics, distinct from ours, with its own unique events. And, of course, instead of two, there could be any number of universe components — a huge bunch of young shoots sprouting from one singularity... The scenario involving just two is, obviously, the simplest and most convenient for analysis.

Of course, a flat sheet with front and back sides is a highly symbolic visualization. Strictly speaking, these two universes are superimposed, occupying the exact same coordinate space simultaneously and permeating one another like ghosts, rather than existing back-to-back in a higher dimension. More rigorously, the aforementioned “sheet of paper” is the same familiar four-dimensional manifold based on Riemannian geometry on which Einstein’s general theory of relativity operates, which stands as the most accepted, studied, and experimentally confirmed theory of gravity. And it is an extension of Einstein's Special Theory of Relativity in the presence of mass-energy with a noticeable gravitational potential. Mathematically, this is a system of partial differential equations, which can be written in a compact tensor form — as is customary in the scientific literature. This results in the single ‘Einstein equation’ that links the curvature of spacetime and the dynamics of matter. Matter governs the geometry, while that geometry dictates the paths the matter must follow. Spacetime curvature is described by a metric tensor, which is often referred to simply as a “metric.” The metric determines the permissible trajectories for all particles in a given spacetime — or as mathematicians put it, geodesics.

So then, the Janus model does not contradict Einstein’s theory. It augments it — adding, so to speak, the apparently missing half. Janus comprises two interconnected Einstein equations with two different metric tensors. On the above manifold-sheet, two metrics are defined, not just one — that’s the reason for the metaphor of two pages. The study of these dual equations shows that under any boundary conditions, their two metrics set different trajectories of motion — the particles of our universe and those of its ‘twin sister’ move through spacetime without ever intersecting each other. Mathematically, they cannot collide — and, therefore, for example, they do not interact electromagnetically: ‘anti’ photons fly past all of our detectors, including our retinas. Therefore, we can neither ‘feel’ the twin universe with instruments nor ‘see’ its light. But all these particles, these two universes, jointly curve our space; that is, they interact through gravity. And we can estimate this interaction by observing how our matter moves and distributes in a jointly deformed space.

The Mathematical Basis – Connection to Group Theory

The Janus model is not merely a "let's distort everything" exercise. It is a natural extension of Einstein’s theory, which stems from dynamical group theory [13].

Modern physics distinguishes four fundamental interactions. General Relativity describes gravity, and Quantum Field Theory describes the other three. The cornerstone, one might say the basis, of all these theories is Einstein’s Special Theory of Relativity, or rather its principle of the metric structure of spacetime. Roughly speaking, this principle can be formulated as follows: we live in Minkowski space, which, in General Relativity, is generalized to allow for curvature. The metric structure of Minkowski space possesses a symmetry described by the Poincaré group. It can be said that in our spacetime, only those types of motion can exist — that is, only those particles move — that correspond to the allowable transformations of the Poincaré group.

The scientific mainstream focuses on the restricted Poincaré group and its transformations (Lorentz transformations), specifically those that preserve the forward direction of time. In contrast, the full Poincaré group permits transformations involving time reversal (so-called time-reversal Lorentz transformations), but theories that incorporate them, whether in classical or quantum physics, are ruthlessly discarded – excluded from consideration on the grounds that they lack physical meaning. This is not a consequence of mathematics; it’s just a hypothesis, an assumption, a collective agreement if you like.

So, the Janus model, just like Sakharov’s, allows for all transformations of the full Poincaré group, including those corresponding to time reversal. But it’s obvious that the particles of the ‘negative’ or ‘anti-’ sector described by the Poincaré group must have their own properties — if only because the antiquarks of the ‘sister’ universe evolve more slowly than our ordinary quarks. They must move differently; therefore, one equation and a single metric will not suffice. Hence, the two coupled equations with two separate metrics – and their form is derived from the following mathematical fact: time reversal requires a change in the sign of another component of the Poincaré group. Specifically, the one corresponding to the energy of any object moving along the reverse time axis – as follows from a theorem established by the French mathematician Jean-Marie Souriau [14]. Particles of the twin universe, both in Sakharov’s and Janus models, must have negative energy and hence negative mass. This is a fundamental property of spacetime, proven by rigorous mathematics. And it is the negativity of mass-energy that leads to the fact that the solutions of the equations for ‘our’ universe and its ‘pair’ give non-intersecting trajectories of motion — that is, to the fact that the twin universe is gravitationally perceptible but electromagnetically invisible [15].

Note that theories involving negative mass were investigated as early as the middle of the last century – and immediately stumbled upon the well-known ‘runaway paradox’ [16]. Ever since then, it has been considered taboo to mention that a mass or energy may be negative. Yes, if we place particles with positive and negative masses on just one of the ‘sheet sides’ — that is, in a space with a single metric — then they do hurtle into unrestrained acceleration, violating the laws of conservation. According to both Einstein and, in a more simplified manner, Newton, the particles will feel cramped – but if we assign to the negative mass a separate sector, introducing its own metric tensor and placing it on the opposite ‘side,’ then everything falls into place. Both positive and negative masses behave correctly in their own spaces — that is, a massive particle is attracted to a massive particle. There is no runaway anymore — and the antipodal particles repel each other, sensing one another through the boundary that is transparent to gravitation. Roughly speaking, the masses bend the sheet from two sides toward each other, and this helps to explain much of what we observe without introducing artificial entities like dark matter and dark energy [17]. We also note that this repulsion causes ‘positive’ and ‘negative’ matter to aggregate, forming clusters — where one predominates, the other is scarce. For example, the ‘back side of our solar system is likely to have very little ‘negative’ matter — meaning particles with a significant rest mass that could influence the motion of our planets. That is why Einstein’s theory of general relativity with a single metric works so well in our vicinity.

Summary: Key Properties of the Model

Let’s summarize what the Janus model asserts:

– Our universe is ‘one-half’ of a CPT-symmetric spacetime formation.

– The ‘missing’ antimatter is the matter of our ‘sister’ universe; it is our antipode not only in terms of charge but also in parity: some properties of its particles are, so to speak, mirror-reflected.

– Time in the twin universe flows in the opposite direction — and, as dictated by group theory, this means that its particles possess energy and, consequently, mass that is negative relative to ours.

– We do not directly ‘see’ the particles of the twin universe because the trajectories of their motion do not intersect with the trajectories of our particles. But both twin components bend spacetime together.

Let’s also note: inverse directions of time arrows imply opposing changes in entropy. When in our universe the entropy increases, in the other it lessens — moving toward our future, we are climbing into the past of the ‘sister’ universe. Probably, the total entropy of the pair of universes fluctuates within some statistically reasonable range — maybe this is the key to the entropy paradox: why was the initial entropy of our universe so unimaginably low, as evidenced by studies of the cosmic microwave background?

And, of course, the issue of primordial origin cannot be avoided. The question of creation or even a creator. How did our pair of universes come about? When? Out of what?... Alas, there is no answer to all this. We can only say that our ‘sheet’-manifold with its two universal components-‘sides’ exists. One can only guess about the rest, imagining how, from some kind of fluctuation-singularity, a bubble with two surfaces emerged, which are closed onto themselves, perhaps resembling a Möbius strip with a special point. The one that is called the Big Bang — not the most apt name, to be frank.

Our pair of universal components may pass through this point many times — maybe an infinite number of times. What’s there, at that point — an unlimited smallness? Or is it a finite smallness, a kind of narrow bottleneck? A complete standstill of all particles? An alteration of physical constants, including the speed of light?... There is a theory that the speed of light tends toward infinity there — this is an alternative to the currently accepted inflationary model. To me, this sounds more elegant than a contrived inflation... Some theories claim that you can never come to this point; you can only get so close. This is true zero, a vanished boundlessness that has absorbed an infinite amount of everything in an extremely symmetrical state. Its essence cannot be grasped by the mind, yet it will always remain in our thoughts — as the principal challenge.

Experimental Evidence

First, let’s note: due to the dissimilar properties of ordinary matter and its antipode, the structures of our universe and its twin are very different. In ours, we observe galaxies twisted in spirals, their clusters stretched out into filaments, and, most importantly, we have stars, thermonuclear furnaces — they create new elements, from which all of us are formed. In the anti-universe, on the contrary, everything is sad — its huge hot spherical clouds do compress over time, but very, very slowly. They may never cool down to the point where they become ‘anti-stars’, generators of elements heavier than hydrogen and helium. The twin universe, alas, is devoid of intelligent life — at least that’s how it looks to us now from here.

However, this does not prevent it from influencing our common space! Its gigantic globular assemblies confine our matter — at the global, universal level — into filamentary structures. Currently, these ‘anti-clusters’ are gradually compressing — along the arrow of time, inverse to ours. That means, along our arrow of time, they, on the contrary, grow; we move into their past. They grow, pushing our galactic matter apart; our galaxies seem to disperse and drift away from the centers of expanding quasi-spherical formations. And there is no need to invoke any additional "dark energy" to explain this expansion [18]! Does this align with observational data? Yes, and remarkably so. The Janus model shows an excellent fit to the luminosity and distance data from 740 distant type Ia supernovae – widely regarded as the critical test for any cosmological model attempting to explain the universe’s accelerated expansion [21].

A number of other cosmological problems are also addressed elegantly by the Janus model [19,20,21]. Among them:

- The large-scale “web-like” structure of the universe, which the standard ΛCDM (Lambda Cold Dark Matter) model – the prevailing consensus cosmological theory – struggles to explain in detail.

- The repulsive effect of the Dipole Repeller (a structure discovered in January 2017). The recession velocities of galaxies measured near this region contradict ΛCDM predictions but align with the forecasts of Janus.

- The issue of galaxy formation, including their shape and rotation characteristics. First, thanks to the pressure from the surrounding negative mass, galaxies become localized – as if caught in a trap. Second, calculations show that they twist into a spiral – due to a sort of gravitational "friction" between the positive and negative components. Third, the galactic spirals turn out to be flat, and their rotational speeds match observations. And "dark matter" is no longer needed! Instead, it is sufficient to consider two universes interacting gravitationally.

- The parameters of gravitational lensing, which, according to the Janus model, is primarily caused by the influence of the negative mass surrounding our galaxies and galaxy clusters. As a result, the need to invoke mysterious dark matter is once again eliminated.

- The fact that distant galaxies with a strong redshift appear too faint, making them seem like dwarfs. According to the Janus model, the light they emit is defocused as it passes through clouds of negative mass due to an inverse gravitational lensing effect (roughly speaking, it is "squeezed" outward). This explanation once again allows for the abandonment of the dark matter concept.

This is an impressive set of correlations with observed phenomena, which, along with the verified mathematical consistency of the Janus model, makes it a very serious competitor to the standard ΛCDM theory.

The Position of Modern "Official" Science

Here, things are complicated – for the reasons mentioned above: the Janus model is a serious challenge, a powerful alternative to the officially accepted ΛCDM theory. It radically changes our cosmological views – which, understandably, greatly irritates the scientific establishment. After all, we are talking about big money and big scientific egos. About grants, dissertations, jobs, and also – the esteem of colleagues and institutional authority. And what on earth are we supposed to do with all those who have spent the last decade mainly calculating the distribution of dark matter?...

Jean-Pierre Petit devoted more than forty years to developing the Janus model. All these years, he tried to bring his results to “grateful humanity,” which, in response, gleefully disregarded his work. Gleefully – because it felt the power of the majority. The majority is ruthless, especially when it is defending a state of affairs that serves its interests.

Admittedly, the situation is slowly changing. More and more papers are appearing in reputable journals (a detailed bibliography is available here). It is becoming increasingly difficult to simply dismiss the model. Nevertheless, ΛCDM remains the prevailing consensus in the scientific community, while Janus still languishes on the periphery and is viewed with skepticism.

Importantly, no one disputes the fact that the Janus model is mathematically sound and locally compatible with Einstein's General Theory of Relativity (it reduces to GTR in regions dominated by positive mass). There are no grounds for ignoring the model. Nonetheless, they still try to ignore it: mentioning it in official scientific discourse is considered "taboo."

We are observing a typical vicious cycle: achieving recognition requires validation against a broader array of experimental cosmological data, and for that, a larger number of scientists need to be working on the model. As long as it continues to be marginalized from mainstream theoretical circles, its adoption will proceed slowly. But to me, it is obvious: the acceptance of the Janus model is only a matter of time. It will be a repeat of the situation with Benoît Mandelbrot, whom they also refused to acknowledge for a long time with his fractals – and then, suddenly, they "saw the light" and began to shower him with awards and honorary titles...

I would very much like for Jean-Pierre Petit, who is no longer young, to live to witness that moment.