Dark Universe: just an idea

I was a physicist. I said "was" since I am no more. When I got my degree, in fact, I joined IBM and began a completely different career in the information technology sector. Since being a physicist is a vocation, anyway, not a job, I continued to get in touch with the most recent discoveries of scientific community by reading various specialized magazines and journals. At the beginning I was reading only articles about high energies particles, because I worked in that area at CERN, SLAC, and DESY, but later on I began more and more to read mostly everything, from astronomy to anthropology, from archeology to psychology. By the way, I am subscribed to "Le Scienze", the Italian version of "Scientific American", since 1978.

I was a physicist, but not a theoretical one: I was a researcher. So, even if I had good math foundations, I was more oriented to observation and testing, rather than filling sheets of paper by formulas. Anyway, after 22 years, my ability to play with integrals and derivatives is dramatically decreased to pre-scholar levels. So, I have no more the elements to represents ideas and hypotheses by using mathematics.

One of the subjects I am very interested too in this period is cosmology. In particular how the Universe is shaped and why, its behaviour, its structure, everything related to the Cosmos. As you probably know, two intriguing areas that are currently investigated by scientists are about the existence of dark energy and dark matter.

Dark energy is a hypothetical form of energy that permeates all of space and tends to increase the rate of expansion of the universe. According to theoreticians, it accounts for 74% of the total mass-energy of the universe.

On the other hand, dark matter is hypothetical matter that does not interact with the electromagnetic force, but whose presence can be inferred from gravitational effects on visible matter. According to theoreticians, it accounts for 22% of the total mass-energy of the universe.

So, 96% of Cosmos is dark, that is, made of matter and energy that hardly interact with the matter and energy that for centuries we thought were the components of our Universe, the visible one.

Is there a relationship between dark energy and dark matter? Is there a model of such a hidden universe? Well, here is why I am writing this article. I had an idea, or if you prefer, an intuition. As I said, I am not able to elaborate it to make a real scientific theory. It is just a flash. So I had two possibilities: forget it, or expose it. The first one presents no risk at all, but generates no value too. The second one would lay myself open to criticism by experts, even bitter ones. In the worst of cases my idea could be considered insubstantial, maybe even ridiculous.

So, what is to be done? No doubt: I decided to run the risk and to publish my intuition. In the worst of cases it will be ignored, but it is also possible that it might become the starting point for further considerations. So here it is.

As you know, the universe is a space-time continuum which is curved by the presence of matter. You can imagine it as a wide elastic membrane on which balls of various masses are placed. The larger is the mass, the stronger is the deformation of the membrane. The amount of deformation is called strain. If a ball moves on that membrane its path will depend on the shape of the surface. Passing close to an heavy mass, the small ball will deviate towards it, like in a whirlpool, giving the appearance to be attracted by the other mass. That is gravity.

Now, what if that membrane is not just a mass-less and energy-less geometrical element? What if the space itself has a mass? And what if we could consider it really as an elastic membrane, a physical one, with a linear relationship between stress and strain? For a spring, the relationship between strain and applied force, is ruled by the Hooke’s law, that is,

F = -kx

where x is the displacement, F is really the force exerted by the spring – notice the negative sign – and k is the spring constant. Therefore, the larger is the spring constant, the more elastic is the spring.

In a three-dimensional space, the law is a little bit more complicated, since the proportionality constant between stress and strain is a 4th order tensor, but the principle is the same. The strain tensor is a matrix of 81 elements based on 21 independent elastic coefficient. Furthermore, if the membrane is made of an isotropic materials, whose properties are independent of direction in space – and we can assume that space continuum is isotropic – the strain tensor is a symmetric one. In such a case all coefficient may depend only on two scalar constants: E, called modulus of elasticity, and ν, known as Poisson’s ratio.

When we deform a spring, we store in it a potential energy that is released when the spring is relieved. That amount of energy is given by

V = ½ kx2

This is true for the membrane too, even if the formula is much more complicated. In such a case the potential energy will depend on E and ν, of course. If an heavy ball is removed from the surface, in fact, assuming that the membrane has no hysteresis, that is, exhibits no memory of deformation, the surface will take again the original shape.

My first hypothesis is that the dark energy is the total amount of potential energy associated to the strain of space generated by all the visible matter. It practically would depend on the overall visible mass of universe and the elasticity coefficients of space.

Let us go back to the membrane representing the space, now. Let us assume it has a thickness and a uniform density, that is, let us suppose that space has a finite mass itself. Let us also assume that when a mass warps the space, the thickness of membrane decreases so that the total mass of deformed zone does not change. Since gravity is determined by the strain, the mass of the membrane itself has no effect on the individual balls, but has to be considered when we think the Universe as a whole.

So, my second hypothesis is that dark matter is due to the membrane itself, that is, to the mass of space. It is a constant, because while the Universe is expanding, the space becomes thinner and thinner, that is, the membrane density uniformly decreases. By the way, we know that Universe is not infinite. So it is not the space mass.

But what happens to a real membrane if we stretch it? Well, the strain caused by balls decreases too but also the coefficients of elasticity would change. So it is very possible that the density of dark energy will remain the same. This is the typical case where intuition fails and I would have to perform some calculation.

And why dark energy is responsible for the acceleration of expansion of Universe? Why does it oppose to gravity? According to current theories, a positive density of dark energy generates a negative pressure, and therefore accelerate the expansion of Universe.

In the model I am proposing, the dark energy is associated to the potential energy related to the deformation due to visible masses. Imagine now that our membrane is really a balloon. What is happening to that potential energy as the balloon is inflated? The membrane is getting thinner and thinner, I said. Locally it is also getting flatter and flatter and the tension reduces the strain, that is, the deformation due to a certain mass is decreased. In theory we could say that gravity force is weakening. But if gravity is weakening, the clusters of visible matters tend to spread. Maybe the structure of the space itself is weakening. So, whatever caused the expansion of Universe is finding less and less resistance to expansion. Is it this an explanation? I do not know. At this point, it is necessary to define a mathematical model based on my intuition and see if it works or not.

If anybody is willing to work on this, he/she is welcome.