A New Mathematical Dark Matter Discovery

While fooling around with some gravity equations, I discovered some intriguing results. First, let's define the variables we will use:

Dark matter and dark energy are currently treated as two different entities, but the diagram below shows they could be two sides of the same coin:

The above diagram shows galaxies (circles) being pushed apart by dark energy (arrows). But notice how the dark-energy arrows are pushing in on the center galaxy. Any galaxy in the universe could be deemed the center and experience inward pressure from dark energy. Of course there is also bound to be outward pressure. If the two are equal and opposite, nothing interesting happens. But if the two are unequal, things get mighty interesting!

The next diagram takes a rectangular volume of a spiral galaxy and some surrounding space. The volume is divided into section A, a volume of space, and section B which includes space and baryonic matter (stars, gases, etc.). Each section has a length of distance r. The arrows represent the directions of expanding dark energy.

Since the galaxy is rotating, it has angular momentum q. The angle of this momentum is approximately 90 degrees relative to r. In the next slide we zoom in closer and see more details:

Section A has dark energy, mass m and little or no baryonic matter m' to slow down the expansion momentum (p) along r. Section B has baryonic matter m' and mass m. To conserve energy, outgoing momentum p' is less than incoming momentum p. Mass m normally is attributed to dark matter, but below we redefine it and define the other variables in more detail:

Equation 1 describes the total momentum at the cosmological horizon(light speed * vacuum mass or mass equivalent). Equation 2 shows that dark energy momentum is a function of distance r and Hubble's constant. As r increases, the speed of expansion increases; i.e., dark energy is more kinetic relative to the observer. So momentum p increases. Equation three shows that the converse is true: when r is relatively short, expansion velocity is slower. When r is zero, expansion velocity is zero. In that case dark energy is less kinetic and behaves more like mass or potential energy. So variable m becomes dark-energy rest mass (or something equivalent if it is mass-less). Equation 4 shows variable p' is equal to itself plus an angular momentum q term.

At equation 5 (Einstein's energy equation) below, the left side represents section A, the right--section B. Both sections have distance r which is short compared to the distance to the cosmological horizon. Applying equations 2 and 3 we get a dark energy that has nearly zero momentum (p) and nearly 100% mass (m). We start with the assumption that sections A and B are filled with nothing but dark energy.

At equation 6 we add some baryonic matter (m') and angular momentum (q) to the right side. Doing so reduces dark-energy momentum from p to p'. (Caveat: If momentum is too small, then dark-energy mass is reduced.) Equations 7 and 8 show that, at 90 degrees and on average, the momentum q term is zero. That leaves us with equation 9.

And from equation 9 we can derive equation 22:

You will note equation 22 has an extra mass term which is necessary if you are measuring the gravity of a galaxy. If you measure gravity on solar and planetary scales, the extra mass term becomes insignificant--the equation reduces to Newton's law of gravitation. Also, at the cosmological horizon, the extra term vanishes. Equations 23 and 24 demonstrate these contingencies.

Now let's have some fun! Below are some typical numbers you will find on the web. However, we are going to assume there is no dark matter and substitute dark energy.

We want to calculate percentages and proportions, so we divide the above numbers by 4. That way baryonic matter is equal to 1. We divide dark-energy rest mass again by 2, so sections A and B can have equal portions. We plug and chug below:

As you can see, the result is fairly consistent with dark matter estimates. Now, let's do our galaxy. Here's some more numbers pulled off the web:

We plug and chug again:

According to our calculations, our galaxy consists of only 12% baryonic matter. The extra mass is called dark matter, but at least some of it could be dark-energy rest mass (or mass equivalent).