Article 16:
Calculating the Acceleration of the Expansion of the Universe

This is a supplementary article. To go to the main introductory article about Stationary Energy Theory, and its links to other supplementary articles, please click here.

Stationary Energy Theory’s equation for gravity gives a rate of acceleration for the expansion of the Universe that is close to the observed value

To try to get a rough estimate of what this theory predicts the acceleration of the expansion of the Universe is, we will first use Equation 34, and also this theory's basic equation for gravity, Equation 32, (both derived in Article 15) to calculate how much gravitational repulsion there is between two adjacent “flat spot swirls.”

The Pisces-Cetus Supercluster Complex, that our Local Supercluster is a part of, measures about a billion light years wide by about 150 million light years deep, and has a mass of 10¹⁸ suns. According to this theory this supercluster complex must exist within one flat spot swirl, since there are no voids between any parts of it. We will assume the average size of flat spot swirls is about the same as this complex but a little less wide and more deep at about 800 million light years wide and 200 million light years deep, and that these complexes are separated by voids about as wide as the flat spot swirls are wide, placing them at an average of about 1.6 billion light year centers. Looking at the sizes of some of the Supercluster Complexes, which are up to 10 billion light years long (3 giga parsecs), this fairly high figure of 1.6 billion light-year average separation seems justified. We will also assume the same mass as the Pisces-Cetus Complex of 1.0 x 10¹⁸ suns, the equivalent of about 1000 superclusters the size of our small local supercluster in each “flat spot swirl.” We will assume these dimensions for each of our flat spot swirls to calculate how much they would accelerate away from each other. We’ll then sum the accelerations across one radian of the Universe to get a “ballpark” figure for the acceleration of the expansion of the Universe. I’m sure a more rigorous analysis would be possible, but this is a start.

Equation 34, one of the forms of Stationary Energy Theory’s formula for gravity, is:

F_g = Gm₂(m₁ – (0.77358d²/f))/d²

As previously discussed, the flatness is f = 1 because the masses are on separate flat spot swirls. Also, since m₂ = m₁ and F = ma, a = F/m and so: a = F/m₂. So:

a = Gm₂(m₂ – (0.77358d²))/m₂d² or:

a = G(m₂ – (0.77358d²))/d²

Converting m₂ from suns to kilograms we get: m₂ = 1.0 x 10¹⁸ x 1.98843 x 10³⁰ = 1.9884 x 10⁴⁸ kg

Converting d from light years to meters we get: d = 1.6 x 10⁹ x 9.461 x 10¹⁵ = 1.5138 x 10²⁵ m

So:

a = 6.6739 x 10^-11(1.9884 x 10⁴⁸ - ((0.77358 x (1.5138 x 10²⁵)²))/(1.5138 x 10²⁵)²

= -5.10 x 10^-11 m/s/s

Now we will calculate the same thing using the following basic equation for gravity of this theory:

F_g = ½m₂c²(α – σ)/d    .           .           .           .           .           .           .           (32)

where:
α = m₁ x 1.485143333754 x 10^-27/d    .           .           .           .           .           (30)

σ = d x 1.14888 x 10^-27/f    .           .           .           .           .           .           (33)

and f = 1

This requires us to calculate the values of α and σ and plug them into the basic equation, so we get:

α = 1.9884 × 10⁴⁸ × 1.48513333754 × 10^-27 / 1.5138 × 10²⁵ = 0.000195076

σ = 1.5138 × 10²⁵ × 1.14888 × 10^-27 / 1 = 0.01739

So α - σ = -0.01720

To get the acceleration due to gravity, we use Newton's equation a = F/m to modify the basic equation for gravity to get a = ½mc²(α - σ)/md, which, cancelling out the 'm's, gives: a = ½c²(α - σ)/d

Evaluating this we get:

a = 0.5 × (299,792,458)² × (-0.01720) / 1.5138 × 10²⁵ = -5.10 × ^-11 m/s/s

This is the same value as the one-step Equation 34 gave us. The minus sign means this is a repulsive acceleration rather than an attractive one. This is however, just the acceleration between two repelling flat spot swirls (without any other flat spot swirls around them pressing back on them) about two degrees apart in the 4-D sphere of the Universe. To get the acceleration of the Universe, we need the accumulated acceleration across a whole radian of the Universe, which will be 57.3/2 = 28.65 times higher. To be more precise, the radius of the universe is 46 billion light years, and we are assuming the complexes are 1.6 billion light years apart, so there will be 46/1.6 = 28.75 of them per radian. We also need to account for the fact that each of the flat spot swirls will be “pushing back” on each other as well, and will not be free to just accelerate into nothing. This cuts the total acceleration in half. This means the acceleration of the expansion of the Universe would be:

a = (28.75/2) x 5.10 x 10^-11 m/s/s, so:

a_calculated = 7.34 x 10^-10 m/s/s.

How does this compare with what astronomers have observed? The figure for the observed acceleration I have seen quoted is: 73.8 ± 2.4 km/s/Mpc (Mpc = million parsecs)

= 73.8 km/s/3.26 x 10⁶ ly. Since looking out a light year in space is the equivalent of looking back in time one year, this gives an actual acceleration of:

73.8 km/s/3.26 x 10⁶ years = (73.8 ± 2.4 x 1,000)/(3.26 x 1,000,000 x 365.25 x 24 x 3,600) m/s/s

a_observed = 7.17 ± 0.23 x 10^-10 m/s/s.

As you can see, the calculated value is within the error limits of the observed value! What are the chances of two totally different calculations, one from this theory and the other from an observed value, giving this close to the same answer if this theory's equation for gravity doesn't accurately describe how gravitation actually works in our universe?

Of course, considering all the assumptions and approximations made in calculating what the acceleration should be according to this theory, it can only be, as we started by saying, a ballpark value. Considering this, it is rather a coincidence that it agrees so closely with the observed value. For instance, the exact average distance apart of flat spot swirls is not known, and this has a big effect on the result due to the number of them fitting into one radian. The average distance value we have used of 1.6 billion light years would have to be between 1.59 and 1.69 billion light years at the mass we used to give an acceleration result within the error limits of the observed value. However, we did calculate earlier that flat spot swirls would average about 800 million ly in diameter, and if the expansion of the Universe has separated them by that much again, then the 1.6 billion ly separation seems quite reasonable. As for the mass of the superclusters in each flat spot, there is only a minimal variation between any reasonable values. Any mass between 20% of and 5.5 times the mass we used will give acceleration results within the error limits of the observed value.

From the above, it can be seen that this theory predicts that, if the measured rate of the acceleration of the expansion of the universe holds to its current value, the average distance between complexes of superclusters of galaxies will be turn out to be between about 1.6 and 1.7 billion light years. It is already clear this is, at least, close to what the figure must be.

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