What was the size of the universe at big bang?

At the big bang all the energy of the universe existed within a small ball. What was the size of the ball for the solution where the ball was not rotating at high speed? Mathematicians like to say that the universe was the size of a pinpoint. From an engineering viewpoint that is not a practical answer. Yet in one respect it may appear that some part of the ball was very tiny. Thus a more likely solution is that at big bang we have a Doppler Spherical solution.

For linear Doppler space time, the mass in the front of a moving object is very large and the ruler is tiny. Thus as we head toward light speed C, the frontal length of an object heads toward zero but the rearward length heads toward infinity. Thus the gravitational length as per Einstein is

Lg =Lo[1-(v/c)2]0.5

The inertial Doppler length to the front is Lg C/(C+V)

The inertial Doppler length to the rear is Lg C/(C-V)

In effect an object moving near the speed of light C has a tiny frontal dimension and a long tail. This is for a linear solution but the spherical solution will be similar although the math is much more complex.

At big bang, the spherical Doppler length in the front at the pinpoint wave tiny whereas to the rear the wave was quite large. The energy of the pinpoint was huge but the size of the universe was fairly large. The concentration of all the energy at the pinpoint converted spherical energy flowing into the point, which had linear spherical momentum of the entire sphere, into a huge amount of linear and orbital energy. At the same time the entire wave of energy was flowing into the pinpoint. Thus the pure spherical energy with an axial spherical flow continued into the pinpoint.

The explosion produced mass out of energy. This expanded quickly but the flow from the spherical field was still going on. Thus there was still a lot of spherical energy flowing into the pinpoint and then flowing out of it thereby expanding the universe rapidly.

It is possible that the spherical tail was huge. It is possible that the pre-universe in spherical energy was billions of light years in size. Presently we are 13.78 billion light years from the big bang center but the entire universe in dark spherical energy is 27.56 from the absolute center.

In the future mathematicians will study spherical space time and orbital space time in much greater detail than the engineering solution presented here. Then they will have a better picture of what the size of the universe was at big bang.

We then have two possibilities. The entire universe could have been a simple ball of energy at big bang or it could have been a dynamic Doppler flow of mass/energy at a pinpoint which exploded and in which the energy kept flowing into the pinpoint pushing the material world further outward. Any other ideas?