Cosmic Rays

At some point, around 1895, Tesla started investigating all kinds of radiation and in particular he seemed to be interested in cosmic rays.

Primary Cosmic Rays
When an electrode is subjected to a high voltage (either positive or negative) it will develop a tendency to discharge to anything that comes close to it. But what would happen if there is nothing to discharge to, as in a vast vacuum space? According to Tesla, a pressure will build up until the point where it will rip tiny particles off of atoms which will then be propelled with great force and achieve extremely high velocities, many times higher than the speed of light.
Due to their excessively high velocities, these particles are very difficult to detect.
According to Tesla, all stars are electrodes at an extremely high electrical (positive) potential and are therefore emitting this kind of particle rays. So, no matter where you are in the universe, you are always bombarded with these rays from every direction.
Most of these particles, however, will pass through matter unhindered. Only a very small portion will interact and cause radioactive decay of large nuclei.

Secondary Cosmic Rays
When interacting with interstellar dust or planets, these primary cosmic rays can produce secondary cosmic rays which are of an electromagnetic nature. This effect is known as "bremsstrahlung".
This is Tesla's explanation for what we know today as cosmic background radiation and assume to be the remnants of the "Big Bang".

As the Big Bang is an utterly impossible theory, I would say Tesla's explanation for this observed CBR is much more plausible.
Then again, any theory is more plausible than an utterly impossible one.

Experimental evidence
Tesla writes that he was able to reproduce primary cosmic rays with his coils that could generate over 4 million volts. I have tried the same and found that it was very difficult to shield the vacuum tube and protect it against these high voltages. I have not found a way to safely submit my reproduction of Tesla's vacuum tube to potentials of 1 million volts.
It is obvious however, that the surroundings of the tube will act as second electrode and pull electrons from the aluminium electrode inside the tube. These electrons are accelerated and will hit the glass of the tube where they produce x-rays.
This looks like what Tesla describes but I think that his primary cosmic rays consist of particles smaller than an electron.