The Universities of Berlin and Leipzig hosted him, and he was able to learn from Albert Einstein, Max Planck, Erwin Schrödinger, and Werner Heisenberg.

"[4]With Georges Lemaître, a Belgian physicist and Catholic priest, Vallarta theoretically predicted that the intensity of cosmic rays should vary with latitude because these charged particles are interacting with the Earth's magnetic field.

They also worked on a theory of primary cosmic radiation and applied it to their investigations of the Sun's magnetic field and the effects of the galaxy's rotation.

While at UNAM, he worked with Luis Alvarez and Arthur Compton on experiments to show that cosmic rays were composed of protons.

He served on and led a number of commissions for the Mexican government, mostly relating to science policy, and represented his country at numerous international conferences.