Tom said
The pressure at the center of the Earth is immense--somewhere between 3 and 4 million times the pressure of the atmosphere at the Earth's surface. To assume that a small loss in atmospheric pressure, measure in a few pounds per cubic inch, would cause any measurable decrease in the gravitational load that creates this core pressure is ludicrous. The idea that macroscopic gas could exist at this pressure, at almost ANY temperature, is ludicrous.

I agree that the pressure at the center of the Earth is immense, and I assume that the pressure is created by the amount of mass that surrounds that center. Also I assume that the atmosphere is composed of mass, further assumption is that the mass that makes up the Earth, both the core and the mantle, is somewhat compressible, the compressibility will be greater if there are spaces or bubbles of gas either microscopic, macroscopic or anything in between.

As for the "few pounds per cubic inch", I have no idea how high the atmospheric pressure may have been back in those early years. There is irrefutable evidence that the Earth's atmosphere is being lost to space today, from this evidence that the loss is occurring today I make the assumption that the loss has been continual during the Earth's existence. If there were some numbers indicating the amount of atmosphere loss today, then it would be possible to get some idea of how much of the Earth's atmosphere has been lost during the millions of years that it has existed.
Mean radius of Earth 3963 miles. Surface area 4*3.1415*15705369=197353666.854 square miles converts to 38207669902934.5 square inches. Since atmospheric pressure today is about 14.7 lb. per sq. in. Then 14.7*38207669902934.5 = 561652747573137 lb. per sq. inches today and in the early years it may have been ten times higher, if so then 147*38207669902934.5 = 5.6165274757e15 was the pressure then and the difference is 5.5783198058e15 lb. to the surface area.

Would such a difference in surface pressure have any effect on the cavities within the planet, I do not know, but the idea is intriguing.
Keep smiling
Johannes