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If the universe is expanding, the "pressure" of the "vacuum" in space is decreasing, the earths Atmosphere is expanding, atmospheric pressure is decreasing.

Taking into account: the rate of expansion of the universe/atmosphere, the atmospheric volume increasing/decreasing by chemical activity in the core of the planet and on it's surface, effect of cosmic radiation and the rate of evolutionary adaption of our means of respiration, the lung. could it be possible to determine a moment in time when earth's atmosphere is no longer breathable due to the reduction in atmospheric pressure?

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The expansion of the universe is a cosmological effect, which is relevant between groups of galaxies. Within a galaxy, more ordinary gravitational attraction overwhelms the cosmological expansion, and you can ignore it.

The primary mechanism for mass loss from Earth's atmosphere is probably its interaction with the solar wind, but Earth's magnetic field mostly steers the solar wind away from interacting with the atmosphere directly. There is some amount of replenishment due to outgassing from Earth's interior, most dramatically in volcanic eruptions.

The abstract of this 2020 paper suggests that we don't have very much data about the history of Earth's atmospheric pressure over geological time.

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