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We know that the universe is expanding at an increasing accelerated rate, but the ratio of dark energy to observable matter remains constant as dark energy remains constant (please correct me on this).

Moreover, some say that new galaxies are no longer formed excluding the galaxies that collide and form a new galaxy.

Now my question is will the below pie-chart always stay the same, if so then what will eventually cause the expansion to stop and mark the end of the universe?

enter image description here

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The pie chart will change as the universe expands. If our current understanding is correct then the matter density will decrease as the universe cube of the scale factor (think of that as the distance between a pair of galaxies). Dark matter and ordinary matter behave in the same way, so their 5:1 ratio will remain constant.

However, the dark energy density remains constant and so the pie will become increasingly dominated by dark energy as the universe expands; the Hubble parameter will reach a constant value and the expansion will become exponential with time. Nothing will cause the expansion to stop; it will continue at an accelerating rate.

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