How would you imagine the size of the universe will change in the future?
The universe will grown so big and diffuse that the universe will experience a heat death that leaves nothing left but very low level heat energy.
As the universe continues to increase its rate of expansion, the universe will continue to expand. The amount of matter and energy in the universe will remain constant. ( according to the first law of thermodynamics) The same amount of matter spread out over an increasing and possibly infinite amount of space will become increasingly diffuse.
The matter as it spreads out will be converted to energy and the energy will decrease in its level and organization ( According to the second law of thermodynamics.) This process will result in there being no matter left in the universe. The energy will be such that the temperature of the universe will be close to absolute zero though out the universe. There will be no useful energy or matter left. This future is referred to as the heat death of the universe.
The increasing size of the universe will result in the end of the universe, there will be nothing left that is useful or visible.