How will the Universe end? Or will it go on expanding forever?

This depends on how much matter exists in the cosmos. If it exceeds the so-called cosmic density, gravity will bring the current cosmic expansion to the halt and trigger eventual collapse presumably into a Big Crunch billions of years from now. Some cosmologists derive a sort of hope from this catastrophe. They think it is possible that after the Big Crunch the Universe will experience a kind of cosmic ‘bounce’, and begin to re-expand. This is the concept of oscillating Universe, as envisioned in Hindu cosmology. If our future is the Big Crunch, it presumably also is our past. The present expanding universe would only be the phase following the last contraction and bounce. Looking farther back, we can imagine an endless cycle of expansion and contraction.
The present consensus, however, is that the Universe will continue to expand forever. In fact, the rate of expansion is accelerating due to mysterious repulsive force which the astronomers call dark energy. Scientific data has revealed that 74% of the mass-energy composition of the universe is dark energy. If the expansion continues, stars and galaxies will recede beyond each others’ horizon and our cosmos will quietly go into the night.

Additional reading:
Universe (Wikipedia)
Accelerating universe (Wikipedia)
Metric expansion of space (Wikipedia)

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