According to current scientific understanding, the heat death of the universe is a hypothetical event that is predicted to occur in an extremely distant future. However, it is important to note that our understanding of the universe is still evolving, and future discoveries may refine or revise these predictions.
The concept of heat death is based on the idea that the universe is expanding and cooling down over time. As the universe continues to expand, galaxies will become further apart, and eventually, stars will run out of fuel and cease to shine. As a result, the universe will become a dark, cold place, with only low-level radiation remaining.
Estimating the time until the heat death of the universe is challenging due to uncertainties in our understanding of dark energy and other cosmological factors. Based on current knowledge, some theories suggest that the heat death could occur trillions upon trillions of years in the future, possibly even beyond 10^100 years.
As for the question of whether time would cease to exist during the heat death of the universe, it's a topic of speculation. Time, as we perceive it, is closely linked to the dynamics and interactions of matter and energy. In a universe devoid of matter and with only radiation left, the concept of time as we know it may lose its conventional meaning. However, it's important to note that our understanding of the nature of time is still an active area of research, and there is no definitive answer to this question at present.