In a universe where the scale factor is proportional to t^α, where t is time and α is a constant less than one, the universe has:
* the sign of the acceleration is undetermined
* negative acceleration
* positive acceleration
* zero acceleration
In order to determine the sign of the acceleration in the given universe, we need to understand the behavior of the scale factor as the universe evolves over time.
The scale factor represents the overall size of the universe at a given time. In this case, the scale factor is proportional to t^α, where t is time and α is a constant less than one.
If α is positive, it means that the scale factor increases with time. This implies that the universe is experiencing expansion, and as a result, the acceleration of the expansion is positive.
If α is negative, the scale factor decreases with time. This indicates that the universe is contracting or collapsing. In this scenario, the acceleration of the contraction is negative.
If α = 0, then the scale factor does not change with time. As a result, the universe remains constant in size, and the acceleration is zero.
Therefore, if α is positive, the universe has positive acceleration, if α is negative, the universe has negative acceleration, and if α is zero, the universe has zero acceleration. The sign of the acceleration is determined by the value of α.