Which changes would cause the fusion rate in the sun’s core to increase?

Explanation

There are two factors that can cause the fusion rate in the sun's core to increase.

1) Rise in the temperature of core:

If the temperature of the sun's core increases then it will increases the nuclear fusion reaction. The nuclear fusion reactions has such a strong dependency on temperature that even a smallest rise in temperature will results in the higher rate of reaction. That is why these reactions happen in the hottest core of the stars.

2) Reduction in the radius of the core:

Density plays a huge role in the nuclear fusion reactions. If the radius of the sun's core decrease then there will be an increase in the density of the core. Thus the gravitational pressure will also increases. In order to resist this increase in pressure the fusion reactions will speed up and their rate becomes higher.