Is the universe gravitationally dominated by nonbaryonic dark matter?

A new method for deriving a lower limit of the mean density of the universe using the maximum temperature of the X-ray-emitting hot gas in clusters of galaxies is proposed. This method is applied to the present record holder for the highest temperature among X-ray clusters, A2163. I find that the probability that the observed volume, in which complete X-ray observations are performed, contains at least one cluster with a temperature as high as the temperature of A2163 is very small for a low-density universe. Even if we take the most conservative upper limit of the baryon density of the universe derived from big bang primordial nucleo-synthesis theories, the possibility that the universe is made from only baryonic matter can be rejected with more than 99.99% confidence. Applying the condition that the expectation of finding a cluster which has a temperature higher than A2163 in the observed volume is at least 1, the mean density of the universe must be more than twice the baryon density of the universe. I conclude that it is very probable that our universe is gravitationally dominated by non-baryonic dark matter.