Cotton fiber length variation is typically expressed by the uniformity index. The uniformity index is a measure of the evenness of the fiber length in a cotton sample. It is calculated by comparing the length of the shortest fibers to the length of the longest fibers in a sample. A high uniformity index indicates that the fiber lengths are uniform, meaning the fibers are of similar length. Conversely, a low uniformity index means that the fiber lengths vary significantly.
The other options are related to fiber length variation, but they describe different aspects. For example, the limit irregularity (B) measures the variation in fiber length but does not provide as complete a picture as the uniformity index. The index of irregularity (D) is another measure of variation, but the uniformity index is the most commonly used to express fiber length variation.
Thus, the correct answer is uniformity index.
Final Answer: \boxed{(A) Uniformity index}