Modern models and direct cosmic ray experiments deal with heliospheric modulation of cosmic rays only during the recent times of rather high overall solar activity level. On the other hand, the question of cosmic ray modulation during the exceptional conditions of very quiet heliosphere is important. In the present paper we compare the variations of cosmic ray intensity with solar and auroral activity during the Maunder minimum (1645--1715) when the Sun was extremely quiet. We use the newly presented group sunspot number series as a measure of early solar activity, the auroral observations in central Europe as an indicator of transient phenomena in the inner heliosphere, and the radiocarbon data as a proxy of cosmic ray intensity. We find that both cosmic ray intensity and auroral activity closely follow the dominant 22-year cyclicity with sunspot activity during the Maunder minimum. Moreover, the strict antiphase between the 22-year variation of cosmic ray intensity and sunspot activity suggests that the 22-year variation in cosmic ray intensity can be explained by the diffusion-dominated terms of cosmic ray modulation without significant drift effects. We also discuss the possible origin of the behavior of the 10Be data which is different from all other parameters during the Maunder minimum. ¿ 2001 American Geophysical Union