The theory you propose is an interesting one, but it is important to note that it goes beyond our current understanding of the universe based on scientific evidence and theories. I can outline some points regarding the believability or potential issues with this theory, but please keep in mind that it remains speculative:
Lack of observational evidence: Currently, there is no direct observational evidence supporting the existence of multiple big crunches or dark matter preventing them. Our understanding of the universe is primarily based on the observations of cosmic expansion and the presence of dark matter inferred from its gravitational effects on visible matter.
Alternative explanations: The observed accelerated expansion of the universe, rather than a big crunch, is supported by substantial evidence from observations of distant supernovae, the cosmic microwave background, and large-scale structure formation. The leading explanation for this accelerated expansion is the presence of dark energy, a mysterious force with repulsive effects on the universe's large-scale structure.
Complexity of dark matter: Dark matter is still a topic of active research, and its exact nature remains unknown. While it is believed to exist due to its gravitational influence on visible matter, the idea of dark matter preventing a big crunch would require a detailed understanding of its properties and its ability to counteract gravitational collapse. Presently, we do not have enough knowledge to support this idea.
Consistency with current models: The theory you propose should align with existing well-established scientific models, such as general relativity and the Standard Model of particle physics. It would need to provide a coherent framework that explains various observational phenomena and fits within the mathematical descriptions of these models.
Occam's Razor: Occam's Razor suggests that the simplest explanation is often the most likely. Introducing multiple big crunches and the specific role of dark matter to prevent them may complicate the theory unnecessarily, as it would require additional assumptions and mechanisms without substantial evidence.
In summary, while your theory is an intriguing concept, it currently lacks empirical evidence and may contradict well-established scientific models. To gain broader acceptance, it would require substantial observational and theoretical support from the scientific community. Science continuously evolves, so future discoveries may shed light on the questions you raise, but at present, these ideas remain speculative.