Final answer:
REM sleep has influenced dream research by revealing its critical role in memory, learning, and emotional processing. Scientists have found a connection between REM sleep and these cognitive processes, with REM rebound exemplifying the homeostatic regulation of REM sleep.
Step-by-step explanation:
Rapid eye movements (REM) have significantly influenced dream research, especially in understanding the connection between dream sleep and various cognitive processes. The correct answer to your question on how REM has influenced dream research is 'C. Scientists have connected dream sleep with memory and learning through REM research.' Various studies have shown that REM sleep plays a critical role in both learning and memory. Additionally, REM sleep is implicated in emotional processing and regulation which may contribute to its involvement with psychological health, though direct links to psychological health per your options have not been explicitly established as in 'B.'
REM rebound occurs when individuals deprived of REM sleep tend to spend more time in REM stages when allowed to sleep undisturbed, highlighting the importance of REM in the body's sleep regulation. Rosalind Cartwright's research further supports the connection of REM sleep with cognitive processes by finding correlations between daytime thoughts and REM sleep dream content.