Healthy cerebral cortex function requires complex neuronal population activity with a diverse repertoire of timescales, from fleeting response to sensory input ($\sim$10-100 ms), to execution of complex body movements ($\sim 100-1000 ms$), to even longer timescales of working memory ($\sim 1-10 s$). How does cortex generate such a broad range of timescales? How is the timescale repertoire tuned in response to shifting behavioral demands? One potential explanation is that cortex operates close to criticality, i.e., close to a boundary between two different dynamical regimes. At criticality, fluctuations have no characteristic timescale; the timescale repertoire is maximally diverse. Criticality also offers exceptional tunability, as small changes in the parameters of a system near criticality elicit dramatic changes in dynamics. Fundamental understanding of how systems behave near criticality came from renormalization group (RG) theory, but RG for neural systems remains largely undeveloped. Here we developed a temporal RG (tRG) for analysis of typical neuroscience data. We analytically identified multiple types of criticality (tRG fixed points) and developed tools to assess proximity to each fixed point from short snippets of neural activity. We leveraged the high time resolution of our tools to track how rapid changes in behavioral state affect proximity to criticality, finding that visual cortex of freely-behaving mice is closest to criticality during the relaxed awake state. Deviation from criticality during deep sleep and the hyper-aroused awake state drives collapse of the repertoire of cortical timescales