Quantum effects in gravitational interactions and space-time structure can have different implications, some of them relevant for cosmology. On dimensional grounds and using the classical understanding of covariance, one expects an effective action with higher-curvature corrections. These terms are very small in standard cosmological regimes and cannot leave significant imprints on observable structures. However, the notion of covariance may itself receive quantum corrections, allowing new and potentially larger cosmological effects. Examples have been found in loop quantum gravity, with implications especially for the tensor-to-scalar ratio. In high-curvature regimes where general relativity becomes singular, loop quantum gravity implies quantum corrections so strong that they turn Lorentzian space-time into Euclidean 4-space.