Quantum gravity at Hubble scales determines the cosmological constant and the amplitude of primordial perturbations

Gravity controls the amount of information that is accessible to any specific observer. We quantify the notion of cosmic information ('CosmIn') for the case of an eternal observer in the universe. Demanding the finiteness of CosmIn requires the universe to have a late-time accelerated expansion phase. Combined with some generic features of the quantum structure of spacetime, this leads to the determination of (i) the numerical value of the cosmological constant, as well as (ii) the amplitude of the primordial, scale invariant perturbation spectrum in terms of a single free parameter, which specifies the energy scale at which the universe makes a transition from a pre-geometric phase to the classical phase. This formalism also shows that the quantum gravitational information content of spacetime can be tested by using precision cosmology.