We investigate how degeneracies in quasi-de Sitter backgrounds, in the sense of Wands’ duality, are reflected in real-space quantum correlations of primordial perturbations. Using the continuous-variable Gaussian formalism for coarse-grained scalar fluctuations, I will show how to construct the covariance matrix of a pair of spatially localized modes in inflationary spacetime, and extract the symplectic invariants of the system. For a generic Wands-dual pair of backgrounds, we will find that while the individual entries of the covariance matrix are highly background-dependent, the symplectic eigenvalues – and hence the entanglement entropy, mutual information, quantum discord and log-negativity – all coincide for the two dual realizations. Our results unveil a new “quantum-informatic symmetry” of the de Sitter vacuum, according to which local linear entanglement witnesses constructed from coarse-grained fields cannot distinguish between Wands-dual inflationary histories, even though their background trajectories differ. I will show that the special nature of the Wands-duality symmetry (of being local, scale-independent canonical transformations) is at the heart of this duality.

We propose a possible microscopic origin of cosmic horizon entropy based on thermal interactions between the apparent horizon and the matter fluid (inside the horizon). In particular, we argue that the heat energy lost by the matter fluid through the divergence from the horizon is equal to the heat energy absorbed by the horizon. Based on this thermal interaction and by using the underlying statistical theory of matter fluid, we determine the entropy of cosmic horizon for Einstein gravity as well as for modified theories of gravity. It turns out that Einstein gravity supports the Bekenstein-Hawking (BH) like entropy, and remarkably, we get logarithmic correction (as leading order correction over the BH entropy) in horizon entropy for modified gravity theories.