Neutron star (NS) being rich in baryons can act as a natural laboratory to test dark matter (DM)-baryon interactions with the advent of new telescopes like JWST as well as gravitational waves detector facility at LVK collaboration. In this talk, I shall discuss how astrophysical evidences indicate dark matter intervention in resolving mysteries regarding NSs. In particular, I shall show bosonic DM capture in NSs has a rich phenomenology in deciding various NS observables. If bosonic DM forms condensate and annihilates inside the NS, old neutron stars glow brighter than usual, in turn, become detectable by the JWST. On the other hand, if DM is non-annihilating, the gravitational collapse of the dark core can initiate transmutation of a neutron star into a solar mass black hole, which warrants dedicated GW searches at LVK facility. All these phenomena can be realized in a realistic DM model, especially in freeze-in DM scenarios.

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.