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I will discuss an attempt at approaching quantum features of spacetime from a microscopic point of view. In combination with quantum gravity, one can consider a scenario in which spacetime has structure at the level of quantum interactions, and classical spacetime emerges at larger scales. This type of scenario would require entangling interactions, and a reliance on information exchange would have effects on the classical field theory.

The conservation law for the total (orbital plus spin) angular momentum of a Dirac particle in the presence of gravity requires that spacetime is not only curved, but also has a nonzero torsion. The coupling between the spin and torsion in the Einstein–Cartan theory of gravity generates gravitational repulsion at extremely high densities, which prevents a singularity in a black hole and may create there a new, closed, baby universe undergoing one or more nonsingular bounces. We show that quantum particle production caused by an extremely high curvature near a bounce creates enormous amounts of matter and can generate a finite period of inflation. Our scenario has only one parameter, does not depend significantly on the initial conditions, does not involve hypothetical scalar fields, avoids eternal inflation, and predicts plateau-like inflation that is supported by the Planck observations of the cosmic microwave background. This scenario suggests that our Universe may have originated from a nonsingular bounce in a black hole existing in another universe.

Von Neuman entropy. Classical data compression. Shannon's source coding theorem. Quantum data compression and Schumacher compression. Shannon's channel compression theorem. Mutual information.

Strong gravitational lenses with measured time delays between the multiple images can be used to determine the Hubble-Lemaitre constant (H0) that sets the expansion rate of the Universe. An independent determination of H0 is important to ascertain the possible need of new physics beyond the standard cosmological model, given the tension in current H0 measurements. A program initiated to measure H0 to <3.5% in precision from strongly lensed quasars is in progress, and I will present the latest results and their implications. Search is underway to find new lenses in imaging surveys. An exciting discovery of the first strongly lensed supernova offered a rare opportunity to perform a true blind test of our modeling techniques. I will outline a new research program on lensed supernovae, showing their bright prospects as a competitive and unique probe of cosmology and stellar physics.