We show that Dark Matter consisting of bosons of mass of about 1eV or less has critical temperature exceeding the temperature of the universe at all times, and hence would have formed a Bose-Einstein condensate at very early epochs. We also show that
the wavefunction of this condensate, via the quantum potential it produces, gives rise to a cosmological constant which may account for the correct dark energy content of our universe. We argue that massive gravitons or axions are viable candidates for these constituents. In the far future this condensate is all that remains of our universe.
We compute quantum corrections to the Raychaudhuri equation, by replacing classical geodesics with quantal (Bohmian) trajectories, and show that they prevent focusing of geodesics, and the formation of conjugate points. We discuss implications for th
e Hawking-Penrose singularity theorems, and for curvature singularities.
Almost all theories of Quantum Gravity predict modifications of the Heisenberg Uncertainty Principle near the Planck scale to a so-called Generalized Uncertainty Principle (GUP). Recently it was shown that the GUP gives rise to corrections to the Sch
rodinger and Dirac equations, which in turn affect all non-relativistic and relativistic quantum Hamiltonians. In this paper, we apply it to superconductivity and the quantum Hall effect and compute Planck scale corrections. We also show that Planck scale effects may account for a (small) part of the anomalous magnetic moment of the muon. We obtain (weak) empirical bounds on the undetermined GUP parameter from present-day experiments.
