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 the 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 Schrodinger 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.
We review aspects of the thermodynamics of black holes and in particular take into account the fact that the quantum entanglement between the degrees of freedom of a scalar field, traced inside the event horizon, can be the origin of black hole entropy. The main reason behind such a plausibility is that the well-known Bekenstein-Hawking entropy-area proportionality -- the so-called `area law of black hole physics -- holds for entanglement entropy as well, provided the scalar field is in its ground state, or in other minimum uncertainty states, such as a generic coherent state or squeezed state. However, when the field is either in an excited state or in a state which is a superposition of ground and excited states, a power-law correction to the area law is shown to exist. Such a correction term falls off with increasing area, so that eventually the area law is recovered for large enough horizon area. On ascertaining the location of the microscopic degrees of freedom that lead to the entanglement entropy of black holes, it is found that although the degrees of freedom close to the horizon contribute most to the total entropy, the contributions from those that are far from the horizon are more significant for excited/superposed states than for the ground state. Thus, the deviations from the area law for excited/superposed states may, in a way, be attributed to the far-away degrees of freedom. Finally, taking the scalar field (which is traced over) to be massive, we explore the changes on the area law due to the mass. Although most of our computations are done in flat space-time with a hypothetical spherical region, considered to be the analogue of the horizon, we show that our results hold as well in curved space-times representing static asymptotically flat spherical black holes with single horizon.
