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In our recently proposed quantum theory of gravity, the universe is made of 'atoms'" of space-time-matter (STM). Planck scale foam is composed of STM atoms with Planck length as their associated Compton wave-length. The quantum dispersion and accompanying spontaneous localization of these STM atoms amounts to a cancellation of the enormous curvature on the Planck length scale. However, an effective dark energy term arises in Einstein equations, of the order required by current observations on cosmological scales. This happens if we propose an extremely light particle having a mass of about 1 0 − 3 3 eV/c 2 , forty-two orders of magnitude lighter than the proton. The holographic principle suggests there are about 1 0 1 2 2 such particles in the observed universe. Their net effect on space-time geometry is equivalent to dark energy, this being a low energy quantum gravitational phenomenon. In this sense, the observed dark energy constitutes evidence for quantum gravity. We then invoke Dirac's large number hypothesis to also propose a dark matter candidate having a mass halfway (on the logarithmic scale) between the proton and the dark energy particle, i.e. about 1 0 − 1 2 eV/c 2 . [ABSTRACT FROM AUTHOR]

We show that Kompaneetz equation describing photon diffusion in an environment of an electron gas, when linearized around its equilibrium distribution, coincides with the relativistic diffusion discussed in recent publications. The model of the relativistic diffusion is related to soluble models of imaginary time quantum mechanics. We suggest some nonlinear generalizations of the relativistic diffusion equation and their astrophysical applications (in particular to the Sunyaev–Zeldovich effect). [ABSTRACT FROM AUTHOR]