Cosmological mass of the photon and dark energy as its Bose–Einstein condensate in de Sitter space

Abstract

AbstractI develop a physical picture of dark energy (DE) based on fundamental principles and constants of quantum mechanics (QM) and general relativity (GR) theories. It derives from a conjecture of nonzero masses for nearly standard-model photons or gluons, based on QM localization at a cosmological scale. Dark energy is associated with de Sitter space and that has a fundamentally invariant event horizon, which provides the basis for my DE model. I conceive of DE as a Bose–Einstein condensate (BEC) of cosmologically massive photons, and I estimate fundamentally the binding energy per particle originating from an effectively attractive QM potential in that BEC. Since massive photons may stand at rest in a de Sitter universe with flat spatial geometry, I solve the time-independent Schrödinger equation for a nonrelativistic attractive spherical-well potential self-confining at the de Sitter horizon. The minimal critical potential depth that binds a particle state at the top of that well, combined with the prototypical condition of dark energy-pressure relation in the standard flat $$\Lambda $$ Λ -CDM model, provides an estimate of the photon mass, $$m_g$$ m g . That is supported by an independent calculation of the vacuum energy of the BEC in a de Sitter static metric with coordinate-time slicing. I also consider classical gravitational collapse for a uniform dark energy density, approaching Schwarzschild condition. These QM and GR estimates provide compatible accounts of dark energy condensation, bridging a chasm between nuclear and cosmological scales. I then investigate statistical properties of equilibrium between the g-BEC phase and the ordinary ‘vapor’ phase of $$m_g$$ m g photons. Resulting corrections to the Planck spectrum of the CMB are too small to be detectable, at least currently. Most notably, I consider a system of cosmological units, or ‘g-units,’ that complements the fundamental system of Planck units in various ways. The geometric mean of Planck and g-mass turns out to be remarkably close to current estimates of neutrino masses, suggesting that even masses of the lightest known fermions may be deeply related to both GR and QM fundamental constants $$\Lambda $$ Λ , G, c and h.