Dark energy from instantons

Abstract

We show that in imaginary time quantum metric fluctuations of empty space form a self-consistent de Sitter gravitational instanton that can be thought of as describing tunneling from "nothing" into de Sitter space of real time (no cosmological constant or scalar fields are needed). For the first time, this mechanism is activated to give birth to a flat inflationary Universe. For the second time, it is turned on to complete the cosmological evolution after the energy density of matter drops below the threshold (the energy density of instantons). A cosmological expansion with dark energy takes over after the scale factor exceeds this threshold, which marks the birth of dark energy at a redshift $1+z\approx 1.3$ and provides a possible solution to the "coincidence problem". The number of gravitons which tunneled into the Universe must be of the order of $10^{122}$ to create the observed value of the Hubble constant. This number has nothing to do with vacuum energy, which is a possible solution to the "old cosmological constant problem". The emptying Universe should possibly complete its evolution by tunneling back to "nothing". After that, the entire scenario is repeated, and it can happen endlessly.