Nonlocal cosmology II. Cosmic acceleration without fine tuning or dark energy

Abstract

We present an improved version of our original cosmological model to explain the current phase of cosmological acceleration without resorting to a cosmological constant or any other mass scale. Like the original, this phenomenological approach is based on an effective quantum gravitational action, but now depends on the original nonlocal dimensionless scalar X = □−1 R only through Y = □−1 gμν X,μ X,ν. Both X and Y are quiescent during the radiation-dominated (R=0) era, both only grow logarithmically during matter dominance, and neither affects the propagation of gravitational radiation. However, while X has the same sign for gravitationally bound systems as for cosmology, we show that the sign of Y differs for the two cases: it is positive for cosmology and negative for strongly gravitationally bound systems. We can therefore enforce the ΛCDM expansion history by making a suitable choice of the nonlocal distortion function f(Y) for Y > 0, while ensuring that there is no change in the heavily constrained solar system phenomenology simply by making f vanish for Y < 0 without discontinuity. The required f(Y>0) is determined numerically to have a strikingly simple exponential form.