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 $X = \square^{-1} R$ only through $Y = \square^{-1} g^{\mu\nu} X_{,\mu} X_{,\nu}$. 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 $\Lambda$CDM 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.