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.

arXiv comment18 pages, 4 figures, uses LaTeX2e version 2 revised for publication

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