Nonlocal Cosmology II — Cosmic acceleration without fine tuning or dark energy. (arXiv:1902.08075v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Deser_S/0/1/0/all/0/1">S. Deser</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Woodard_R/0/1/0/all/0/1">R. P. Woodard</a>
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 $Y = square^{-1} g^{munu} X_{,mu} X_{,nu}$.
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
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 phenomenology of gravitationally bound systems simply by
making $f$ vanish for $Y < 0$. We numerically determine the required function
$f(Y>0)$: it has a surprisingly simple exponential form.
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 $Y = square^{-1} g^{munu} X_{,mu} X_{,nu}$.
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
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 phenomenology of gravitationally bound systems simply by
making $f$ vanish for $Y < 0$. We numerically determine the required function
$f(Y>0)$: it has a surprisingly simple exponential form.
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