Interstellar Extinction Curve Variations Toward the Inner Milky Way: A
  Challenge to Observational Cosmology
  We investigate interstellar extinction curve variations toward $\sim$4
deg$^{2}$ of the inner Milky Way in $VIJK_{s}$ photometry from the OGLE-III and
$VVV$ surveys, with supporting evidence from diffuse interstellar bands and
$F435W,F625W$ photometry. We obtain independent measurements toward $\sim$2,000
sightlines of $A_{I}$, $E(V-I)$, $E(I-J)$, and $E(J-K_{s})$, with median
precision and accuracy of 2%. We find that the variations in the extinction
ratios $A_{I}/E(V-I)$, $E(I-J)/E(V-I)$ and $E(J-K_{s})/E(V-I)$ are large
(exceeding 20%), significant, and positively correlated, as expected. However,
both the mean values and the trends in these extinction ratios are drastically
shifted from the predictions of Cardelli and Fitzpatrick, regardless of how
$R_{V}$ is varied. Furthermore, we demonstrate that variations in the shape of
the extinction curve has at least two degrees of freedom, and not one (e.g.
$R_{V}$), which we conform with a principal component analysis. We derive a
median value of $<A_{V}/A_{Ks}>=13.44$, which is $\sim$60% higher than the
"standard" value. We show that the Wesenheit magnitude $W_{I}=I-1.61(I-J)$ is
relatively impervious to extinction curve variations.
  Given that these extinction curves are linchpins of observational cosmology,
and that it is generally assumed that $R_{V}$ variations correctly capture
variations in the extinction curve, we argue that systematic errors in the
distance ladder from studies of type Ia supernovae and Cepheids may have been
underestimated. Moreover, the reddening maps from the Planck experiment are
shown to systematically overestimate dust extinction by $\sim$100%, and lack
sensitivity to extinction curve variations.
