  Since general relativity is the unique theory of massless spin 2 particles at
large distances, the most reasonable way to have significant modifications is
to introduce one or more light scalars that mediate a new long-range force.
Most existing studies of such scalars invoke models that exhibit some kind of
"screening" at short distances to hide the force from solar system tests.
However, as is well known, such modifications also exhibit superluminality,
which can be interpreted as a form of acausality. In this work we explore
explicitly subluminal and causal scalar field models. In particular, we study a
conformally coupled scalar $\phi$, with a small coupling to matter to obey
solar system bounds, and a non-canonical kinetic term $K(X)$
($X=(\partial\phi)^2/2$) that obeys all subluminality constraints and is
hyperbolic. We consider $K(X)$ that is canonical for small $X$, but beyond some
nonlinear scale enters a new scaling regime of power $p$, with $1/2<p<1$ (the
DBI kinetic term is the limit $p=1/2$ and a canonical scalar is $p=1$). As
opposed to screening (and superluminality), this new force becomes more and
more important in the regime of high densities (and subluminality). We then
turn to the densest environments to put bounds on this new interaction. We
compute constraints from precession in binary systems such as Hulse-Taylor, we
compute corrections to neutron star hydrostatic equilibrium, and we compute
power in radiation, both tensor mode corrections and the new scalar mode, which
can be important during mergers.
