Stellar Oscillations in Modified Gravity
  Starting from the equations of modified gravity hydrodynamics, we derive the
equ tions of motion governing linear, adiabatic, radial perturbations of stars
in scalar-tensor theories. There are two new features: first, the eigenvalue
equation for the period of stellar oscillations is modified such that the
eigenfrequencies are always larger than predicted by General Relativity.
Second, the General Relativity condition for stellar instability is altered so
that the adiabatic index can fall below 4/3 before unstable modes appear. Stars
are more stable in modified gravity theories. Specialising to the case of
chameleon-like theories, we investigate these effects numerically using both
polytropic Lane-Emden stars and models coming from modified gravity stellar
structure simulations. The change in the oscillation period can be as large as
50% and the critical adiabatic index for instability falls by a composition
dependent amount of order 10^(-1). By solving the new equation for Cepheid
models, it is found that the change in the inferred distance using the
period-luminosity relation can be up to three times larger than if one had only
considered the modified equilibrium structure. We discuss the implications of
these results for recent and up-coming astrophysical tests and estimate that
previous methods can produce new constraints such that the modifications are
screened in regions of Newtonian potential of order 10^(-8).
