### 3.8 Alternative theories of gravity

Instead of modifying the scalar field potential, one can instead consider alternative theories of gravity.
Constraints on such theories are already significant given the great success of general relativity [221].
However, the fast advance of electromagnetic observations and the anticipated gravitational-wave
observations promise much more in this area, in particular in the context of compact objects that probe
strong-field gravity.
An ambitious effort is begun in Ref. [176], which studies a very general gravitational Lagrangian
(“extended scalar-tensor theories”) with both fluid stars and boson stars. The goal is for observations of
compact stars to constrain such theories of gravity.

It has been found that scalar tensor theories allow for spontaneous scalarization in which the scalar
component of the gravity theory transitions to a non-trivial configuration analogously to ferromagnetism
with neutron stars [62]. Such scalarization is also found to occur in the context of boson-star
evolution [6].

Boson stars also occur within conformal gravity and with scalar-tensor extensions to it [40, 41].

One motivation for alternative theories is to explain the apparent existence of dark matter without
resorting to some unknown dark matter component. Perhaps the most well known of these is MOND
(modified Newtonian dynamics) in which gravity is modified only at large distances [164, 165] (for a review
see [77]). Boson stars are studied within TeVeS (Tensor-Vector-Scalar), a relativistic generalization of
MOND [58]. In particular, their evolutions of boson stars develop caustic singularities, and the authors
propose modifications of the theory to avoid such problems.