Using recent experimental data, bounds on the graviton mass are derived from the Yukawa type fall-off at the graviton Compton wavelength; a potentially modified dispersion relation; and solar system fifth force tests. This includes, for example, the precession of Mercury,

  m_g < 7.2x 10^-23 eV,

the aLIGO measurements of GW150914 (and GW151226),

  m_g < 1.2x 10^-22 eV,

and possible Earth-Moon precession,

  m_g < 10^-32 eV.

The degree of model-dependence of these bounds is discussed (the aLIGO and Mercury bounds being among the most model-independent and rigorous), and where necessary results are interpreted in the context of: DGP, dRGT, Lorentz-violating, Non-local, Non-Fierz-Pauli massive gravity.

In recent years much theoretical progress has been made in constructing self-consistent theories of massive gravitons. Now, with the first direct detections of gravitational waves, we can begin to strictly test some of these theories. A massive graviton would travel slightly slower than light, which leads to a range of interesting effects (for example, acceleration without dark energy). The graviton must be very nearly massless (or else we would have observed its effects before now), but a small mass is still consistent with all experimental data, as outlined in this paper.

Explicit examples of a cubic Galileon cosmology with a stable, non-singular bounce are constructed. Although recent no-go theorems have suggested that any Galileon theory on an FRW background will contain classical pathologies such as ghosts and gradient instabilities, here the counterargument is made that these problems can be made to occur arbitrarily earlier/later than the time interval of interest. If one treats the theory as an effective description of the bounce (restricting attention to a finite time interval near the bounce) it is possible to stably violate the Null Energy Condition and drive a bounce using a scalar field.

A bouncing cosmology may provide a viable alternative to inflation - which, despite the dominant cosmological paradigm, suffers from unresolved issues. Most of these issues stem from our inability to describe gravity quantum mechanically, and so we cannot describe the early Big Bang singularity. A non-singular bounce avoids these problems by maintaining a sufficiently large/cold universe at all times, staying in the regime of our current understanding of physics. However, most attempts to construct a model with a bounce have been plagued by classical instabilities. Examples of theories which bounce in a stable way are therefore very useful, demonstrating that not only is a bounce possible, but that it likely has certain characteristics.