Dark Energy and Doubly Coupled Bigravity
(46 pages)

In the algebraic branch of the bigravity FRW solution, the late time cosmology is
determined. By tuning the graviton mass, the asymptotic dark energy equation of
state can be made arbitarily close to 1. The full theory contains 5+2+2 SVT
modes, the dof of two gravitons (one massive and one massless). The scalar
sectors leads to modifications of structure formation and lensing on large scales
 which are senstive to how the matter is coupled to both metrics. The mass
mixing of the two gravitons leads to a gravitational birefringence.

Studying the modified phenomenology of multimetric theories of gravity provides
valuable cosmological predictions which can be tested as alternatives to General
Relativity. In addition to the dRGT mass terms which can be included in a multi
metric theory, there is also more freedom in how matter couples to gravity  it
may do so through a combination of the two metrics. This paper outlines some of
the different cosmological effects due to different matter couplings.

Generic instabilities of nonsingular cosmologies in Horndeski theory: a nogo
theorem
(7 pages)

While generalized Galileon theories can stably violate the null energy condition
in flat space, when coupling them to gravity (giving the Horndeski theory) any
such violation gives rise to instabilities. This nogo theorem extends previous
work of 1605.05992 to all Horndeski theories, and suggests that Beyond Horndeski
will be necessary in order to have a stable violation of the null energy
condition.

In an FRW universe, the null energy condition keeps the Hubble rate decreasing
with time. As we extrapolate backwards in time to the early Universe, one of two
things must happen: (i) Hubble rate increases to Planck scales and our
understanding of gravity breaks down, or (ii) the null energy condition is
violated. Interest in the latter case goes under the name 'nonsingular
(bouncing) cosmologies', and may provide an alternative scenario to the initial
Big Bang singularity  for example there could be a `bounce' from a contracting
to an expanding universe during a nullenergyconditionviolating phase of the
early universe.

Doubly coupled matter fields in massive bigravity
(17 pages)

Massive bigravity with doubly coupled matter fields admits novel cosmological
solutions. While previous work had investigated the stability of SVT
perturbations around particular branches of solution, this latest paper carries
out a perturbative analysis about completely general equations of motion, and
provides the full quadratic action for the scalar perturbations (which is shown
to contain a ghost if one chooses the nonalgebraic branch).

Providing stability criteria for a whole class of spin2 field theories (namely
two metrics interacting via dRGT mass terms and both coupled to external matter)
plays a crucial role in guiding future phenomenological investigation, allowing
the community to focus their resources on analysing only the stable solutions.
