Modified gravity and coupled quintessence
  The distinction between modified gravity and quintessence or dynamical dark
energy is difficult. Many models of modified gravity are equivalent to models
of coupled quintessence by virtue of variable transformations. This makes an
observational differentiation between modified gravity and dark energy very
hard. For example, the additional scalar degree of freedom in $f(R)$-gravity or
non-local gravity can be interpreted as the cosmon of quintessence.
Nevertheless, modified gravity can shed light on questions of interpretation,
naturalness and simplicity. We present a simple model where gravity is modified
by a field dependent Planck mass. It leads to a universe with a cold and slow
beginning. This cosmology can be continued to the infinite past such that no
big bang singularity occurs. All observables can be described equivalently in a
hot big bang picture with inflation and early dark energy.
