Reconstruction of energy conditions from observations and implications
  for extended theories of gravity
  The attempt to describe the recent accelerated expansion of the Universe
includes different propositions for dark energy models and modified gravity
theories. Establish their features in order to discriminate and even rule out
part of these models using observational data is a fundamental issue of
cosmology. In the present work we consider a class of extended theories of
gravity (ETG) that are minimally coupled to the ordinary matter fields. In this
context, and assuming a homogeneous and isotropic spacetime, we derive the
energy conditions for this ETG class. We then put constraints on these
conditions using a model-independent approach to reconstruct the deceleration
function along with the Joint Light-curve Analysis (JLA) supernova sample, 11
baryon acoustic oscillation and 22 cosmic-chronometer measurements. We also
consider an additional condition imposing the strong energy condition only on
the ordinary matter. This is to guarantee the presence of only attractive
matter in the energy-momentum tensor, at least in the redshift range of the
observations, i.e., the recent accelerated expansion of the Universe is due
solely to the modifications in the gravity theory. The main result of this work
is a general reconstruction of the energy conditions valid for every considered
ETG.
