  We consider the backreaction of the long wavelength tensor modes produced
during a slow-roll inflationary regime driven by a single scalar field in a
spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker background geometry. We
investigate the effects on non-local observables such as the effective
(averaged) expansion rate and equation of state at second order in cosmological
perturbation theory. The coupling between scalar and tensor perturbations
induces at second order new tensor backreaction terms beyond the one already
present in a de Sitter background. We analyze in detail the effects seen by the
class of observers comoving with the inflaton field (taken as a clock) and the
class of free-falling observers. In both cases the quantum backreaction is at
least $1/\epsilon$ (with $\epsilon$ the slow-roll parameter) larger than the
one which can be naively inferred from a de Sitter background. In particular,
we compute the effect for a free massive inflaton model and obtain in both
cases a quantum correction on the background expansion rate of the order of
$H^4/(m^2 M_{Pl}^2)$. A short discussion on the issue of the breakdown of
perturbation theory is given.
