Let us consider scalar and tensor perturbations generated during inflation for the theories (6.2) without
taking into account the perfect fluid (
). In f (R) gravity the contribution of the field
such as
is absent in the perturbation equations (6.11
) – (6.16
). One can choose the
gauge condition
, so that
. In scalar-tensor theory in which
is the
function of
alone (i.e., the coupling of the form
without a non-linear term in
),
the gauge choice
leads to
. Since
in this case, we have
.
We focus on the effective single-field theory such as f (R) gravity and scalar-tensor theory with the
coupling , by choosing the gauge condition
and
. We caution that this analysis
does not cover the theory such as
[500], because the quantity
depends on both
and
(in other words,
). In the following we write the curvature perturbations
and
as
.
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