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 , because the quantity depends on both and (in other words, ). In the following we write the curvature perturbations and as .
This work is licensed under a Creative Commons License.