Understand
Primordial cosmological perturbations are the seeds that were cultivated by inflation and the succeeding dynamical processes, eventually leading to the current Universe.
- In this work, we investigate the behavior of the gauge-invariant scalar and tensor perturbations under the general extended disformal transformation, namely, $g_{\mu\nu} \rightarrow A(X,Y,Z)g_{\mu\nu} + \Phi_\mu\Phi_\nu$, where $X \equiv -\tfrac{1}{2}\phi^{;\mu}\phi_{;\mu}, Y \equiv \phi^{;\mu}X_{;\mu}, Z \equiv X^{;\mu}X_{;\mu} $ and $\Phi_\mu \equiv C\phi_{;\mu} + DX_{;\mu}$, with $C$ and $D$ being a general functional of $(\phi,X,Y,Z)$.
- We find that the tensor perturbation is invariant under this transformation.
- On the other hand, the scalar curvature perturbation receives a correction due the conformal term only; it is independent of the disformal term at least up to linear order.