### Speaker

### Description

We carefully study the implications of adiabaticity for the behavior of

cosmological perturbations. There are essentially three similar but

different definitions of non-adiabaticity: one is appropriate for

a thermodynamic fluid $\delta P_{nad}$, another is for a general matter field

$\delta P_{c,nad}$, and the last one is valid only on superhorizon scales.

The first two definitions coincide if $c_s^2=c_w^2$ where

$c_s$ is the propagation speed of the perturbation, while

$c_w^2=\dot P/\dot\rho$.

Assuming the adiabaticity in the general sense, $\delta P_{c,nad}=0$,

we derive a relation between the lapse function in the comoving sli-cing $A_c$

and $\delta P_{nad}$ valid for arbitrary matter field in any theory of gravity,

by using only momentum conservation.

The relation implies that as long as $c_s\neq c_w$,

the uniform density, comoving and the proper-time slicings

coincide approximately for any gravity theory and for any matter field

if $\delta P_{nad}=0$ approximately.

In the case of general relativity this gives the equivalence

between the comoving curvature perturbation $R_c$

and the uniform density curvature perturbation $\zeta$

on superhorizon scales, and their conservation.

This is realized on superhorizon scales in standard slow-roll inflation.

We then consider an example in which $c_w=c_s$, where $\delta P_{nad}=\delta P_{c,nad}=0$

exactly, but the equivalence between $R_c$ and $\zeta$ no longer holds.

Namely we consider the so-called ultra slow-roll inflation.

In this case both $R_c$ and $\zeta$ are not conserved.

In particular, as for $\zeta$, we find that it is crucial to take into

account the next-to-leading order term in $\zeta$'s spatial gradient expansion

to show its non-conservation, even on superhorizon scales.

This is an example of the fact that adiabaticity (in the thermodynamic sense) is not always enough to ensure

the conservation of $R_c$ or $\zeta$.