Jul 5 – 12, 2017
Venice, Italy
Europe/Zurich timezone
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Adiabaticity and gravity theory independent conservation laws for cosmological perturbations

Jul 7, 2017, 9:30 AM
Room Martinelli (Palazzo del Casinò)

Room Martinelli

Palazzo del Casinò

Parallel Talk Cosmology, Dark Energy, Gravitational Waves Cosmology, dark energy, gravitational waves


Antonio Enea Romano (Universidad de Antioquia (CO))


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 $\zeta$.

Primary author

Antonio Enea Romano (Universidad de Antioquia (CO))

Presentation materials