Minicourse on the Entropy of Cosmological Perturbations

October 18, 21 and 27  

ICTP-SAIFR, São Paulo, Brazil

Third floor Meeting Room of IFT-UNESP

Lecturer: Antonio Enea Romano (Antioquia U., Colombia)

Organizer: Riccardo Sturani (ICTP-SAIFR/IFT-UNESP)


The theory of cosmological perturbations is of fundamental importance, providing a framework to understand the origin of the inhomogeneities we observe in the Universe. The enhancement of primordial perturbations can induce the production of primordial black holes, which could possibly contribute to the dark matter component, or be related to the production of gravitational waves. The enhancement can be achieved either with multi-field models with entropy, or with models with an ultra-slow roll phase. After reviewing the notion of entropy perturbations in different gauges, and clarifying some misconceptions about the relation between conservation laws and adiabaticity, we show that it is possible to model the effects of entropy on comoving curvature perturbations by appropriately defining a momentum dependent effective sound speed (MESS). This model independent approach is shown to work for multi-fields and modified gravity, and allows to constrain phenomenologically the MESS.

1 Review of first order cosmological perturbations
• Scalar-Vector-Tensor decomposition
• Gauge transformations
• Perturbed Einstein’s equations
2 The momentum effective sound speed (MESS) and entropy of cosmological perturbations
• Adiabaticity definitions and conservation laws : uniform density and co-moving gauge
• Are adiabatic perturbations always conserved? Not if ε decreases sufficiently fast (USR)
• Model independent equation for comoving curvature perturbations ζ
• Model independent definition of momentum effective sound speed (MESS)
3 Applications
• Conservation laws
• Multi-fields inflation
• Modified gravity theories
• Mechanisms for primordial black holes production: USR or MESS