Speaker
Description
Due to the general covariance of the Einstein equations and
conservation laws, the linearized equations have solutions which are
gauge-dependent and have, therefore, no physical significance.
In this talk I will show that the decomposition theorems for symmetric
second-rank tensors of the maximally symmetric subspaces of constant
time imply that there are exactly two, unique, gauge-invariant
quantities which describe the true, physical perturbations to the
energy density and particle number density. In the limit of zero
spatial fluid velocity, and hence zero pressure, the set of linearized
Einstein equations and conservation laws, combined with the new
gauge-invariant quantities reduce to the Poisson equation of the
Newtonian Theory of Gravity and the energy-mass relation of the
Special Theory of Relativity. The relativistic gauge transformation
reduces to the Newtonian gauge transformation in which time and space
are decoupled.
The cosmological perturbation theory consists of a second-order
ordinary differential equation (with source term entropy
perturbations) which describes the evolution of perturbations in the
total energy density, and a first-order ordinary differential equation
which describes the evolution of entropy perturbations.
The cosmological perturbation theory is applied to a flat FLRW
universe. For large-scale perturbations the entropy perturbations do
not play a role, so that the outcome is in accordance with treatments
in the literature. In the radiation-dominated era small-scale
perturbations grew proportional to the square root of time and
perturbations in the CDM particle number density were, due to
gravitation, coupled to perturbations in the total energy density.
Therefore, structure formation could have begun successfully only
after decoupling of matter and radiation. After decoupling density
perturbations exchanged heat with their environment. This heat
exchange may have enhanced the growth rate of their mass sufficiently
to explain structure formation in the early universe, a phenomenon
which cannot be understood from adiabatic density perturbations.
https://arxiv.org/abs/1410.0211
https://arxiv.org/abs/1601.01260
