Earliest Structures in the Universe can be explained by a Relativistic Cosmological Perturbation Theory

Abstract

A relativistic cosmological perturbation theory for the Friedmann-Lemaître-Robertson-Walker universe is presented that explains the masses and formation times of the first structures in our universe. First, it is shown that, without a coordinate system being used, quantities intended to represent energy density and particle number density perturbations can be defined in only one way. The Newtonian limit, where the pressure becomes zero, proves that these quantities are indeed the perturbations of the energy density and the particle number density. Then, after selecting a reference frame, a perturbation theory will be formulated based on these quantities. This formulation considers the local perturbation to the spatial curvature resulting from a density perturbation, the local fluid velocity due to pressure gradients caused by the self-gravity of the density perturbation, and entropy perturbations, all of which are necessary for structure formation. Pressure perturbations consist of two components: an adiabatic component caused by the density perturbation itself, and a random, nonadiabatic component resulting from the rapid, chaotic transition to the era when matter and radiation were decoupled. Immediately after decoupling, negative nonadiabatic pressure perturbations in various density perturbations enabled their rapid growth over a short period of time. This brief period ended when the total pressure perturbation became positive. Subsequently, the density perturbations gradually grew toward their nonlinear phase, which was reached early on.

Figures (2)

• Figure 1: The graphs show the redshift and time when a relative perturbation in the energy density with initial scale $\lambda_{\text{dec}}$, and initial values $\delta_\varepsilon(t_{\text{dec}},\bm{q})\approx10^{-5}$ and $\delta^\prime_\varepsilon(t_{\text{dec}},\bm{q})=0$ starting to grow at an initial redshift of $z(t_{\text{dec}})=1090$ has become nonlinear, i.e., when $\delta_\varepsilon(t,\bm{q})=1$. The graphs are labeled with the initial values of the random, nonadiabatic pressure perturbations $\delta_T(t_{\text{dec}},\bm{q})$. For each graph, the Jeans scale is $6.4\,\text{pc}$.
• Figure 2: The graphs show the growth rates $\delta^\prime_\varepsilon$, with initial values $\delta_\varepsilon(t_{\text{dec}},\bm{q})\approx10^{-5}$ and $\delta^\prime_\varepsilon(t_{\text{dec}},\bm{q})=0$, as function of the redshift $z$, or time in million of years. The initial scales $\lambda_{\text{dec}}$ of the perturbations are measured in parsec. The evolution of relative density perturbations started at $z=1090$.