deletions | additions       diff --git a/Accretion law.tex b/Accretion law.tex  index d7a939f..39b7cbd 100644  --- a/Accretion law.tex  +++ b/Accretion law.tex 
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\subsubsection{The \section{The growing Universe}  \subsection{The  accretion law} law}\label{accretion_law}  In literature the universe's expansion is regarded as the expansion of a spherical surface.\\ surface \cite{milne1935}.\\  We see galaxies immersed in a 3-dim space. increasing volume, however, the cosmological principle imposes galaxies placed above a surface. If we add the time at every point of the universe, we obtain a 4-dim spherical surface.\\  If $n$ is the increasing number of steps for each axis, the expansion will be obtained through the relation $N = n^2$, where $N$ are the points on the \emph{increasing} spherical surface that rises with the growing number of points on the radius $R$, following the law $S = 4\pi R^2$.\\  Therefore a universe that \emph{would increases in space}, according to the law $N = n^2$, with $N$ the number of particles and $n$ the number of \emph{time-steps}, would increase \emph{surface} as happens to an expanding spherical surface.\\  However, in an isotropic universe any local observer $O$ puts himself at the center of a sphere with radius $R_i$ and places on its surface the distant galaxies.\\  (figure)\\ % \label{fig_increasing_spacetime}  An observer sees galaxies move away radially in a 3d space, but describes the isotropic expansion as dilatation of a 2d surface.\\  In a universe with increasing space, the radius $R_i$ of any lattice-universe $U_i$ would increase as $R_i (n) = n \lambda_i$. It follows:  \begin{equation}