\documentclass[border=10pt]{standalone}
\usepackage{pgfplots, tikz, amsmath}
\usepackage{filecontents}

\usepgfplotslibrary{colorbrewer}
\usepgfplotslibrary{fillbetween, external}

\definecolor{blueish}{RGB}{48,140,43}

\begin{document}
\begin{tikzpicture}
  \begin{axis}[
 	ylabel={$A(t)/\pi R_o^2$},
	xlabel= $t/T$,
	width = 6cm,
	height = 4.5cm,
	xmin=0,
	xmax=1,
%	cycle list/Paired-5,
	minor tick style={draw=none}
	]
%      \addplot +[blueish, thick, mark options={fill=blueish,scale=0.05}] table[x=x,y=y] {./data/AreaAverage.txt};
      \addplot +[blueish, thick, no marks] table[x=x,y=y] {./data/AreaAverage.txt};
      \addplot [name path=upper,draw=none] table[mark options={fill=blueish,scale=1}, x=x,y expr=\thisrow{y}+\thisrow{err}] {./data/AreaAverage.txt};
      \addplot [name path=lower,draw=none] table[mark options={fill=black,scale=1}, x=x,y expr=\thisrow{y}-\thisrow{err}] {./data/AreaAverage.txt};
      \addplot [fill=black!10] fill between[of=upper and lower];

  \end{axis}
\end{tikzpicture}

%\input{rhoAnt.tex}
\end{document}