exponentially accelerated cosmic expansion drives all objects away from us, and in the future we will think that there would just be the Virgo cluster as an island of galaxies in an otherwise empty Universe. when will that be? (it is funny to imagine that humans then would have historical information about the large-scale structure, but would they believe it?)

with that question we would like to wish our readers a merry Xmas and a happy New Year 2014 and we hope to see you again in January. if you want to contribute to CQW, please drop us a mail at cosmologyquestionoftheweek["AT"]gmail["DOT"]com.

let's rephrase the question a bit: it's asking at what time (or scale factor) in the future would we see an event horizon that is as large as the local group, i.e. roughly 3 Mpc/h, meaning a thousandth of the Hubble scale $\chi_H=c/H_0$ which is 3 Gpc/h. writing down an expression the event horizon at scale factor $a$,

ReplyDelete\begin{equation}

\chi_{eh}(a) = c\int_a^{\infty}\frac{\mathrm{d}a}{a^2H(a)}

\end{equation}

one can determine $a$ by requiring that $\chi_{eh}=10^{-3}\chi_H$, yielding $a\simeq1140$ for $\Lambda$CDM. this scale factor is reached after waiting

\begin{equation}

\Delta t = \int_1^a\frac{\mathrm{d}a}{aH(a)} \simeq \frac{8.1}{H_0}

\end{equation}

which is roughly $10^{11}$ years.