# How far would EGSY8p7 be away now?

Apparently EGSY8p7 is the object with the longest light travel distance, 13.2 gly or a redshift of z = 8.68 (Wikipedia). So the light took 13.2 billion years to travel to us from that object, but we know that the universe has expanded since (I believe with an expansion rate that varied over time). So given our current theories of how the universe expanded, is it possible to calculate the theoretical distance of that object to us right now?

I assume it must be close to what is believed the radius of the observable universe (46.5 Gly) but how would one go about to calculate this?

30.4 billion lightyears.

The current distance — i.e. the distance that one would measure if we froze the Universe and started laying out measuring rods — is called the proper distance, or physical distance, in astronomy. By definition, it corresponds today to another often-used term in astronomy, namely the comoving distance. While the former increases with time, the latter is defined in a coordinate system that expands with the Universe, and so is constant at all times.

That is, the comoving distance to EGSY8p7 was the same when the Universe was half the size of what it is today, but the proper distance was half of this.

For galaxies so distant as EGSY8p7, we don't measure distances directly. Instead we measure the redshift of some spectral absorption or emission lines, and then use a model of the expansion of the Universe to convert this redshift to a distance.

From the FLRW metric, the resulting distance today of an object at redshift $z$ is given by $$d_C = \frac{c}{H_0} \int_0^z dz' \frac{1}{\sqrt{\Omega_r(1+z)^4 + \Omega_m(1+z)^3 + \Omega_k(1+z)^2 + \Omega_\Lambda}},$$ where $c$, $H_0$, and $\{\Omega_r,\Omega_m,\Omega_k,\Omega_\Lambda\}$ are the speed of light, Hubble constant, and density parameters of the various components of the Universe, respectively.

For $z=8.68$ and with the latest cosmological parameters from Planck Collaboration et al. (2016), this integral evaluates to $d_C = 30.4\,\mathrm{Glyr}$.

For $z\rightarrow\infty$, you get $d_C = 46.3\,\mathrm{Glyr}$, which is "the edge of the observable Universe", also known as the particle horizon.

Note though that EGSY8p7 no longer holds the redshift record. The galaxy GN-z11 (Oesch et al. 2016) has a redshift of $z=11.09$, corresponding to a distance of $d_C = 32.2\,\mathrm{Glyr}$.

• Thank you so much, this is answer is exactly what I wanted to know, makes me very happy!
– jpp1
Jul 12 '18 at 13:49
• @Johsm You're very welcome! You may consider conveying your happiness into accepting the answer ;-)
– pela
Jul 12 '18 at 15:29