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My understanding is that quasars are the early phase of formation of galaxies.

At the time quasars were forming, the universe would have been smaller and therefore things closer to each other.

About how close would quasars have been to each other?

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That's an image of two quasars, very close to each other, "separated on the sky by only about 70 thousand light years".

According to this paper the peak density should have been about $10^{-6}$ quasars per Mpc, resulting in a peak mean distance between two quasars of about 100 Mpc. (Density of $10^{-6}$ quasars per Mpc results in one quasar per cube of $10^6 Mpc^3$, hence on average one quasar each $\sqrt[3]{10^6 \mbox{Mpc}^3}=100 \mbox{ Mpc}$)

With about 1 million known quasars in the observable universe I get a mean distance of about half that distance. (With a considered light-travel distance of about $4 \mbox{ Gpc} = 4\cdot 3.26 \mbox{ Gly} = 13.04\mbox{ Gly},~~$ a little less than the 13.81 Gly light travel radius of the observable universe, the volume of a sphere with this radius is about $\frac{4}{3}\pi(4\cdot 10^3 \mbox{Mpc})^3=2.68\cdot 10^{11}\mbox{Mpc}^3$. With 1 million quasars, it's about one quasar per $268000 \mbox{ Mpc}^3$ or one quasar per $\sqrt[3]{268000 \mbox{ Mpc}^3}=64\mbox{ Mpc}$ in one dimension. Due to non-constant quasar frequency over cosmic time, the minimum mean distance should have been below this overall average distance. Using the light-travel distance considers the higher density of the earlier universe better than the comoving distance of 13.8 billion years after big bang. 4 Gpc are used as light travel radius to restrict roughly to redshift z < 7, the range where quasars have been observed. A redshift calculator can be found e.g. here, take $H_0=70.4$, $\Omega_m = 0.265$, $\Omega_{\Lambda}=0.728$, and $z=7$.)

The peak number density seems to be somewhere between a redshift of 2.0 and 2.5 (interpreting the paper). If it will turn out by future observations, that the peak number density has been earlier in the universe, we get much shorter peak mean distances.

So you have at least an order of magnitude: Somewhere between 150 and 300 million lightyears (between 50 and 100 Mpc, 1 parsec equals 3.26 lightyears) should have been the peak average distance between two quasars. Might be this estimate will shrink over time, as more (distant) quasars get known.

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Could you include your calculations in your answer? –  astromax Feb 24 at 5:36
    
@astromax Provided calculations, the estimates have been based upon. –  Gerald Feb 26 at 15:32
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Quasars are simply Active Galactic Nuclei (AGN) viewed from the correct inclination angle from the earth. Quasars are not "the early phase of formation of galaxies." It is currently thought that most galaxies (if not all) contain a supermassive black hole at their center -- for example, at the center of the Milky Way resides Sagittarius A* (Sgr A*), which is thought to be a black hole with mass of $\sim \!4.6 \times 10^6$ solar masses! However, Sgr A* is currently not active.

The answer to your question is that AGN are generally only as close as galaxies are to each other. It is true when the universe was younger, galaxies were closer together. However, as Gerald's link shows, galaxies are still colliding today, so occasionally AGN can become very close and can even merge to form an even larger supermassive black hole.

Also note according to our current understanding of the history of the universe, galaxies and AGN did not form right away. In order for galaxies to form, perturbations of dark matter had to develop which accreted baryonic matter, which then cooled and condensed to form galaxies. The formation of supermassive black holes also takes time. First, you have to create a black hole, which are formed from core-collapse supernovae of stars. Then that black hole has to accrete mass to become large, and smaller black holes are actually less efficient at accreting mass from surrounding gas clouds than bigger ones are. Therefore, there was never a period where most supermassive black holes (and thus quasars) were ever right on top of each other.

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In your explanation of the formation of black holes you are assuming the non-existence of primordial black holes. Have primordial black holes been ruled out as the progenitors of the supermassive black holes at the centers of galaxies we see today? –  astromax Feb 24 at 5:40
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