The cosmological particle horizon
First published 5 June 2026
Looking at the second figure in the post The expanding universe, you might easily conclude that we shall never see, here on Earth, the galaxy at the right of the diagram, beyond the Hubble sphere. Surprisingly, however, in a uniformly expanding universe like the one illustrated, radiation from all galaxies and particles, unless they are infinitely far away, will eventually reach us. Astronomers can point their radio telescopes in any direction and they can detect what we call the cosmic microwave background (CMB). This radiation was generated a relatively short time after the moment of creation, and last bounced off particles that are currently about 46 billion light-years from us. But how is this possible when the Hubble sphere is only around 14 billion light-years away?
The answer is contained in this diagram, but it needs some work to see it, so bear with me. The space and time gridlines are the same as those in the first diagram of the post The expanding universe and, as before, the rays of space gridlines emanating from the moment of creation cut the horizontal “universe now” – our space axis 13.8 billion years after the moment of creation – at equally spaced intervals of 2 billion light-years. Not counting our own vertical world line, I have drawn 20 dotted space gridlines – which we can think of as world lines for galaxies located on these gridlines – labelling some of them with a “#”, as well as our own vertical world line (the thick vertical line which is our time axis) labelled “#0”. This would mean that the 20th ray would cut the universe-now space axis at a distance of 40 billion light-years from us, but there isn’t room on the right of the diagram to show that. The shading between alternate rays is just cosmetic: it is my attempt to make the diagram seem less cluttered.
If you look closely at the extended pattern of nested sweeping curves, you’ll see that they are in fact chains of straight lines. Each “link” in any individual chain is the left arm of a “V” of a light-cone. I have drawn one such light-cone as a sample, with two thick straight black arrows. In this particular case, the ray and the light-cone are tilted sufficiently far to the right that even the left arm of the “V” is leaning slightly to the right; in other words, that point in space is moving away from our world line at that moment faster than the light could travel back towards us. Elsewhere, only the left arms of light-cones are shown – the thick black arrow of the right arm in the sample light-cone is the one exception. So, summarizing, the diagram shows the progress of light emitted towards us (along the left arms of “V”s of light cones) from a vast range of points in time and space.
The angle of the slant of a light cone depends upon how much the scale factor changes as time increases – to put it colloquially, it is determined by how fast space is expanding between us and the light cone. This speed of recession is constant along any given ray – that is what we mean by “uniformly expanding”. Therefore, all light cones drawn on a given ray will be slanted at the same angle, as you can verify if you look up and down any ray: all of the left arms of the “V”s are at the same angle.
The rows of horizontal dotted lines are time gridlines, separated above and below by unequal times. The separation of any given horizontal time gridline from the one below is determined by the time it takes for light to travel along the left arm of the “V” from its starting point on one ray to the next ray above.
Now we see why radiation from all particles and galaxies will eventually reach us in a uniformly expanding, finite universe. If the universe is not infinite, then even the outermost ray starting out from the moment of creation will not be quite horizontal, and so radiation leaving it will eventually intersect our world line #0. To put it another way, even if light starts out at the moment of creation from the outermost ray, and is emitted in our direction, so that it is on the left arm of the “V”, then it will, in due course, reach the next ray up. It will then proceed in turn to the next ray up, and continue to do so, until it has reached the final ray labelled “#0”. The time when it reaches us at #0 may be in the far distant future, but it will get there in the end, provided that the universe is not infinite.
So, in a finite, uniformly expanding universe, light and radiation emitted towards us at the moment of creation will eventually reach us, even if its initial recession velocity exceeds that of light.
The progress of two such light beams is shown in the figure, outlined in thick, dashed, tear-drop-shaped curves. One light beam was emitted not long after the moment of creation along ray #23 (not shown) and has just reached us here and now, in the form of the microwave background radiation, while the world line of its original ray #23 is currently 46 billion light-years from us. In other words, the space between us and the point where the light started out is now 46 billion light-years away, where, no doubt, galaxies have by now developed just like our own. This black tear-drop-shaped curve is our past light cone. This looks different from the past light cone in the second diagram of Step 2.1 (The block universe), which was precisely a cone, with the vertex pointing upwards. The reason for the tear-drop shape is that, early in the history of the universe, the scale factor was much smaller than today, so that the flaring out of the past light cone was pulled in as if the purse-strings were much tighter close to the beginning.
The second light beam was emitted from ray #19. The rays are too crowded close to the moment of creation to see that clearly, but you can work it out if you start from the dashed curve representing the beam that has just reached us from ray #23. The curve just below that dashed curve (formed from the straight-line “links” just like all of the other curves) must have reached us from ray #22, and, continuing to count down like that, you see that the dashed curve must have reached us from ray #19, around 8 billion years after the moment of creation.
Anything further away than 46 billion light-years lies outside of our past light cone, meaning that, at the present time, we can have no direct knowledge of anything beyond that distance. This distance is called our particle horizon or our cosmological particle horizon, since it represents the boundary of our observable universe today.
However, if the universe is finite, as long as the universe expands uniformly as in the diagram, then radiation from any part of the universe that started out at the moment of creation will eventually reach us, and our particle horizon will extend accordingly.
The same reasoning shows that, even in a spatially infinite universe, if we consider any photon emitted in our direction at any time from any position in the universe (so long as the distance from us to the origin of the photon is finite, and not infinite), then that photon will eventually reach us (if it is not absorbed en route). This is, of course, in a uniformly expanding universe, as above. Wherever the photon starts out on its journey towards us as in the diagram, it will be on a tear-drop-shaped curve which inevitably ends up on our vertical world line.
The notion of a uniformly expanding universe is an ideal picture, and observations suggest that the expansion of the universe appears to have been accelerating over the last five billion years of its 14 billion-year life. This doesn’t invalidate the argument in Step 4.4 (Beyond the cosmological horizon), but it does change the outlook, and in a rather bleak way. The effect of the accelerated expansion would be that, rather than looking forward to new galaxies swimming into our ken as the eons tick by, our skies would instead begin to lose the farthest galaxies as they are swept exponentially beyond our cosmological event horizon.
(Recently, the evidence upon which the accelerating expansion theory was built was questioned on the basis that the brightness of Type-Ia supernovae explosions, while predictable, is now also understood to depend upon the age of the stars involved. This, according to some authors, completely recalibrated the expansion theory so that the expansion of the universe seemed now to be decelerating, and not accelerating. (Son, J., Lee, Y.-W., Chung, C., Park, S., Cho, H. Strong progenitor age bias in supernova cosmology – II. Alignment with DESI BAO and signs of a non-accelerating universe. Monthly Notices of the Royal Astronomical Society 544 975-987 (2025) https://doi.org/10.1093/mnras/staf1685). However, that claim has since been strongly rebutted: Wiseman, P., Popovic, B., Sullivan, M., Riess, A. G., et al. Still accelerating: type Ia supernova cosmology is robust to host galaxy age evolution. Monthly Notices of the Royal Astronomical Society 549 stag 797 (2026) https://doi.org/10.1093/mnras/stag797).)