How Big Is the Observable Universe if It Is 13.8 Billion Years Old?

The universe is about 13.8 billion years old. So it seems obvious that we can see 13.8 billion light-years in every direction and no further. That is wrong, and the reason is one of the most beautiful ideas in cosmology. Space has been expanding while the light was travelling, so the most distant matter we can see is now about 46 billion light-years away. Our character Void Whisperer, the face of dark energy on the Void Whisperer tee, lives at that edge. This post builds on our explainer Why Is the Speed of Light the Limit?, because the speed limit still holds here. It just applies differently.

How old is the universe?

OpenStax Astronomy gives the age of the universe as about 13.8 billion years (OpenStax Astronomy, §29.1^[1]). NASA’s WMAP mission determined it to be 13.77 billion years, to within about half a percent (NASA WMAP^[2]). The Planck satellite’s 2018 analysis, assuming the standard ΛCDM model, gives a Hubble constant of H₀ = 67.4 ± 0.5 km/s/Mpc and a matter density parameter of Ωₘ = 0.315 ± 0.007 (Planck Collaboration, 2018^[3]). We use those Planck values for every calculation below.

What is Hubble’s law?

Galaxies are moving apart, and the further away a galaxy is, the faster the distance to it grows. OpenStax writes the relationship as

v = H₀ D

where v is the recession velocity in kilometres per second, D is the distance in megaparsecs (1 Mpc ≈ 3.26 million light-years) and H₀ is the Hubble constant in km/s/Mpc (OpenStax Astronomy, §26.5^[4]). Georges Lemaître and Edwin Hubble both found this relation in the late 1920s; Hubble published his distance–velocity data in 1929 (Hubble, 1929^[5]). Recedra is our character for this law.

In an expanding universe, v here is the rate at which the proper distance grows. It is not the speed of anything moving through space.

Where is the Hubble sphere?

Push Hubble’s law far enough and v reaches the speed of light c. That happens at the Hubble distance

D_H = c / H₀ ≈ 14.5 billion light-years

where c = 299,792.458 km/s. With Planck’s H₀ this is about 4,450 Mpc, or 14.5 billion light-years (our calculation). The surface at that distance is called the Hubble sphere. Tamara Davis and Charles Lineweaver define it simply as the distance at which recession velocity equals c (Davis & Lineweaver, 2004^[6]).

Galaxies beyond the Hubble sphere are receding faster than light today. That sounds like it breaks relativity, but it does not. Special relativity limits how fast anything can move through space past a local observer. It says nothing to forbid the space between two distant galaxies from growing faster than c. Davis and Lineweaver go further: they show that we can see galaxies that have, and always have had, recession velocities greater than the speed of light, and they explain why this does not violate special relativity (Davis & Lineweaver, 2004^[6]).

Why is the edge 46 billion light-years away?

The edge of what we can see is called the particle horizon. It is how far away, today, is the most distant matter whose light has had time to reach us since the Big Bang. Light from it set out about 13.8 billion years ago, but while it travelled the space behind it kept stretching, so its source is now much further away than 13.8 billion light-years.

To calculate this, you add up each small step of the light’s journey, stretched by the expansion since. In ΛCDM, the expansion rate at redshift z is

H(z) = H₀ √(Ωₘ(1+z)³ + Ω_Λ)

where Ωₘ is the matter fraction and Ω_Λ ≈ 1 − Ωₘ is the dark-energy fraction (radiation is tiny today; we include it in our full calculation). Integrating c / H(z) over all redshifts with Planck’s numbers, our calculation gives:

• Particle horizon (edge of the observable universe): about 46 billion light-years.
• Age of the universe from the same model: about 13.8 billion years.
• A galaxy at z = 1: now about 11.1 billion light-years away, receding at about 0.77c. Its light left about 7.9 billion years ago.
• A galaxy at z = 2: now about 17.3 billion light-years away, receding at about 1.19c.
• The gas that emitted the cosmic microwave background, at z ≈ 1100: now about 45 billion light-years away, receding at about 3.1c.

In this model the present recession speed passes c at a redshift of about 1.5. So a galaxy at z = 2, which telescopes see routinely, is receding faster than light today, exactly as Davis and Lineweaver say.

The cosmic microwave background was released about 380,000 years after the Big Bang (ESA^[7]), so it is the most distant light we can see. It comes from just inside the particle horizon. Our Relicta sticker is the character for that first light, and our earlier post What Is the Cosmic Microwave Background? tells its story.

Is redshift just a Doppler shift?

If you used special relativity’s Doppler formula, z = 1 would mean 0.6c and z = 2 would mean 0.8c, never more than c. Davis and Lineweaver tested that reading against supernova brightness and report that it is ruled out at a confidence level of 23 sigma (Davis & Lineweaver, 2004^[6]). Cosmological redshift is better read as the stretching of light by expansion. How best to describe it in words is still argued about; that debate is the subject of a separate post.

What is the cosmic event horizon?

There is a second horizon, and it points to the future. Since 1998 we have known that the expansion is accelerating (Riess et al., 1998^[8]; Nobel Prize 2011^[9]). NASA describes dark energy as the cause and estimates it at about 68% of the universe (NASA^[10]). In an accelerating universe, light emitted today by galaxies beyond a certain distance will never reach us, however long we wait. Our calculation puts this event horizon at about 16.7 billion light-years.

So the galaxies we can see right now, between 16.7 and 46 billion light-years away, are ones whose old light still reaches us but whose present-day light never will. It is an open question in cosmology whether dark energy is truly a constant; our numbers assume it is.

Does any of this break the speed of light?

No. Every photon that reaches us travelled locally at exactly c the whole way. Nothing ever overtakes a light beam next to it. What grows faster than c is a distance between far-apart objects, which special relativity does not restrict. The speed limit is local, and it is never broken.

Quick FAQ

How big is the observable universe?

Its radius is about 46 billion light-years in proper distance today, so its diameter is about 92 billion light-years.

Why is it bigger than 13.8 billion light-years?

Because space expanded while the light travelled, carrying its source further away.

Do galaxies really recede faster than light?

Yes, beyond the Hubble sphere at about 14.5 billion light-years. This is the growth of distance, not motion through space, so it does not break relativity.

Will we eventually see the whole universe?

No. Because the expansion is accelerating, galaxies beyond the event horizon will never send us their present-day light.

References

1. A. Fraknoi, D. Morrison & S. C. Wolff, Astronomy 2e (OpenStax, Rice University), §29.1 “The Age of the Universe”. https://openstax.org/books/astronomy-2e/pages/29-1-the-age-of-the-universe
2. NASA WMAP Science Team, “Will the Universe Expand Forever?” / universe shape and age overview. https://wmap.gsfc.nasa.gov/universe/uni_shape.html
3. Planck Collaboration (2020), “Planck 2018 results. VI. Cosmological parameters,” A&A 641, A6 (arXiv:1807.06209). https://arxiv.org/abs/1807.06209
4. A. Fraknoi, D. Morrison & S. C. Wolff, Astronomy 2e (OpenStax, Rice University), §26.5 “The Expanding Universe”. https://openstax.org/books/astronomy-2e/pages/26-5-the-expanding-universe
5. E. Hubble (1929), “A relation between distance and radial velocity among extra-galactic nebulae,” PNAS 15, 168–173 (DOI 10.1073/pnas.15.3.168; metadata verified via Crossref). https://doi.org/10.1073/pnas.15.3.168
6. T. M. Davis & C. H. Lineweaver (2004), “Expanding Confusion: Common Misconceptions of Cosmological Horizons and the Superluminal Expansion of the Universe,” Publ. Astron. Soc. Aust. 21, 97–109 (arXiv:astro-ph/0310808). https://arxiv.org/abs/astro-ph/0310808
7. ESA, “Planck and the cosmic microwave background”. https://www.esa.int/Science_Exploration/Space_Science/Planck/Planck_and_the_cosmic_microwave_background
8. A. G. Riess et al. (1998), “Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant,” Astron. J. 116, 1009–1038 (arXiv:astro-ph/9805201). https://arxiv.org/abs/astro-ph/9805201
9. NobelPrize.org, The Nobel Prize in Physics 2011 (Perlmutter, Schmidt, Riess). https://www.nobelprize.org/prizes/physics/2011/summary/
10. NASA Science, “Dark Energy”. https://science.nasa.gov/dark-energy/

Written by Pixelated Physics. Every factual claim is linked to the source we checked; points that are still debated are labelled open.