# Can the cosmological constant change with time?

This post is a specialization of the post: Can the proportion of dark energy change?

Can the cosmological constant change with time?

If so, is there a measurement of this evolution up to now, and a prediction for future?
How measure such a change?

• Jun 18, 2014 at 15:37
• @dmckee: I don't think Sébastien is asking about fundamental constants changing. At least, that's not how I interpret the question. Jun 18, 2014 at 17:58

The cosmological constant is the parameter $\Lambda$ in the Einstein equation:

$$G_{\mu\nu} + \Lambda g_{\mu\nu} = 8\pi T_{\mu\nu}$$

and it is by definition a constant, so it cannot change. I think it is best regarded as a geometrical property of the universe (though other views exist) which is why it's normally put on the left hand side of the equals sign.

However the observed acceleration of distant galaxies may be due not to a cosmological constant but to a scalar field called quintessence. This can change, and indeed there have been lots of theories about might be generating the quintessence field, what its properties are and how it might change with time.

To study this, attempts are being made to get very detailed data on the galaxy distance — recession velocity relationship. In principle the exact form of this could distinguish between a cosmological constant and quintessence.

If you're interested in pursuing this further Lawrence Krauss' book is a good starting point.

To expand a bit on John's answer above. Even though the cosmological constant is as its name promises - a constant - there is no way (at least to my knowledge) to independently measure it.

The cosmological constant we measure in observations is acctually composed of two parts: one being the constant geometric factor $\Lambda g_{\mu\nu}$ in Einsteins equation and the second being due to vacuum energy of matter-field which gives rise to a term $\rho_{\rm vac} g_{\mu\nu}$ on the right hand side of the Einsteins equation. This leads to

$$\Lambda_{\rm eff} = \Lambda + \rho_{\rm vac}$$

This fact is what gives rise to the cosmological constant problem. The second term can be estimated from quantum field theory and gives a value $10^{60}-10^{120}$ times the measured value (a more precise value depends on unknown high energy physics) so unless there exist some symmetry in nature that forces $\rho_{\rm vac} = 0$ we need a huge cancellation between the two terms in the equation above (to 60-120 decimal places). See http://arxiv.org/abs/1205.3365 for a great review on the CC problem.

Now to answer the question: even though $\Lambda$ is a true constant, $\rho_{\rm vac}$ can indeed change with time for example under phase-transitions in the early universe (see e.g. http://arxiv.org/abs/astro-ph/0409042). However at our present time we expect the measured value $\Lambda_{\rm eff}$ to be constant.

I realize I may be conflating the cosmological constant with the Hubble constant, here, but this may be what was the intended by the question.
Perhaps someone can articulate why/how these two constants are different from each other.

I am not a physicist, but studied physics for my mechanical engineering degree. Years ago a physicist told me that the "rate" of expansion of the inverse was decreasing, in other words, the rate of acceleration of the universe is decreasing (2nd derivative of velocity is negative). I have been curious about this ever since. According to a Forbes article published in 2018 (written by Ethan Siegel), this does seem to be the case. While the Hubble constant may be constant over space, it is not constant over time. Here is an excerpt from the article ("Surprise! The Hubble Constant Changes Over Time"):

"Only over the past 6 billion years or so has dark energy become important, and we've now reached the time where it's fast becoming the only component of the Universe that has an impact on our expansion rate. If we went back to a time when the Universe was half its present age, the expansion rate was 80% greater than it is today. When the Universe was just 10% of its current age, the expansion rate was 17 times greater than its present value. But when the Universe reaches 10 times its current age, the expansion rate will only be 18% smaller than it is today.

This is due to the presence of dark energy, which behaves as a cosmological constant. In the far future, matter and radiation will both become relatively unimportant compared to dark energy, meaning that the Universe's energy density will remain constant. Under these circumstances, the expansion rate will reach a steady, finite value and stay there. As we move into the far future, the Hubble constant will become a constant not only in space, but in time as well.

In the far future, by measuring the velocity and distance to all the objects we can see, we'd get the same slope for that line everywhere. The Hubble constant will truly become a constant.

If astronomers were more careful about their words, they would have called H the Hubble parameter, rather than the Hubble constant, since it changes over time. But for generations, the only distances we could measure were close enough that H appeared to be constant, and we've never updated this. Instead, we have to be careful to note that H is a function of time, and only today — where we call it H0 — is it a constant. In reality, the Hubble parameter changes over time, and it's only a constant everywhere in space. Yet if we lived far enough in the future, we'd see that H stops changing entirely. As careful as we can be to make the distinction between what's actually constant and what changes now, in the far future, dark energy ensures there will be no difference at all."

It changes. In fact, after 3000 billion years, the constants will have changed so much that all the current structures in the universe will be destroyed, including quarks and electrons.

• Can you prove this statement? May 10, 2016 at 6:54
• As another answer points out, if what we currently term “dark energy” changes over time, then that is not identified as the Cosmological Constant. Your answer, besides stating speculative and no longer serious ideas as ratified, is confusing the semantic question with the effect stipulated in the OP. Jun 6, 2017 at 15:23

Yes it changes. In this case 'dark enargy' is uneccessary. The cosmologicam model which is based on a changing Λ explaines the astronomical data perfectly.Read on this link for more details https://www.scribd.com/doc/279174920/Decreasing-Mass-Cosmology-and-the-Accelerating-Expansion-of-the-Universe Dimitri Deliyiannis.

• This strikes me as just personal speculation more than anything else.
– Sean
Sep 10, 2015 at 9:56
• Do you plan to submit your paper to a peer-reviewed journal? If yes, when? If no, why? If already done, what happened? Sep 10, 2015 at 13:27
• I am going to delete the other two instances of this answer, as we strongly discourage copy-n-past answer which these surely are. Oct 26, 2015 at 14:33