# 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?

• – dmckee --- ex-moderator kitten Jun 18 '14 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. – John Rennie Jun 18 '14 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.

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? – Sebastien Palcoux May 10 '16 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. – JDługosz Jun 6 '17 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 '15 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? – Sebastien Palcoux Sep 10 '15 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. – dmckee --- ex-moderator kitten Oct 26 '15 at 14:33