sixth post by Youness in the "Planck's summer"-series on CQW:

The cosmological constant $\Lambda$, according to our current physical understanding, really constant in time or has its value changed? Think about the question from a quantum field theory perspective.

With that, we wish our readers a nice summer holiday and hope that you join our blog again in October! And many thanks to you, Youness, for providing this awesome set of questions.

Here's the textbook answer by Youness: In fact, the cosmological constant is not constant and has evolved in the very early Universe to eventually harden and take on the value it has today. The reason is that the effective (or 'observable') cosmological constant is a sum of several contributions.

ReplyDeleteFirst, you are all aware of the degree of freedom in general relativity to include a cosmological constant term on the left-hand of Einstein's field equations. Let's assume this term is constant once classical gravity is a good description of space-time (after the Planck epoch). Second, zero-point fluctuations of quantum fields act as an energy density of the vacuum and thus add to the effective cosmological constant. These contributions are somewhat controversial as they suggest an effective cosmological constant of the order of our cutoff scale, which might be as high as the Planck scale.

But third, there are 'classical' contributions to the cosmological constant just given by fields sitting in the potential minimum. For example, you are familiar with the Higgs mechanism and the famous Mexican hat potential. Before the electroweak phase transition, the effective potential was not a Mexican hat but rather had only one minimum at a zero vacuum expectation value. Then, during the electroweak phase transition, the effective mass term became negative and the Mexican hat formed, the field rolled down into a new minimum. The value of the potential has thereby changed, and this corresponds to a change in the effective cosmological constant by $\Delta \rho_\Lambda = -\frac{1}{8} m_H^2 v^2 \approx 10^8 \text{GeV}^4$. And keep in mind: the presently observed cosmological constant is only at $\rho_\Lambda \approx 10^{-47} \text{GeV}^4$!

This illustrates why the cosmological constant problem is so puzzling. The 'primordial' cosmological constant was not tiny. But the various distinct contributions from phase transitions in the very early Universe added up to lead to an extremely small cosmological constant in the late Universe.