Historical research guide · 0451 · 2022
Casimir cosmology
Ulf Leonhardt
In one minute
Ulf Leonhardt, at the Weizmann Institute, writes an introduction to cosmology for people who work on Casimir forces, and hands them an invitation. Dark energy is about 70 percent of everything there is, and the textbook estimate of the vacuum energy that is meant to explain it overshoots the measured value by 120 orders of magnitude. Leonhardt’s answer is that the estimate was never the right calculation. Renormalisation is routine in laboratory Casimir physics, where leaving it out would contradict measurements; do the same in cosmology using Lifshitz theory, and what is left is not zero but a cosmological constant of exactly the right size. He then argues that this constant need not be constant. An expanding universe plays the part a moving mirror plays in the dynamical Casimir effect, so the vacuum energy follows the rate of expansion — and with the cut-off set at the Planck length, the drift it predicts matches the gap between the two rival measurements of the Hubble constant to one percent.
Connection
Chapter 2 holds that the vacuum is a real, structured medium and that the energy driving cosmic expansion is the energy filling space; this is that identification made quantitatively, by the physicist who did the calculation, using the same Lifshitz theory that predicts laboratory Casimir forces. Chapter 13 needs one picture that covers the laboratory bench and the sky at once, and Leonhardt supplies the sentence that joins them: curved spacetime appears to light as a dielectric medium, so the physics of two plates and the physics of an expanding universe are the same physics. The calculation itself is on this site at /library/stm-748797c2ce.
From the source
About 95 percent of the current content of the universe is of unknown nature: dark matter accounts for roughly 25 percent of the total mass density and dark energy, described by Einstein’s cosmological constant, for about 70 percent. Estimates of the vacuum energy from quantum field theory come out 120 orders of magnitude higher than the measured value, but those estimates rest on a naive picture of vacuum fluctuations, while experimental and theoretical work on the Casimir effect has taught us a great deal more about what vacuum fluctuations actually do.Section 1, Introduction, first paragraph
The 120 orders of magnitude disappear once the quantum vacuum is renormalised — a step that is normal in practical Casimir physics, and whose absence would contradict experimental facts. What remains after renormalisation in cosmology is neither exactly zero, as the simple calculation would say, nor approximately zero, as laboratory experience with nanoscale forces would suggest: it is a cosmological constant of exactly the right order of magnitude, consistent with the astronomical data up to the precision of that data.Section 1, Introduction, second paragraph, citing the Lifshitz theory of the cosmological constant
There is no credible evidence that the cosmological constant is absolutely constant. As far as the constant is concerned all the Cosmic Microwave Background data condense into a single number, the scale of the correlation curve, and one data point cannot prove constancy. The usual theoretical argument — that the vacuum must be generally covariant, so its energy-momentum tensor must be constant — fails on its premise: the vacuum is frame-dependent, as the Unruh-Fulling-Davies effect shows, where the vacuum state of Minkowski space appears as thermal radiation to an accelerated observer. The vacuum is an unusual substance, one that does not resist uniform motion but does resist acceleration.Section 5, Hubble tension, paragraphs on the evidence for a constant Lambda
The mechanism is the dynamical Casimir effect written on a cosmic scale. Curved spacetime appears as a dielectric medium to electromagnetic fields, so Casimir theory applies; space is homogeneous but expands in time, and a varying scale factor creates a vacuum energy that depends on the derivatives of that scale factor rather than on the scale factor alone. That makes the vacuum energy non-adiabatic, unlike the radiation and matter densities, so an extra term with pressure equal to minus its own energy density must be added to keep the energy balance — a cosmological term that carries the signature of the cosmological constant but varies, and becomes genuinely constant only in the far future when expansion is exponential and the vacuum energy tends to zero.Section 5, Equations 54, 55 and 56
The theory produces the disputed number. The Hubble constant measured directly from the distance ladder is 73.04 plus or minus 1.04 kilometres per second per megaparsec, at 5 sigma from the value inferred from the Cosmic Microwave Background — a gap of 8.4 percent that has been called the biggest crisis in contemporary astrophysics. Fixing the integration constant to fit the angular scale of the Cosmic Microwave Background and taking the cut-off at exactly the Planck length, about ten to the minus thirty-five metres, the most naive model gives a theoretical variation of the Hubble constant that agrees with the latest data to 1 percent, the precision of the data itself.Section 5, Equations 53 and 57 and the closing paragraph
Leonhardt names six things that would settle it: account for the Hawking partners created on the far side of the cosmological horizon, which is not an event horizon, so they eventually arrive; explain why quantum electromagnetism alone seems to fit the bill and the other fields of the standard model stay silent; analyse the astronomical data more consistently across the Cosmic Microwave Background, baryon acoustic oscillations, supernovae and lensing; test whether the other, subtler tensions at about 3 sigma resolve the same way; run laboratory analogues — the anomaly behind the cosmological constant can be tested with ultracold atoms, and the connection between the Gibbons-Hawking effect and the dynamical Casimir effect can be explored on a bench; and put the renormalisation method on a better foundation, which means finally developing the Casimir theory of inhomogeneous media.Section 6, Outlook
The way in
https://arxiv.org/abs/2202.03862How to cite it
Ulf Leonhardt (2022) Casimir cosmology doi:10.1142/S0217751X22410068