Finding space-time quanta in the cosmic microwave background: Not so simple

“Final theory” is such a misnomer. The long sought-after unification of Einstein’s General Relativity with quantum mechanics would not be an end, it would be a beginning. A beginning to unravel the nature of space and time, and also a beginning to understand our own beginning – the origin of the universe.

The biggest problem physicists face while trying to find such a theory of quantum gravity is the lack of experimental guidance. The energy necessary to directly test quantum gravity is enormous, and far beyond what we can achieve on Earth. But for cosmologists, the universe is the laboratory. And the universe knows how to reach such high energies. It’s been there, it’s done it.

Our universe was born when quantum gravitational effects were strong. Looking back in time for traces of these effects is therefore one of the most promising, if not the most promising, place to find experimental evidence for quantum gravity. But if it was simple, it would already have been done.

The first issue is that, lacking a theory of quantum gravity, nobody knows how to describe the strong quantum gravitational effects in the early universe. This is the area where phenomenological model building becomes important. But this brings up the next difficulty, which is that the realm of strong quantum gravity is even before inflation – the early phase in which the universe blew up exponentially fast – and neither today’s nor tomorrow’s observations will pin down any one particular model.

There is another option though, that is focusing on the regime of where quantum gravitational effects are weak, yet strong enough to still affect matter. In this regime, relevant during and towards the end of inflation, we know how the theory works. The mathematics to treat the quantum properties of space-time during this period is well-understood because such small perturbations can be dealt with almost the same way as with all other quantum fields.

Indeed, the weak quantum gravity approximation is routinely used in the calculation of today’s observables, such as the spectrum of the cosmic microwave background. That is right – cosmologists do actually use quantum gravity. It becomes necessary because, according to the currently most widely accepted models, inflation is driven by a quantum field – the “inflaton” – whose fluctuations go on to seed the structures we observe today. The quantum fluctuations of the inflaton cause quantum fluctuations of space-time. And these, in return, remain visible today in the large-scale distribution of matter and in the cosmic microwave background (CMB).

This is why last year’s claim by the BICEP collaboration that they had observed the CMB imprint left by gravitational waves from the early was claimed by some media outlets to be evidence for quantum gravity. But the situation is so simple not. Let us assume they had indeed measured what they originally claimed. Even then, obtaining correct predictions from a theory that was quantized doesn’t demonstrate the correct theory must have been quantized. To demonstrate that space-time must have had quantum behavior in the early universe, we must instead find an observable that could not have been produced by any unquantized theory.

In the last months, two papers appeared that studied this question and analyzed the prospects of finding evidence for quantum gravity in the CMB. The conclusions, however, are in both cases rather pessimistic.

The first paper is “A model with cosmological Bell inequalities” by Juan Maldacena. Maldacena tries to construct a Bell-type test that could be used to rule out a non-quantum origin of the signatures that are leftover today from the early universe. The problem is that, once inflation ends, only the classical distribution of the, originally quantum, fluctuation goes on to enter the observables, like the CMB temperature fluctuations. This makes any Bell-type setup with detectors in the current era impossible because the signal was long gone.

Maldacena refuses to be discouraged by this and instead tries to find a way in which another field, present during inflation, plays the role of the detector in the Bell-experiment. This additional field could then preserve the information about the quantum-ness of space-time. He explicitly constructs such a model with an additional field that serves as detector, but calls it himself “baroque” and “contrived.” It is a toy-model to demonstrate there exist cases in which a Bell-test can be performed on the CMB, but not a plausible scenario for our universe.

I find the paper nevertheless interesting as it shows what it would take to use this method and also exhibits where the problem lies. I wish there were more papers like this, where theorists come forward with ideas that didn’t work, because these failures are still a valuable basis for further studies.

The second paper is “Quantum Discord of Cosmic Inflation: Can we Show that CMB Anisotropies are of Quantum-Mechanical Origin?” by Jerome Martin and Vincent Vennin. The authors of this paper don’t rely on the Bell-type test specifically, but instead try to measure the “quantum discord” of the CMB temperature fluctuations. The quantum discord, in a nutshell, measures the quantum-ness in the correlations of a system. The observables they look at are firstly the CMB two-point correlations and later also higher correlation functions.

The authors address the question in two steps. In the first step they ask whether the CMB observations can also be reproduced in the standard treatment if the state has little or no quantum correlations, ie if one has a ‘classical state’ (in terms of correlations) in a quantum theory. They find that for what already existing observables are concerned, the modifications due to the lack of quantum correlations are existent but unobservable.

“[I]n practice, the difference between the quantum and the classical results is tiny and unobservable probably forever.”

They are tentatively hopeful that the two cases might become distinguishable with higher-order correlation functions. On these correlations, experimentalists have so far only very little data, but it is a general topic of interest and future missions will undoubtedly sharpen the existing constraints. In the present work, the authors however do not quantify the predictions, but rather defer to future work: “[I]t remains to generate templates […] to determine whether such a four-point function is already excluded or not.”

The second step is that they study whether the observed correlations could be created by a theory that is classical to begin with, so that the fluctuations are stochastic. They then demonstrate that this can always be achieved, and thus there is no way to distinguish the two cases. To arrive at this conclusion, they first derive the equations for the correlations in the unquantized case, then demand that they reproduce those of the quantized case, and then argue that these equations can be fulfilled.

On the latter point I am, maybe uncharacteristically, less pessimistic than the authors themselves because their general case might be too general. Combining a classical theory with a quantum field gives rise to a semi-classical set of equations that lead to peculiar violations of the uncertainty principle, and an entirely classical theory would need a different mechanism to even create the fluctuations. That is to say, I believe that it might be possible to further constrain the prospects of unquantized fluctuations if one takes into account other properties that such models necessarily must have.

In summary, I have to conclude that we still have a long way to go until we can conclude that space-time must have been quantized in the early universe. Nevertheless, I think it is one of the most promising avenues to pin down the first experimental signature for quantum gravity.