A cosmic shadow on CSL

International audienceThe Continuous Spontaneous Localisation (CSL) model solves the measurement problem of standard quantum mechanics, by coupling the mass density of a quantum system to a white-noise field. Since the mass density is not uniquely defined in general relativity, this model is ambiguous when applied to cosmology. We however show that some well-motivated choices of the density contrast already make current measurements of the cosmic microwave background incompatible with other laboratory experiments. Addressing the measurement (or macro-objectification) problem is a central issue in quantum mechanics, and three classes of solutions have been put forward [1]. One can either (1) leave quantum theory unmodified and consider di↵erent interpretations (e.g. Copenhagen, many worlds, Qbism, etc.); (2) extend the mathematical framework and introduce additional degrees of freedom (e.g. de Broglie-Bohm); or (3) consider that quantum theory is an approximation of a more general framework and that, outside its domain of validity, it di↵ers from the standard formulation. Dynamical collapse models [1-5] follow this last reasoning and introduce a non-linear and stochastic modification to the Schrödinger equation. Remarkably, the structure of this modification is essentially unique. Through an embedded amplification mechanism, this allows microscopic systems to be described by the standard rules of quantum mechanics, while preventing macroscopic systems from being in a superposition of macroscopically distinct configurations. It also allows the Born rule to be derived rather than postulated. Because they lead to predictions that are di↵erent from that of conventional quantum mechanics, dynamical collapse models are falsifiable contrary to the other options mentioned before (except de Broglie-Bohm theory in the out-of-equilibrium regime [6, 7]). Di↵erent versions of dynamical collapse theories correspond to di↵erent choices for the collapse operator (energy, momentum, spin, position), the nature of the stochastic noise (white or non-white) and whether dis-sipative e↵ects are included or not. Only a collapse operator related to position can ensure proper localisa-tion in space, and three iconic theories have been proposed: (1) the Ghirardi-Rimini-Weber (GRW) model, which is historically the first one but is not formulated in terms of a continuous stochastic di↵erential equation, (2) Quantum Mechanics with Universal Position Local-isation (QMUPL), where the collapse operator is position but where the stochastic noise depends on time only, and (3) the Continuous Spontaneous Localisation (CSL) model [4], where the stochastic noise depends on time and space and where the collapse operator is the mass density. This version is the most refined of all three, and features the modified Schrödinger equation d| i= ⇢ iĤdt + p m 0 Z dx p ⇥⇢ sm (x p) h⇢ sm (x p)i ⇤ dW t (x p) 2m 2 0 Z dx p [⇢ sm (x p) h⇢ sm (x p)i] 2 dt | i , (1) whereĤ is the standard Hamiltonian of the system, hÂi ⌘ h |Â| i, is the first free parameter of the theory, m 0 is a reference mass (usually the mass of a nucleon), W t (x p) is an ensemble of independent Wiener processes (one for each point in space), and⇢ sm is the smeared mass density operator ⇢ sm (x p) = 1 (2⇡) 3/2 r c 3 Z dy p⇢ (x p + y p) e |yp| 2 2r 2 c , (2) where r c is the second free parameter of the theory. The two parameters and r c have been constrained in various laboratory experiments. The strongest bounds so far come from X-ray spontaneous emission [8], force noise measurements on ultracold cantilevers [9], and gravitational-wave interferometers [10]. These constraints leave the region of parameter space around r c ⇠ 10 8 10 4 m and ⇠ 10 18 10 10 s 1 viable, where ⌘ /(8⇡ 3/2 r 3 c), corresponding to the white region in Fig. 3. Dynamical collapse models can also be constrained in a cosmological context [11-15]. Indeed, the typical physical scales involved in cosmology are many orders of magnitude di↵erent from those encountered in the lab and this may lead to competitive constraints (in the early universe , energy scales can be as high as ⇠ 10 15 GeV, corresponding to densities of ⇠ 10 80 g ⇥ cm 3). Moreover, one can argue that the quantum measurement problem is even more acute in cosmology than in the lab [16], due to the di culties in introducing an "observer" as in the standard Copenhagen interpretation [17]. Since the quantum state of cosmological perturbations, | 2 sq i, is not an eigenstate of the Cosmic Microwave Background arXiv:1906.04405v1 [quant-ph