Bell Violation in Primordial Cosmology

Bell Violation in Primordial Cosmology According to the inflationary model, the primordial fluctuations which we see in CMB (Cosmic Microwave Background) were produced by quantum mechanical effects in the early universe. These fluctuations are the origin for the formation of large-scale structure, but the fluctuations we observe at present are actually classical in nature. The highly-entangled quantum mechanical wave function of the universe plays a very important role during quantum mechanical interpretation of the required fluctuations. Hence, one can use the Hartle–Hawking wave function in de-Sitter space. Due to this fact, quantum mechanical fluctuations can be theoretically demonstrated, and can also be implemented in the context of primordial cosmology—if and only if we perform a cosmological experiment using the highly-entangled quantum mechanical wave function of the universe which is defined in inflationary period and eventually violate Bell’s inequality [1]. To describe the background methodology, it is important to mention that in the context of quantum mechanics, Bell test experiment can be described by the measurement of two non- commutating physical operators. These operators are associated with two distinct locations in space-time. Thus, using same analogy in the context of primordial cosmology, we can perform cosmological observations on two spatially separated and causally disconnected places up to the epoch of reheating (after inflation). During these observations we can measure the numerical values of various cosmological observables (along with cosmic variance), and can also be computed from scalar curvature fluctuation. However, it is important to note that for all such observations, we cannot measure the value of associated canonically conjugate momentum. Hence, for these cosmological observables, we cannot measure the imprints of two non-commuting operators in primordial cosmology. There is subtle point, however, which is that if these observables satisfy the minimum requirements of decoherence effect, then we can possibly perform measurements from two exactly commuting cosmological observables, and therefore we will be able to design a Bell’s inequality violating cosmological experimental setup. We know that in quantum theory, to design such an experimental setup one has to perform a number of repeated measurements on the same object (which in this context is the same quantum state of the universe), and therefore in such a physical situation we can justify the appearance of each and every measurement using a single quantum state. In the case of primordial cosmology, we can do the same thing; that is, consider two spatially-separated portions in the sky which plays the same role of performing repeated cosmological Bell’s inequality violating experiment using the same quantum mechanical state. Therefore, we have the advantage of choosing the required properties of two spatially-separated portions in the sky in order to setup Bell’s inequality violating experimental setup. It is completely possible to set up a Bell’s inequality violating cosmological experimental setup if we can find a link which connects these non-commutating cosmological observables and classical probability distribution function originated from model of inflation (see Reference [2,3,4] for more details). In this article, we explore this possibility in detail. See also References [5,6,7,8], where the authors have also studied various consequences of the violation of Bell’s inequalities in other areas.