Bell violation in the sky

Abstract

In this work, we have studied the possibility of setting up Bell's inequality violating experiment in the context of cosmology, based on the basic principles of quantum mechanics. First we start with the physical motivation of implementing the Bell inequality violation in the context of cosmology. Then to set up the cosmological Bell violating test experiment we introduce a model independent theoretical framework using which we have studied the creation of new massive particles by implementing the WKB approximation method for the scalar fluctuations in the presence of additional time-dependent mass contribution in the cosmological perturbation theory. Here for completeness we compute the total number density and the energy density of the newly created particles in terms of the Bogoliubov coefficients using the WKB approximation method. Next using the background scalar fluctuation in the presence of a new time-dependent mass contribution, we explicitly compute the expression for the one point and two point correlation functions. Furthermore, using the results for a one point function we introduce a new theoretical cosmological parameter which can be expressed in terms of the other known inflationary observables and can also be treated as a future theoretical probe to break the degeneracy amongst various models of inflation. Additionally, we also fix the scale of inflation in a model-independent way without any prior knowledge of primordial gravitational waves. Also using the input from a newly introduced cosmological parameter, we finally give a theoretical estimate for the tensor-to-scalar ratio in a modelindependent way. Next, we also comment on the technicalities of measurements from isospin breaking interactions and the future prospects of newly introduced massive particles in a cosmological Bell violating test experiment. Further, we a

Bell Violation in Primordial Cosmology

“…We know that in the theory of inflation, all such fluctuations become classical in nature as they exit the horizon, and inside the horizon, all of them are quantum in nature. In de Sitter space, 3 → 0 as ηk → 0 at the end of inflation, which is the signature of Bell inequality violation in our cosmological setup. Hence, when reheating occurs after inflation, a classical measure can be written down, or more precisely, a classical probability distribution function of fluctuation, as follows:…”

“…Effect of the massive particles on the scalar curvature fluctuations can be described if we take the second-order action derived as [3]:…”

“…Here it is important to mention that one can treat a measurement as a specific unitary evolution of the combined effect of physical system as well as measuring apparatus. Such physical states can be visualized as classical objects in the context of cosmology, and in a direct sense are not very useful (for more detail, see References [2,3]). Here we need to follow a few steps to overcome the difficulties [3].…”

“…See Figure 3, where we have shown the behaviour of all the toy models of mass profile for massive particles with conformal time scale. The equation of motion for the massive field is [3].…”

“…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.…”