Abstract
The nonclassicality of primordial gravitational waves (PGWs) is characterized in terms of sub-Poissonian graviton statistics. The sub-Poissonian statistics are realized when quantum states are squeezed coherent states. In the presence of matter fields, the Universe experiences the squeezed coherent state during inflation. The condition to realize the sub-Poissonian graviton statistics is translated into the frequency range of gravitational waves. If the initial state is the Bunch-Davies vacuum, there is another necessary condition between phases of squeezing and coherent parameters. Here, we extend the initial state to entangled states. We consider $\alpha$-vacua as the initial entangled state that are more general de Sitter invariant vacua than the Bunch-Davies vacuum. We find that, unlike the Bunch-Davies vacuum, PGWs generated in the initial entangled state become sub-Poissonian without requiring the condition between the phases.
Highlights
One of the greatest achievements of inflationary cosmology is that the connection between the quantum theory of the microscopic world and the large scale structure of the macroscopic world
We found that the presence of matter fields during inflation makes graviton statistics subPoissonian
We explored the conditions for primordial gravitational waves (PGWs) to be nonclassical
Summary
One of the greatest achievements of inflationary cosmology is that the connection between the quantum theory of the microscopic world and the large scale structure of the macroscopic world. We characterize nonclassicality of PGWs in terms of sub-Poissonian graviton statistics as is known in quantum optics [14]. In our previous work [15], we studied graviton statistics of the inflationary Universe when the initial state is the Bunch-Davies vacuum. We show that unlike the Bunch-Davies vacuum, PGWs generated in the initial entangled state become subPoissonian without requiring the condition between phases. In Appendix A, we give some formulas used in the computation in Sec. V, Appendix B gives short notes on useful relations between coherent and squeezing operators, and Appendix C contains the details of the result of graviton statistics in the initial entangled state
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