Quantum entanglement and cosmological Friedmann equations

Quantum entanglement the most important part of quantum information theory, represents the intrinsic property of quantum states. It is a magical physical phenomenon in the form of nonlocality in the multi quantum system. The entanglement entropy as a measure of quantum information, has become an important tool, which provides a new research method for various subjects in physics. The study of the notion of quantum entanglement can provide a tool for understanding the cosmological features.In this work, we consider the cosmological applications of the entanglement in order to understand the cosmological dynamics from the entanglement point of view. The relation between the quantum information theory and the cosmology is studied. Employing Fermi normal coordinates (FNC) and conformal Fermi coordinates, we establish a relation between Friedmann equations of Friedmann-Lemaitre-Robertson-Walker universe and entanglement. Assuming that the entanglement entropy in a geodesic ball is maximized in a fixed volume and the entanglement is the basic element of the spacetime, we derive Friedmann equations from the first law of entanglement. Friedmann equations are first derived in the Fermi normal coordinate system, where the diamond size l is much smaller than the local curvature length, but still much larger than Planck scale lp. If the diamond size is comparable to the UV scale lUV, the quantum gravity effect becomes strong. Then we extend the discussion about the area deficit of the geodesic ball so that a freely falling observer can report observations and local experiments. In the cosmological context, the FNC are only valid on a scale much smaller than the Hubble horizon. Then we relax the small ball limitation by introducing conformal Fermi coordinates (CFCs). In the CFC system, we mainly focus on the flat universe with vanishing curvature of the space k=0. The Friedmann equations are derived in the CFC system. From the first law of entanglement the emergence of gravity can be described by the change in entanglement SA caused by matter HA angle.In this paper, we study the cosmology in a new framework with the viewpoint that spacetime geometry is viewed as an entanglement structure of the microscopic quantum state, and derive the Friedmann equations for the universe from the first law of entanglement We also briefly review the first law of entanglement. The study shows that there is a basic relation between the gravitation and quantum entanglement, which is valid for the solution of the gravitational field equation.