Quantum Structure of Spacetime and Its Entropy in a Cyclic Universe with Negative Curvature I: A Theoretical Framework

TL;DR

This paper develops a theoretical model of a cyclic universe incorporating quantum information theory, predicting dynamical dark energy and dark matter with specific entropic and quantum properties, and deriving cosmological equations consistent with observations.

Contribution

It introduces a quantum-thermodynamical framework linking spacetime structure with quantum information, predicting new matter terms and curvature effects in a cyclic universe model.

Findings

Predicts dynamical dark energy and dark matter from quantum entanglement.

Identifies a residual matter term with w_r=-1/3 and negative spatial curvature.

Derives cosmological equations consistent with Robertson-Walker metric.

Abstract

We construct a model of the Cyclic Universe from a joint theory of General relativity, Thermodynamics and Quantum information theory. Friedmann equations and the thermodynamical Gibbs-Duhem relation determine a general form of the Hubble function which predicts a dynamical Dark Energy (DE) and a dynamical Dark Matter (DM) described by new entropic terms and by the equations of state w_0=-1 and w_M=0, respectively, at all z. We posit that the spacetime has a quantum structure described by the Quantum information theory. We identify the space quanta \rho with two-qubit quantum states of of massless gravitons with helicity states |\pm 2>. All space quanta carry quantum information entropy S(\rho). All entangled quanta carry entanglement entropy S_E(\rho) and form DE. All non-entangled quanta form DM. In the absence of Baryonic matter DM and SE are described by probability distributions p(\vec{x},S) and q(\vec{x},\chi) where \chi=S_E(\rho)+S(\rho). Fisher information metric generates from these distributions the vacuum gravitational fields of DM and DE. Tn the presence of the Baryonic matter the distributions are displaced p->p' and q->q'. Fisher metric then defines the displaced fields. In Einstein's theory of General relativity Space is a gravitational field which we identify with the gravitational fields of DE and DM. The theory predicts the existence of a new "residual" matter term with equation of state w_r=-1/3 in the Hubble function, and a negative spatial curvature the consequence of which are constraints on cosmological parameters. We recover Robertson-Walker metric and the Friedmann equations from the gravitational fields of Dark Energy and Dark Matter at cosmological scales. The predictions of the theory are tested and confirmed in the Part II of this work.