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