The cosmological primordial perturbations of the universe, implicitly defined by the Wheeler–DeWitt equation:

a partial differential equation determining a wave-function not defined in space or time or spacetime, with:

and $\psi$ satisfies an approximate Schrödinger equation:

are clearly quantum in origin. One of the central foundational philosophically pressing problems in physics is to describe a 'collapse' dynamics that explains the classical features consistent with astrophysical data. Given the 'no-time'-property of the Wheeler–DeWitt equation: namely, that it lacks an external time parameter and it lacks a first derivative with an imaginary Schrödinger time-factor, as well as its linearity and symmetrization, we face a deep conflict with the Lindblad equation:

given that its central properties are time-asymmetry and entanglement-entropic-irreversibility, and whose Lindbladian:

describes the non-unitary evolution of the density operator, with:

Besides the problem of the undefinability of the Lindbladian system-bath interaction:

and

in the quantum gravitational cosmology context: see Derivation of the Lindblad Equation for technical details, we already face the tripartite conflict of time

Before discussing the canonical formulation of Einstein’s TGR and the relation it bears to string-dynamics and the critical relation between the total string-theory action and the Nieh–Yan-Barbero-Immirzi action, note that the Hilbert action is a functional of the metric tensor, given by:

also note a crucial relation to the D-p-brane partition function for closed strings, which is:

where ${\not D^{SuSy}}$ is the supersymmetry group covariant derivative. Since the closed string action satisfies the variational equation:

thus no topology in the sum is degenerate, and hence the closed string has a solvable action in 4-D curved space-time described by ${S_D}$ that needs no renormalization, where the closed string action coupled to the instanton field is:

Recall that in the canonical formalism for Einstein’s TGR as developed by Dirac and Arnowitt, Deser and Misner