Cosmic Inflation in an Extended Non-Commutative Foliated Quantum Gravity: The Wave Function of the Universe

Authors:
Preprint
Publisher website
Google Scholar
Abstract
We propose a novel extension to the recently developed non-commutative Riemannian foliated branch-cut quantum gravity (BCQG). On basis in an extended Faddeev–Jackiw symplectic deformation of the conventional Poisson algebra, we investigate non-commutativity effects on a symplectic topological manifold that provides a natural isomorphic setting composed by a triad of canonically conjugate scalar complex fields which comprise quantum complementary dualities. The resulting extended manifold spans the canonical BCQG cosmic scale factor and, in addition to its complementary quantum counterpart, outlined in the perfect fluid domain of Hermann Weyl, a scalar-complex inflaton-inspired field. By constructing a triad of quantized fields underlying a noncommutative spacetime, this extension allows the elaboration of a scenario where the original branch-cut domain coexists with a complex scalar inflaton-type field, settled on a plateau of a strong gravity interaction structure. Alongside shaping this structure settled on a background composed by the primordial energy, radiation-, quintessence-, stiff-, baryon- and dark matter, combined with the spacetime components of the scalar Ricci curvature at different orders, cosmic inflation is driven. The presence of the inflaton field in the present formulation transcends the character of a simple reference field, to the extent that its original motivation has been to driven inflation, a role played by the original formulation of the BCQG. The resulting symplectic algebraic extension allows additionally a liaison with primordial cosmic density perturbation predictions based on heuristic derivations of the scale invariance of the primordial spectrum of the Universe, as well as with eternal inflation and primordial chaotic cosmic mechanisms proposals. Given the peculiar characteristic of BCQG in overcoming the primordial singularity, the non-commutative symplectic extension proposal, due to the complex character of the constituent fields, additionally outlines the evolutionary process of the mirror Universe that encompasses analytically continued complex conjugate Friedmann's-type equations. This brings unique characteristics to the main scenario for the BCQG cosmic evolution, with a mirrored parallel evolutionary Universe, adjacent to ours, nested in the structure of space and time. The evolutionary process of the mirror Universe occurs in the negative sector of cosmological thermal time, and is characterized by a continuous cosmic contraction, with a systematic and continuous increase in temperature and a decrease in entropy before reaching the transition region to the current stage of the Universe. In contrast, the subsequent present evolutionary stage of cosmic expansion is characterized by a positive complex cosmological-time sector, accompanied by a systematic decrease in temperature and increase in entropy. On basis on complementary analytically continued Friedmann’s-type equation, combined with a quantum approach based on the Ho\v{r}awa-Lifshitz quantum gravity, we describe the dynamic evolution of the Universe’s wave function, unfolding unprecedented predictions for the cosmic evolution and inflation. This approach offers a new perspective to explain the accelerated cosmic expansion of the Universe, strongly suggesting that non-commutative algebra induces the late accelerated growth of the wave function of the Universe as well as of the corresponding scale factor and its complementary quantum counterparts. In contrast to the conventional inflationary model, where inflation requires a remarkably fine-tuned set of initial conditions in a patch of the Universe, non-commutative foliated quantum gravity, analytically continued to the complex plane, captures short and long scales of spacetime, leading to an evolutionary cosmic dynamic through a topological reconfiguration of the primordial cosmic matter and energy content. Still, we consider in this work the interplay between naturalness and a fine-tuning set constraining of the cosmological initial conditions. This result introduces new speculative framework elements regarding the reconfiguration of matter and energy due to an underlying non-commutative spatio-temporal structure as a driver of spacetime cosmic acceleration.

This publication has 17 references indexed in Scilit: