Reevaluation of Inflationary Dynamics in Extended General Relativity with Perturbatively and Tensorially Structured Conformal Metric

TL;DR

This paper reexamines inflationary dynamics using a quantum-deformed conformal metric, deriving analytical formulas for inflationary observables with quantum corrections that suggest new physical interpretations.

Contribution

It introduces a novel quantum-deformed conformal metric framework to compute inflationary observables, incorporating quantum corrections into the inflationary paradigm.

Findings

Derived analytical formulas for scalar and tensor power spectra.

Quantum corrections relate to measure scaling and kinetic deformation.

Modified inflationary observables with controlled quantum effects.

Abstract

Based on the conventional metric tensor and driven by a nearly constant energy density, cosmic inflation, characterized by a remarkably accelerated expansion, was proposed as an early epoch in the Universe. The energy density is typically modeled through a slow-rolling scalar field, whose potential energy dominates the dynamics. This mechanism addresses horizon, flatness, and relic problems, while also generating quantum fluctuations that are stretched to cosmological scales, leading to emergence of primordial curvatures and tensor perturbations. Despite its empirical success, significant questions remain regarding identity of the inflaton, origin of the potential, and role of quantum gravity. A quantum-deformed conformal metric that is both perturbatively and tensorially structured and expanded is employed to reexamine the dynamics of inflation, thus enabling the computation of a range of inflationary observables in presence of quantum-induced corrections. We have established a closed and internally consistent set of analytical formulas for scalar and tensor power spectra, including their spectral tilts, runnings, and the tensor-to-scalar ratio, among other parameters. The quantum corrections appear to provide a clear physical interpretation related to measure scaling and momentum-induced kinetic deformation, which facilitates modifications to the inflationary observables in a controlled and predictive manner. While maintaining the classical limits, these corrections provide a well-defined phenomenological perspective on potential quantum-gravitational structures in the early Universe.