A Quantum Gravity Extension of the Inflationary Scenario (1209.1609v2)

Abstract: Since the standard inflationary paradigm is based on quantum field theory on classical space-times, it excludes the Planck era. Using techniques from loop quantum gravity, the paradigm is extended to a self-consistent theory from the Planck scale to the onset of slow roll inflation, covering some 11 orders of magnitude in energy density and curvature. This pre-inflationary dynamics also opens a small window for novel effects, e.g. a source for non-Gaussianities, which could extend the reach of cosmological observations to the deep Planck regime of the early universe.

• The paper presents its main contribution by extending the inflationary paradigm with loop quantum gravity to incorporate Planck-scale physics and resolve singularities.
• It employs a quantum kinematics framework that separates background and perturbations, enabling numerical simulations consistent with WMAP observations.
• The study forecasts subtle deviations from the Bunch Davies vacuum, suggesting observable non-Gaussian effects in the cosmic microwave background.

A Quantum Gravity Extension of the Inflationary Scenario

The paper in question provides an extension of the standard inflationary paradigm through the incorporation of quantum gravity effects, specifically utilizing techniques from loop quantum gravity (LQG). This method extends the framework of inflation to include dynamics that cover 11 orders of magnitude in energy density and curvature, addressing some key inconsistencies of the conventional approach regarding the Planck-scale physics.

The standard inflationary paradigm has been significant in explaining cosmic microwave background (CMB) inhomogeneities, which are precursors to the large-scale structure of the universe. However, conceptual limitations arise when its foundation in quantum field theory rests on classical spacetime models, neglecting the Planck era. This results in unresolved issues, such as the persistence of the big bang singularity, the assumption of the Bunch Davies (BD) vacuum, and the trans-Planckian modes problem when perturbations are traced backward.

LQG provides a natural framework to tackle these limitations by extending the scope of inflation deeper into the quantum regime where quantum geometric effects dominate. This facilitates singularity resolution across various cosmological models. This paper pursues a known LQG strategy: initially truncating the classical theory pertinent to the problem, then employing LQG techniques to build the quantum theory.

The key is to replace classical space-time with quantum geometry and to propound the dynamics of inflationary perturbations upon these quantum geometries. The authors present an innovative formulation whereby the dynamics are not reliant on a classical constraint. Instead, they rely on a vector field describing these quantum perturbations on classical Friedmann backgrounds, focusing on first-order perturbations. The quantum dynamics establish that the quantum fields propagate on a quantum geometry described by a state, rather than a classical metric, which naturally leads to a resolution of singularities.

The introduction of quantum kinematics separates the total Hilbert space into components for background homogenous fields and perturbations. The remarkable feature in this quantum setting is that the computations for the power spectrum indicate that, for a significant range of initial conditions, the predictions are consistent with the BD vacuum at the onset of slow roll inflation. However, a notable deviation arises if pre-inflationary dynamics are considered, which has implications for non-Gaussianities observable in potential deviations from the BD vacuum structure.

The paper successfully performs numerical simulations confirming that for certain initial conditions the background quantum geometry can lead to viable inflationary dynamics consistent with the WMAP data. It is found that variations within the BD vacuum deviations are minor in observational scopes, verifying the self-consistent treatment of perturbations as test fields without significant back-reaction.

The results imply that future cosmological observations might access this Planck regime by identifying potential signatures in the form of $\mu$-type CMB distortions or non-Gaussianities, potentially constraining initial conditions further. The approach effectively bridges the gap between LQG and cosmological perturbations, offering initial insights into incorporating quantum gravity into cosmological observations. The paper efficiently addresses quantum loop cosmology by demonstrating potential pathways for integrating quantum effects with classical cosmological models, proposing an expanded reach for observational cosmology into quantum regimes. This integration aligns with advancing the theoretical foundation of early-universe scenarios and deepening our understanding of quantum gravitational effects within a cosmological context.