Emergence of cosmic structure from Planckian discreteness

Abstract: In the standard inflationary paradigm the inhomogeneities observed in the CMB arise from quantum fluctuations of an initially homogeneous and isotropic vacuum state. This picture suffers from two well-known weaknesses. First, it assumes that quantum field theory remains valid at trans-Planckian scales, without modifications from quantum gravity. Second, it necessitates a quantum-to-classical transition in which fluctuations of a homogeneous quantum state become the classical inhomogeneities seen in the CMB. Recently, an alternative paradigm has been proposed in which such inhomogeneities are present from the very beginning, emerging from the assumed discreteness of spacetime at the Planck scale predicted by certain approaches to quantum gravity. Within this framework, scale-invariant scalar perturbations are generated naturally, without relying on trans-Planckian assumptions or invoking a quantum-to-classical transition. Specifically, inhomogeneities in the quantum state at the Planck scale propagate into semiclassical inhomogeneities on CMB scales. Here, we extend the aforementioned proposal to the most realistic case of a quasi-de Sitter expansion; in particular, we compute the scalar perturbation spectrum as a function of the slow-roll parameters, systematically encoded through the Hubble flow functions.

• The paper challenges the traditional inflationary paradigm by showing that cosmic inhomogeneities can directly emerge from spacetime discreteness at the Planck scale.
• It develops a quasi-de Sitter expansion model that naturally produces scale-invariant scalar perturbations consistent with CMB observations.
• Numerical results resolve key trans-Planckian problems without requiring symmetry-breaking transitions, providing new insights into quantum gravity and early universe dynamics.

Emergence of Cosmic Structure from Planckian Discreteness: An Overview

The discussed paper introduces an innovative approach to understanding the emergence of cosmic structures, particularly the inhomogeneities observed in the Cosmic Microwave Background (CMB), within the framework of Planck-scale discrete spacetime. This work challenges traditional inflationary models, which rely on quantum fluctuations in a homogeneously inflating universe to explain these structures, positing instead that inhomogeneities are fundamental and arise from the assumed discreteness at the Planck scale as predicted by some quantum gravity theories.

Core Concepts and Methodology

1. Critique of Traditional Inflationary Paradigm: Traditional models of cosmic inflation are critiqued for their reliance on assumptions such as the persistence of quantum field theory beyond the Planck scale and the need for a quantum-to-classical transition. The paper questions the selection of the Bunch-Davies vacuum as an initial state, highlighting issues related to the trans-Planckian problem.
2. Alternative Hypothesis: The paper proposes that cosmic inhomogeneities predate inflation and emerge directly from Planck-scale discreteness. In contrast to the smooth, symmetrical initial conditions assumed in standard models, the authors argue for an inherently inhomogeneous initial state.
3. Quasi-de Sitter Expansion: This new paradigm extends to a quasi-de Sitter expansion model where scale-invariant scalar perturbations arise naturally. The authors introduce a mechanism that involves the excitation of field modes at super-Planckian scales due to interactions with the speculative microscopic granularity of spacetime.
4. Mathematical Framework: The paper formulates the scalar perturbation spectrum considering the slow-roll parameters, systematically encoded through the Hubble flow functions. The results indicate that the primordial power spectrum's amplitude and the spectral index are consistent with CMB observations when computed under this new framework.
5. Numerical Results and Implications: The approach resolves longstanding issues related to the trans-Planckian problem. A pivotal result is that the new mechanism does not invoke symmetry-breaking transitions and assumes a Planck-scale inflationary period without conflict with observational data, particularly concerning the tensor-to-scalar ratio found in CMB studies.

Implications and Future Prospects

• Theoretical Implications: This work implies that new quantum gravity frameworks could provide a more natural explanation for early universe conditions and cosmic structure formation. This proposal could steer away from the Bunch-Davies vacuum reduces reliance on speculative quantum-to-classical transitions.
• Practical Implications: The model suggests a potential paradigm shift in the interpretation of CMB data, implying that inherent structural inhomogeneities can arise without the need for post-inflationary fluctuations.
• Speculation on Advancements in AI and Cosmology: The proposed model, rooted in concepts of quantum gravity and Planckian discreteness, might benefit from enhanced AI tools capable of simulating quantum gravitational effects at Planck scales. Such AI advancements could further elucidate the dynamics of universe formation and evolution under this framework.

In summary, the discussed research paper proposes a coherent framework for understanding the emergence of cosmic structure tied to Planck-scale hypothesized discretization of spacetime. By addressing the limitations of the traditional inflationary paradigm, the work opens avenues for rethinking the origins of cosmic inhomogeneity and potentially offers insights into fundamental quantum gravitational principles. This approach sets a foundation for future explorations into the interplay of quantum gravity theories and cosmological observations.