The Hubble tension from the standpoint of quantum cosmology (2211.16394v3)

Abstract: The Hubble tension is analyzed in the framework of quantum cosmological approach. It is found that there arises a new summand in the expression for the total energy density stipulated by the quantum Bohm potential. This additional energy density acts similarly to a stiff matter component, modifying the expansion history of the early universe and decaying with scale factor $a$ as $a^{-6}$, faster than radiation, in late universe. Taking account of this matter-energy component of quantum nature can, in principle, eliminate a discrepancy between the direct late time model-independent measurements of the Hubble constant and its indirect model dependent estimates. The considered model allows one to extend the standard cosmology to quantum sector.

• The paper proposes that a quantum energy density from the Bohm potential adds a stiff matter-like component to mitigate the Hubble tension.
• It employs a Wheeler-DeWitt–inspired approach with an explicit time variable to naturally derive an a⁻⁶ scaling of the quantum correction.
• Numerical estimates suggest that a 10% increase in pre-recombination energy density can reconcile discrepancies between local and CMB-based Hubble constant measurements.

The Hubble Tension from a Quantum Cosmology Perspective

The paper examines the longstanding issue of the Hubble tension within the framework of quantum cosmology. This approach leverages quantum cosmology to provide a plausible solution by introducing a quantum energy density component into the standard cosmological model. The authors argue that this additional term, derived from the Bohm quantum potential, behaves similarly to a stiff matter component and could potentially reconcile differences between the local measurements of the Hubble constant and those extrapolated from the Cosmic Microwave Background (CMB) under the standard $\Lambda$CDM model.

Quantum Cosmology and the Bohm Potential

Central to this approach is the extension of classical cosmology into the quantum regime. Here, the authors employ a Wheeler-DeWitt-like equation but incorporate the Dirac approach to constrain the dynamics with an explicit time variable. This framework naturally yields the Bohm potential as a correction to the energy density in the universe's Friedmann equation. Notably, the Bohm potential induces an additional energy density that scales with the scale factor as $a^{-6}$, mimicking the behavior of a stiff fluid. This additional quantum component is proposed to couple dynamically, potentially resolving tensions intrinsic to non-quantum cosmological models.

Implications for the Hubble Tension

The paper's bold proposition is that accounting for the quantum-corrected energy density could eliminate or at least significantly alleviate the Hubble tension. By modifying the expansion history of the universe during its early phases, this component would increase the Universe's energy budget before recombination, thereby modifying the inferred expansion rate and reconciling it with local measurements.

Comparison with Existing Models

The concept of early dark energy (EDE) has been a contender in addressing the Hubble tension by postulating an additional energy component that peaks before recombination. However, EDE models tend to rely on specific potential forms and face fine-tuning issues. By contrast, the proposed quantum cosmological model integrates the additional energy density naturally through the Bohm potential, with the quantum mechanical formalism inherently providing the necessary scaling without additional assumptions.

Numerical Results and Physical Viability

Numerical estimations in the paper suggest that a quantum correction leading to an effective 10% increase in energy density before recombination is sufficient to resolve the tension. The factor $\gamma$, which characterizes the quantum correction, can reach meaningful values without contrived tuning, especially during a "coasting period" of the universe. This potentially offers a fitting explanation for the observed Hubble tension without invoking intricate new physics or mechanisms beyond established quantum mechanics.

Future Directions

Drawing from the analysis in this paper, future developments in cosmology might focus on assessing the broader implications of integrating quantum corrections more comprehensively into cosmological models. Considering alternative forms of quantum corrections and their potential impacts on different epochs of the universe could form an interesting avenue for future research. Additionally, examining the constraints astrophysical observations place on the scale of Bohm-like corrections would be a necessary step in further substantiating this approach.

Ultimately, this paper integrates quantum cosmological principles into the ongoing discourse on the Hubble tension, proposing a theoretical avenue that complements both empirical results and the theoretical structure of modern quantum field theories. While further empirical validation is necessary, the results highlight the potential of quantum cosmology to illuminate and perhaps resolve outstanding cosmological puzzles.