Quantum maximally symmetric space-times (2504.02786v3)

Abstract: We show that 4-dimensional maximally symmetric spacetimes can be obtained from a coherent state quantisation of gravity, always resulting in geometries that approach the Minkowski vacuum exponentially away from the radius of curvature. A possible connection with the central charge in the AdS/CFT correspondence is also noted.

Quantum Maximally Symmetric Space-Times: An Analytical Overview

The paper "Quantum Maximally Symmetric Space-Times" by Meert, Giusti, and Casadio provides an in-depth examination of four-dimensional maximally symmetric spacetimes through the lens of coherent state quantization of gravity. The authors propose that such spacetimes can be modeled using coherent states, resulting in geometries that exhibit an exponential convergence to the Minkowski vacuum outside the radius of curvature. Intriguingly, the paper also suggests potential ties to the central charge in AdS/CFT correspondence, hinting at implications for quantum gravity.

Key Contributions

1. Coherent State Quantization Framework: The authors leverage coherent state quantization, a corpuscular approach wherein spacetime geometry emerges from the collective behavior of gravitons. This method contrasts traditional quantization techniques by viewing gravity as a coherent collective state originating from Minkowski spacetime.
2. Quantum Corrections in Spacetime: The paper discusses quantum corrections for spacetimes such as de Sitter (dS) and Anti-de Sitter (AdS). These corrections provide insights into how spacetime metrics can be modified at large distances via a coherent state, thereby avoiding divergences typical of classical black hole geometries.
3. Numerical Analysis of Occupation Numbers: The authors derive that the occupation number corresponding to the coherent state scales with spatial volume, diverging at $$\mathcal{N}_{\sigma\Lambda} \sim (R_\infty^6) / (m_P^2 L^4)$$ in units of $L^2$. This implies that an infrared cutoff $R_\infty$ is vital for the coherent state to remain well-defined.
4. Effective Cosmological Constant: With the introduction of quantum corrections, the paper posits an effective cosmological constant $\Lambda_{\rm eff}$ that grows towards an infrared scale $R_\infty$. This effect could partially explain observed discrepancies, such as the local Hubble tension, assuming $R_\infty$ is significantly larger than the cosmological scale.
5. Implications for AdS/CFT Correspondence: The occupation number scaling is similar to the central charge derived from stress tensor 2-point functions in AdS/CFT. This correspondence underlines the theoretical interplay between gravitational degrees of freedom in AdS spaces and conformally invariant field theories.

Potential Implications and Future Directions

The research provides foundational insights into how quantum coherence might inform our understanding of spacetime structure, particularly regarding the cosmological constant's role in quantum gravity. It suggests intriguing implications for understanding inflationary cosmology and dark energy in cosmology through coherent quantum states. The AdS/CFT connection hints at deeper gravitational-CFT dualities that might be explored further through coherent state quantization frameworks.

Potential future studies could explore whether quantum corrected geometries provide additional well-known holographic results or remain coincidental. The research opens avenues for bridging quantum and classical gravitational theories via concepts like coherent states, suggesting that such quantum states could offer tangible observational signatures or new theoretical constructs in high-energy physics.

In conclusion, this paper constitutes a valuable contribution to the field of quantum gravity by exploring the domains of coherent state quantization of symmetrical spacetime structures, with noteworthy implications for theoretical physics and cosmology.