Ab Initio: Building spacetime towards the singularity

• Applicant: Dr. Ana Alonso Serrano, Ph.D.
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 516730869

Our current theory of gravity gives a very accurate description of the nature of spacetime, but loses its predictive power when considering regions in the vicinity of singularities. In those regions, the evolution of the spacetime becomes chaotic and the spatial points causally disconnected. It finishes in a breakdown of the theory. This chaotic and ultra-local behavior of the spacetime was derived from the asymptotic expansion of the classical gravitational solutions near singularities and constitutes the so-called BKL conjecture. Understanding the vicinity of singularities is crucial to developing consistent cosmological models, but the BKL-like behavior of spacetime while being a key part of the analysis, has not been integrated into our predictions and theories. This project aims to construct an appropriate description of the behavior of spacetime and fields when approaching classical singularities under the consideration of quantum gravity effects expected to be dominant in the surrounding of the singularities. To this goal, first, I propose a complete and innovative analysis of the behavior of spacetime near singularities. First, I plan to establish a physical scale for the emergence of oscillations and causal disconnection of spatial regions, that remains still unknown, providing an extension for BKL effects, that will play also a relevant role in determining the whole BKL behavior when I find out the quantum modification of the standard picture, showing the range of validity of the classical BKL conjecture. Secondly, I aim to formulate a new derivation of the BKL conjecture in light of a general description of the phenomenology of quantum gravity. This phenomenological method is based on a derivation I developed within the framework of thermodynamics of spacetime, which gave rise to a phenomenological quantum-gravity dynamics that it is not only recovered by any approach to quantum gravity, but it will establish constraints on the candidate theories. From these equations, I plan to formulate a new asymptotic expansion of the modified gravitational solutions deriving an extended BKL conjecture and determining the persistence (or not) of oscillations and existence of quantum correlations among the classically disconnected regions when reaching the scale where quantum effects are relevant. This novel quantum-modified conjecture can also prove a general avoidance of singularities and provide constraints to the candidate quantum-gravity theories. In order to complete the results, I also plan to develop a numerical approach, similar to the one developed in the classical BKL conjecture that can address the appearance of inexplicable spikes in the classical model. This project will close the research gap on the classical BKL conjecture and quantum effects close to the singularity, addressing the chaoticity and ultra-locality of spacetime and providing a new window to approach the current conundrums in cosmology and black hole models.

• DFG Programme: Research Grants