Researchers reveal interacting group field theory dynamics and emergence of dynamical dark energy

The fundamental nature of dark energy and its influence on the expansion of the universe remain among the most challenging questions in cosmology, and new approaches to quantum gravity may hold the key to understanding it. Tom Ladstätter from Ludwig-Maximilians-Universität München and Luca Marchetti from both the Okinawa Institute of Science and Technology Graduate University and the Kavli Institute for the Physics and Mathematics of the Universe, along with their colleagues, investigate how interactions within a quantum gravity framework give rise to cosmological dynamics. Their work explores a specific approach using group field theory, revealing that certain interactions naturally produce a cosmological constant, similar to Einstein’s original idea, or even a form of dynamic dark energy, which evolves over time. Importantly, the research demonstrates that the behaviour of matter and geometry are intertwined, and that a consistent description of the universe requires specific properties of the scalar field potential, or alternatively, a changing strength of gravity itself, uniquely determined by the properties of matter.

Researchers study the relational cosmological dynamics arising from interacting group field theory models, which are minimally coupled to both a massless clock scalar field and a self-interacting scalar field. By treating these interactions perturbatively, the team extracts the effective cosmological dynamics using mean-field techniques. Within the geometric sector, they identify appropriate classical limits of the resulting dynamics, characterised by the emergence of a cosmological constant term in pseudotensorial models.

Loop Quantum Gravity and Cosmological Spin Foams

This extensive collection of references focuses on Quantum Gravity, particularly Loop Quantum Gravity (LQG) and Group Field Theory (GFT), with strong connections to Cosmology, Dark Energy, and Inflation. The core of the bibliography centers on Loop Quantum Gravity, exploring its foundational principles, spin foam models, and attempts to quantize spacetime itself. Group Field Theory, a second quantization of spin foams, receives significant attention, with researchers investigating its condensate cosmology and the emergence of spacetime from its dynamics. A large portion of the bibliography connects quantum gravity to cosmology, applying LQG and GFT techniques to understand the very early universe and address the Big Bang singularity.

Models where the Big Bang is replaced by a bounce from a contracting phase, avoiding the singularity, are a major focus, alongside investigations into inflation, dark energy, and the origin of structure in the universe. The collection also includes references to mathematical and formal aspects of these theories, such as Functional Renormalization Group, Hamiltonian Formalism, and Coherent States. Furthermore, the bibliography demonstrates connections to Particle Physics, including investigations into axions and the Higgs mechanism, and even indirect comparisons with String Theory. Key researchers frequently appearing in the collection include Daniele Oriti, Simone Gielen, Carlo Rovelli, and Lee Freidel. The bibliography reveals a clear trend towards increasing research activity in Group Field Theory, particularly its application to cosmology, and a growing emphasis on connecting quantum gravity models to observational data. There is also a growing effort to develop the mathematical foundations of GFT and LQG, ensuring the consistency and well-definedness of the theories, and a willingness to connect quantum gravity with other areas of physics.

Group Field Theory Reproduces Early Universe Cosmology

Researchers have achieved a significant breakthrough in understanding the early universe by applying group field theory (GFT) to model quantum gravity coupled with scalar fields. This work demonstrates how interactions within GFT models generate cosmological dynamics, successfully reproducing key features of classical cosmology while offering insights into quantum gravity effects. The team discovered that different types of GFT interactions, classified as pseudotensorial and pseudosimplicial, lead to distinct cosmological outcomes, revealing a connection between the fundamental interactions and the universe’s evolution. In the pseudotensorial case, the analysis shows that matching with classical Friedmann dynamics is possible for specific interaction strengths, naturally giving rise to a cosmological constant.

This emergence of a cosmological constant is accompanied by an effective mass term in the scalar field dynamics, with the sign of the mass term being inversely proportional to the cosmological constant. A consistent description requires either a specific class of scalar field potentials or a running gravitational coupling, where the strength of gravity changes over time. Similarly, the pseudosimplicial case also matches classical dynamics for specific interactions, but with a distinct scalar field potential. Importantly, this model predicts that quantum gravity effects break any potential shift symmetry in the original classical action, resulting in a discrete symmetry reminiscent of effects observed in axion physics, and leading to a time-dependent dark energy component.

Quantum Interactions Drive Emergent Cosmology

This research investigates how cosmological dynamics emerge from a specific approach to quantum gravity known as group field theory. The team explores models where fundamental quantum geometric building blocks interact, and how these interactions give rise to effective cosmological descriptions resembling our universe. They find that different forms of interaction, pseudosimplicial and pseudotensorial, lead to distinct behaviours, with pseudotensorial models suggesting a cosmological constant and pseudosimplicial models indicating dynamical dark energy. The results show that a consistent description of matter and geometry requires specific forms of the effective scalar field potential, but this requirement can be relaxed by allowing the gravitational coupling to vary with scale. This scale-dependent coupling is uniquely determined once the scalar field potential is specified, offering a potential link between quantum gravity and the observed properties of dark energy. The authors acknowledge that the analysis relies on perturbative approximations and mean-field techniques, and plan to explore non-perturbative effects to provide a more complete understanding of the emergent cosmological dynamics and to test the predictions against observational data.