Modified Gravity Links Matter and the Universe’s Earliest Moments

Researchers are increasingly exploring modifications to general relativity to address outstanding cosmological puzzles. Serkan Doruk Hazinedar and Yaghoub Heydarzade, both from Bilkent University, alongside Shahram Jalalzadeh from Izmir Institute of Technology, present a detailed investigation into quantum cosmology within f(R, T) gravity, a theory extending Einstein’s model by incorporating a coupling between geometry and matter. Their collaborative work derives the foundational equations for describing the early universe using Schutz’s perfect fluid formalism, revealing how matter actively participates in the evolution of spacetime and cosmic time itself. This analysis, which yields the wave function of the universe for specific scenarios, is significant because it offers insights into the role of matter-geometry coupling in shaping cosmological dynamics and potentially provides an alternative to dark energy explanations for the accelerating expansion of the universe.

This work advances the theory of modified gravity, specifically f(R, T) gravity, an extension of Einstein’s general relativity where gravity’s strength depends not only on the curvature of spacetime but also on the distribution of matter and energy. Researchers have successfully derived the wave function of the universe for specific gravitational models, revealing how the coupling between matter and spacetime geometry influences the emergence of cosmological dynamics. The study employs a Friedmann, Lemaitre, Robertson, Walker (FLRW) universe, a standard model describing a homogeneous and isotropic expanding universe, within the f(R, T) framework. A key innovation lies in the application of Schutz’s perfect fluid formalism, which extracts a time parameter directly from the matter content of the universe itself. This approach circumvents the traditional “problem of time” in quantum cosmology, allowing for a Schrödinger-like equation to describe the evolution of the universe’s wave function and enabling a probabilistic interpretation of its quantum state. By deriving the gravitational Hamiltonian, canonical momenta, and potential, the team constructed the Schrödinger, Wheeler, DeWitt (SWDW) equation, a central equation in canonical quantum cosmology, and obtained solutions for specific forms of the f(R, T) function. The resulting quantum states and wave packets offer insights into the universe’s initial conditions, singularity behaviour, and the potential for non-singular quantum cosmologies that avoid the problematic infinite density at the Big Bang. This work establishes a transparent canonical setting for exploring the quantum realm of modified gravity and lays the groundwork for future investigations into the emergence of the universe from its earliest quantum state. Employing Schutz’s perfect fluid formalism, the research establishes a time parameter directly emerging from the matter sector within the framework of f(R, T) gravity. Specifically, the wave function of the universe was obtained for the minimally coupled case, f(R, T) = F₀(R) + G₀(T), where the coupling between geometry and the energy-momentum tensor’s trace is present but the mixed curvature-matter derivative vanishes. This choice simplifies the analysis while retaining key physical features of the theory. The resulting analysis reveals a transparent canonical setting for the SWDW equation, complete with a well-defined inner product and Hermitian factor ordering. Early universe limits were explored, leading to tractable reduced Hamiltonian and wave equations, and explicit quantum states were derived for representative choices of F₀(R) and G₀(T). These calculations demonstrate the influence of matter-geometry coupling on the dynamics within the minisuperspace, particularly concerning boundary condition requirements and the potential for non-singular quantum behaviour. Wave-packet constructions, utilising DeWitt-type suppression as a parameter approaches zero, further illuminate the emergence of quantum behaviour. A 72-qubit superconducting processor forms the foundation of this work, though the methodology diverges from direct hardware implementation to focus on quantum cosmology within extended theories of gravity. This theory extends general relativity by allowing the gravitational Lagrangian to incorporate both the Ricci scalar and the trace of the energy-momentum tensor. The study leverages Schutz’s perfect fluid formalism to extract a time parameter directly from the matter sector itself. This is advantageous because the coupling between geometry and the energy-momentum tensor’s trace in f(R, T) gravity makes matter an active participant in the dynamics of spacetime, allowing for an internally generated notion of time. By employing this formalism, the gravitational Hamiltonian, canonical momenta, and potential were derived, ultimately leading to the Schrödinger, Wheeler, DeWitt (SWDW) equation. To simplify the model, the analysis focused on the minimally coupled class of f(R, T) functions, defined as f(R, T) = F₀(R) + G₀(T), where the mixed curvature-matter derivative vanishes. The early universe limit was then explored, deriving tractable reduced Hamiltonian and wave equations to obtain explicit quantum states for representative choices of F₀(R) and G₀(T). This approach defines time using Schutz’s fluid degrees of freedom, remaining directly applicable to the minimal f(R, T) sector and allowing for the assessment of matter-geometry coupling on minisuperspace dynamics. Wave-packet constructions were then used to investigate the emergence of non-singular quantum behaviour, potentially resolving issues with classical singularity theorems. Supporting analytic details regarding the trace sector and asymptotic behaviour are provided in an appendix, ensuring the robustness of the presented results. The persistent challenge of reconciling general relativity with quantum mechanics has driven decades of theoretical exploration, and this work offers a fresh perspective by examining early-time cosmology within an extended gravity framework. Physicists have struggled to define the initial conditions of the universe, hampered by singularities and the difficulty of applying quantum principles to the entirety of spacetime. This research sidesteps the need for entirely new physics by modifying gravity itself, allowing the gravitational Lagrangian to couple with the trace of the energy-momentum tensor, creating a model where matter actively influences the geometry of spacetime, potentially smoothing out problematic singularities. What distinguishes this approach is the use of Schutz’s perfect fluid and the Schrödinger-Wheeler-DeWitt equation to derive a wave function for the universe, providing a framework for understanding the emergence of cosmological dynamics from a quantum perspective and offering a potential pathway towards a more complete theory of quantum gravity. The results, while preliminary, demonstrate a consistency with existing models and highlight the crucial role of matter-geometry coupling. However, the model relies on specific forms of the coupling function, and the behaviour near the initial singularity remains a complex issue. Future work will likely focus on refining the model, exploring different coupling functions, and comparing the theoretical predictions with increasingly precise cosmological data. Ultimately, this line of inquiry represents a valuable contribution to the ongoing effort to understand the universe at its most fundamental level, and may pave the way for a deeper understanding of the interplay between gravity, matter, and quantum mechanics.