Cosmic Dawn of Particles: A New View of Creation

Author: Denis Avetisyan

A novel computational approach reveals how particle creation in the early universe is shaped by fundamental interactions and expanding spacetime.

The study demonstrates that particle production in a massless scalar field theory, initially predicted by analytical calculations and observed through the evolution of excited state probabilities, is suppressed by even slight interactions introduced via fermion mass, a phenomenon signaled by a decreasing ratio of measured to free-theory probabilities and momentarily obscured by state mixing during rapid level crossings-effects quantified within a system defined by <span class="katex-eq" data-katex-display="false">N=20</span>, <span class="katex-eq" data-katex-display="false">a=1</span>, and a lightest meson mass of <span class="katex-eq" data-katex-display="false">M\_1=0.25</span>. — The study demonstrates that particle production in a massless scalar field theory, initially predicted by analytical calculations and observed through the evolution of excited state probabilities, is suppressed by even slight interactions introduced via fermion mass, a phenomenon signaled by a decreasing ratio of measured to free-theory probabilities and momentarily obscured by state mixing during rapid level crossings-effects quantified within a system defined by $N=20$ , $a=1$ , and a lightest meson mass of $M\_1=0.25$ .

This work presents the first non-perturbative study of particle production in interacting quantum field theories within an expanding cosmological background using matrix product states.

Understanding real-time dynamics in curved spacetime-a longstanding challenge in theoretical physics-requires non-perturbative approaches beyond standard approximations. This is addressed in ‘Quantum dynamics of cosmological particle production: interacting quantum field theories with matrix product states’, which employs tensor network methods to investigate particle creation in expanding universes. Our central finding demonstrates that self-interactions within quantum field theories suppress gravitational particle production and alter entanglement growth compared to free-field scenarios. Will these techniques unlock a more complete understanding of quantum phenomena in strong gravitational fields and the very early universe?

The Illusion of Complexity: Why Simple Models Still Matter

Quantum field theory (QFT) relies heavily on perturbative methods – approximations that treat interactions as small deviations from free particle behavior. However, when interactions become strong, these approximations break down, yielding infinite or nonsensical results. This failure arises because the perturbative series, designed for weakly interacting systems, diverges or oscillates violently. Consequently, understanding particle production in regimes like the early universe, or within the cores of neutron stars-where coupling strengths are substantial-necessitates non-perturbative approaches. These techniques, such as lattice QFT and functional renormalization group methods, aim to solve the equations of motion directly, circumventing the limitations of approximations and providing insights into the fundamental dynamics governing strongly coupled systems. The inability to accurately model these regimes represents a significant challenge in modern physics, driving the development of increasingly sophisticated computational and analytical tools.

Despite their deceptively simple formulations, the Schwinger model – a QED-like theory in 1+1 dimensions – and $\lambda\phi^4$ theory reveal unexpectedly rich and complex behaviors when tackled beyond standard perturbative calculations. These systems serve as vital testing grounds for non-perturbative techniques because the usual expansion around free field theory breaks down in the strongly coupled regimes, leading to phenomena like dynamical chiral symmetry breaking and the formation of bound states that are inaccessible through conventional methods. Researchers employ lattice simulations, functional renormalization group approaches, and other advanced tools to probe these regimes, uncovering intricate phase diagrams and critical phenomena. The insights gained from studying these seemingly abstract models are not merely academic; they have profound implications for understanding confinement in quantum chromodynamics, the behavior of strongly correlated electron systems, and even the earliest moments of the universe.

The intricacies of confined dynamics extend far beyond the realm of theoretical high-energy physics, proving essential for accurately modeling a surprisingly diverse range of physical phenomena. Investigations into strongly coupled systems, initially motivated by understanding particle creation, provide critical insights into the early universe, where extreme temperatures and densities dictated the formation of matter. Similarly, the behavior of electrons within condensed matter systems-governed by complex many-body interactions-requires the same non-perturbative techniques developed for quantum field theory. From the emergent properties of novel materials like high-temperature superconductors to the quark-gluon plasma created in heavy-ion collisions, a comprehensive grasp of these confined dynamics is paramount for deciphering the fundamental laws governing matter in its most extreme states and unlocking advancements in materials science and cosmology.

Simulations of the Schwinger and <span class="katex-eq" data-katex-display="false">\lambda\phi^4</span> models reveal that the time-averaged, vacuum-subtracted entanglement entropy exhibits distinct behavior during an expansion quench-indicated by shading intensity proportional to <span class="katex-eq" data-katex-display="false">\partial_t \Omega^2</span>-and varies with the fermion mass-to-coupling ratio or simulation parameters. — Simulations of the Schwinger and $\lambda\phi^4$ models reveal that the time-averaged, vacuum-subtracted entanglement entropy exhibits distinct behavior during an expansion quench-indicated by shading intensity proportional to $\partial_t \Omega^2$ -and varies with the fermion mass-to-coupling ratio or simulation parameters.

Decoding the Quantum Field: Tensor Networks as a Predictive Tool

Tensor Network Methods represent a computational approach to simulating quantum field theories by efficiently encoding many-body quantum states as a network of interconnected tensors. Specifically, applications to the Schwinger model – a simplified quantum electrodynamics theory – and $\lambda\phi^4$ theory, a common scalar field theory, demonstrate the method’s versatility. These simulations represent quantum fields on a discrete spacetime lattice, allowing for numerical investigation of field dynamics. The effectiveness of Tensor Networks stems from their ability to approximate high-dimensional wavefunctions with a reduced number of parameters compared to traditional methods, facilitating calculations previously intractable due to the exponential growth of Hilbert space dimensionality with system size.

Matrix Product States (MPS) provide a parameterization of the many-body quantum state, enabling its representation with a computational cost that scales polynomially with system size – a significant improvement over the exponential scaling of traditional methods. This efficiency stems from expressing the wavefunction as a network of interconnected matrices, effectively capturing entanglement structure. The Time-Dependent Variational Principle (TDVP) is then employed as the core dynamical evolution algorithm. TDVP minimizes the energy functional at each time step, iteratively updating the MPS parameters to approximate the time evolution operator. This variational approach ensures the propagated state remains within the representable MPS manifold, preventing uncontrolled growth of entanglement and maintaining computational tractability. The combination of MPS and TDVP facilitates simulations of quantum field theories by efficiently representing the quantum state and evolving it in time, allowing access to dynamical properties and real-time behavior.

Tensor network methods, specifically those employing Matrix Product States and the Time-Dependent Variational Principle, extend the reach of quantum field theory simulations beyond the limitations of analytical techniques. These numerical approaches enable the study of real-time dynamics – the evolution of quantum states over time – and finite-density systems, where particle number is not fixed, both of which are analytically challenging. Recent simulations utilizing these methods have demonstrated the suppression of particle production in certain scenarios, evidenced by a reduction in the amplitude of oscillations observed in two-point correlation functions $G(x,t)$ , indicating a diminished rate of particle-antiparticle pair creation.

Simulations of the Schwinger model with <span class="katex-eq" data-katex-display="false">mf/gf=1/8</span>, <span class="katex-eq" data-katex-display="false">M_1=0.25</span>, <span class="katex-eq" data-katex-display="false">N=30</span>, and <span class="katex-eq" data-katex-display="false">a=1</span> reveal that an initial decrease in dynamical entanglement entropy, mirroring ground-state behavior, transitions to oscillations due to particle production during an expansion quench indicated by the shaded region representing <span class="katex-eq" data-katex-display="false">\partial_t\Omega^2</span>. — Simulations of the Schwinger model with $mf/gf=1/8$ , $M_1=0.25$ , $N=30$ , and $a=1$ reveal that an initial decrease in dynamical entanglement entropy, mirroring ground-state behavior, transitions to oscillations due to particle production during an expansion quench indicated by the shaded region representing $\partial_t\Omega^2$ .

The Foundation of Prediction: From Dirac to Functional Integrals

The Schwinger model serves as a valuable, analytically tractable system for testing calculations in Quantum Field Theory (QFT). Based on the Dirac equation, which describes relativistic fermions, the model considers Quantum Electrodynamics (QED) in 1+1 dimensions. This dimensionality reduction significantly simplifies calculations without sacrificing key QFT features like particle-antiparticle creation and annihilation. Specifically, the Schwinger model allows for the examination of phenomena such as dynamical chiral symmetry breaking and confinement, offering insights into the more complex 3+1 dimensional world. The model’s simplicity facilitates benchmarking of numerical techniques, including lattice gauge theory and tensor networks, providing a means to validate results and explore regimes inaccessible to perturbation theory. $\psi(x) = \sqrt{2} \begin{pmatrix} \chi(x) \\ i \sigma_2 \chi^*(x) \end{pmatrix}$

The Hamiltonian formulation is essential for numerical implementation of quantum field theory models, allowing for discrete-time evolution and approximation techniques. This approach defines the system’s dynamics through the Hamiltonian operator, $H$ , and enables calculations of time-dependent states. Two primary interpretations facilitate these calculations: the Schrödinger Picture, where operators are time-independent and states evolve in time, and the Heisenberg Picture, where states are time-independent and operators evolve. Both pictures are equivalent, but offer distinct computational advantages depending on the specific problem; the Heisenberg picture is frequently employed in lattice gauge theory due to its ability to simplify calculations involving time-dependent operators.

The Functional Integral formalism provides a method for calculating quantum field theory amplitudes by summing over all possible field configurations, weighted by a phase factor determined by the action $S$ . This approach offers a complementary pathway to calculations performed using methods like tensor networks, allowing for verification of results and providing independent confirmation of theoretical predictions. Studies employing functional integrals within the Schwinger model demonstrate an inverse relationship between interaction strength and particle production; increasing the strength of the interaction between particles results in a measurable decrease in the rate of particle creation, a phenomenon consistent across multiple calculation methods.

Correlators of two-point charge <span class="katex-eq" data-katex-display="false">{\mathcal{Q}_{2}^{\rm lat.}(n,t)}</span> and field <span class="katex-eq" data-katex-display="false">{\mathcal{C}_{2}^{\rm lat.}(n,t)}</span> densities, calculated for varying fermion mass-to-coupling ratios (left) and in <span class="katex-eq" data-katex-display="false">{\lambda\phi^{4}}</span> theory (right) with fixed lightest meson mass and lattice parameters, demonstrate the expansion quench as indicated by shading intensity proportional to <span class="katex-eq" data-katex-display="false">{\partial_{t}\Omega^{2}}</span>, and align with analytical continuum results for a free scalar theory. — Correlators of two-point charge density ${\mathcal Q}_2^{\rm lat.}(n,t)$ and field ${\mathcal C}_2^{\rm lat.}(n,t)$ densities, calculated for varying fermion mass-to-coupling ratios (left) and in ${\lambda\phi^{4}}$ theory (right) with fixed lightest meson mass and lattice parameters, demonstrate the expansion quench as indicated by shading intensity proportional to ${\partial_{t}\Omega^{2}}$ , and align with analytical continuum results for a free scalar theory.

Scaling the Framework: Constraints and Cosmological Implications

The Schwinger model, a simplified framework for understanding quantum electrodynamics, relies heavily on Gauss’s Law to maintain mathematical consistency. This fundamental law of electromagnetism doesn’t simply describe electric fields; within the model, it acts as a powerful constraint, dictating the permissible configurations of quantum fields. Without enforcing this constraint, calculations quickly become divergent and physically meaningless. Specifically, Gauss’s Law ensures that the total electric charge within any volume remains constant, preventing the spontaneous creation or annihilation of charge which would violate fundamental conservation laws. This constraint dramatically simplifies the complex equations of quantum field theory, allowing researchers to obtain reliable predictions about particle behavior and interactions, and forms a crucial foundation for extending these calculations to more complex scenarios – including the study of quantum fields in the expanding universe.

The Friedmann-Lemaître-Robertson-Walker (FLRW) metric serves as the foundational spacetime geometry for applying quantum field theory to the cosmos. This metric describes a homogeneous and isotropic expanding universe, accommodating the observed cosmological principle on large scales. By embedding quantum fields-the fundamental constituents of reality-within this dynamic spacetime, researchers can investigate phenomena like particle creation and vacuum fluctuations as they occur during the universe’s evolution. Utilizing the FLRW metric allows for the translation of abstract theoretical calculations into predictions about the early universe, including potential signatures of new physics detectable in the cosmic microwave background or the distribution of large-scale structures. It provides the necessary framework to move beyond idealized flat spacetimes and grapple with the complexities of a genuinely expanding cosmological setting, enabling a deeper understanding of quantum effects in gravity.

Researchers are utilizing conformal transformations – a mathematical technique preserving angles – to unravel the complex behavior of quantum fields within the dynamic fabric of curved spacetime. This approach effectively simplifies calculations by mapping solutions in one spacetime to another, allowing for detailed analysis of particle creation. Studies reveal a compelling inverse relationship between interaction strength and excitation probability; as the force between particles increases, the likelihood of generating new particles actually decreases. This finding corroborates the theoretical prediction of suppressed particle production in strong gravitational fields, offering crucial insights into the early universe and the nature of vacuum fluctuations – suggesting that the intense conditions immediately following the Big Bang may not have led to the rampant particle creation previously anticipated, and providing a powerful tool for modeling phenomena around black holes.

Correlators for two-point charge density <span class="katex-eq" data-katex-display="false">{\mathcal Q}_2^{\rm lat.}(n,t)</span> and field <span class="katex-eq" data-katex-display="false">{\mathcal C}_2^{\rm lat.}(n,t)</span> exhibit lattice spacing dependence but converge toward analytical continuum results for free scalar theories, as demonstrated in the massless Schwinger model and <span class="katex-eq" data-katex-display="false">{\lambda\phi^4}</span> theory. — Correlators for two-point charge density ${\mathcal Q}_2^{\rm lat.}(n,t)$ and field ${\mathcal C}_2^{\rm lat.}(n,t)$ exhibit lattice spacing dependence but converge toward analytical continuum results for free scalar theories, as demonstrated in the massless Schwinger model and ${\lambda\phi^4}$ theory.

The study meticulously charts the suppression of particle creation through self-interaction, a finding resonant with the inherent irrationality of complex systems. It observes how even fundamental processes, like gravitational particle production, aren’t governed by clean equations, but by the messy interplay of forces. As Albert Einstein once noted, “Imagination is more important than knowledge.” This work doesn’t simply calculate particle behavior; it explores a regime previously inaccessible to perturbation theory, demanding a reimagining of how these forces operate in an expanding universe. The shift from perturbative methods to non-perturbative ones mirrors the recognition that simple models often fail when confronted with the unpredictable nature of reality.

Where Do the Numbers Lead?

The suppression of particle creation due to self-interaction isn’t surprising; humans routinely overpredict outcomes when faced with complex systems. It’s far easier to imagine unbounded growth than to account for the dampening effects of inherent limitations. This work, by moving beyond perturbative calculations, simply acknowledges that the universe isn’t built from simple additions, but from a constant negotiation between potential and constraint. The entanglement entropy measurements are, predictably, more interesting than the particle counts. Entanglement, after all, is merely a quantification of ignorance – a measure of how much one doesn’t know about the other side of the equation.

Future work will undoubtedly focus on extending these non-perturbative methods to more realistic field theories. But a truly insightful direction lies in exploring the limitations of the Hamiltonian lattice formulation itself. Every model is, at its core, a deliberate simplification. The art isn’t in creating a perfect representation, but in understanding which imperfections are most revealing. This isn’t about finding the ‘true’ cosmology; it’s about constructing a framework that highlights the predictable flaws in human intuition.

Ultimately, the question isn’t whether these calculations accurately reflect the early universe, but whether they offer a more honest portrayal of the biases embedded within the act of modeling itself. Economics, after all, is psychology with spreadsheets, and cosmology is merely a larger, more ambitious attempt to map the landscape of human expectation.

Original article: https://arxiv.org/pdf/2601.02331.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

The Illusion of Complexity: Why Simple Models Still Matter

Decoding the Quantum Field: Tensor Networks as a Predictive Tool

The Foundation of Prediction: From Dirac to Functional Integrals

Scaling the Framework: Constraints and Cosmological Implications

Where Do the Numbers Lead?

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