Early Universe Inflation and Scalar Field Dynamics in Einstein–Gauss–Bonnet Gravity

Understanding the nature of the early Universe remains one of the most profound and challenging problems in modern fundamental physics. Cosmological inflation — a period of exponential expansion that occurred fractions of a second after the Big Bang — has become a cornerstone of contemporary cosmology. Inflation successfully explains the horizon problem, the flatness problem, and the origin of primordial density fluctuations that later evolved into galaxies and large-scale cosmic structures. Nevertheless, the precise physical mechanism driving inflation, the nature of the fields involved, and their interaction with gravity are still subjects of active theoretical investigation.

In order to address these fundamental questions, researchers at Al-Farabi Kazakh National University (KazNU) are implementing a fundamental research project for 2025–2027 devoted to the study of scalar field dynamics interacting with Einstein–Gauss–Bonnet gravity during the inflationary epoch. The project is designed to contribute to the advancement of modern theoretical cosmology in Kazakhstan while remaining fully aligned with leading international research directions in high-energy theoretical physics and astrophysics.

In most inflationary models, inflation is driven by a scalar field known as the inflaton, whose potential is constrained by cosmological observations, particularly measurements of the cosmic microwave background radiation. However, the energy scales characteristic of inflation are vastly higher than those accessible today. At such energies, additional gravitational corrections beyond Einstein’s General Relativity are expected to emerge.

Effective field theory approaches, as well as more fundamental frameworks inspired by quantum gravity, predict possible interactions between scalar fields and the Gauss–Bonnet invariant. Such interactions modify both the Einstein field equations and the Klein–Gordon equation governing scalar fields. As a result, the standard dynamics of inflation may be significantly altered, leading to new stationary solutions, modifications of symmetry structures in particle physics, and potentially observable cosmological consequences.

The primary objective of the project is to determine how Einstein–Gauss–Bonnet gravity modifies the dynamics of scalar fields during inflation and how these modifications influence symmetry breaking patterns and the generation of cosmological perturbations.

The first research direction focuses on scenarios of symmetry breaking and symmetry restoration during inflation. The coupling of a scalar field to the Gauss–Bonnet term generates an effective potential that may produce new stationary points in de Sitter or quasi-de Sitter vacua. These stationary points can trigger spontaneous breaking or restoration of discrete and continuous symmetries during the inflationary phase. Such behavior differs substantially from conventional cosmological scenarios, where symmetries are typically assumed to be broken either before or after the observable stage of inflation.

The second direction addresses the formation of topological defects arising from symmetry breaking. Spontaneous symmetry breaking can lead to the emergence of domain walls, cosmic strings, and magnetic monopoles. Within this project, a new class of defects induced by Gauss–Bonnet coupling will be systematically investigated for the first time. Analytical and numerical solutions describing these defects will be derived and compared with their counterparts in standard Einstein gravity. Particular attention will be given to their evolution during and after inflation, as well as to their possible observational signatures.

The third research direction concerns multi-scalar Gauss–Bonnet couplings. While much of the existing literature focuses on single-field models, more realistic scenarios may involve multiple interacting scalar fields. Multi-field dynamics can lead to the appearance of new stationary solutions, enhancements of scalar and tensor perturbations, and potentially to the formation of primordial black holes and a stochastic gravitational wave background.

Tensor perturbations — that is, gravitational waves — depending on their amplitude and frequency, may be detectable by future space-based observatories. Among the most prominent missions are LISA and DECIGO, both designed to probe gravitational waves of cosmological origin. In addition, the international radio interferometry project Square Kilometre Array (SKA) provides complementary opportunities to study low-frequency gravitational wave backgrounds indirectly. The comparison between theoretical predictions and the sensitivity curves of these experiments opens a window for testing nontrivial inflationary dynamics.

The project is purely fundamental in nature. No laboratory experiments are conducted; however, publicly available cosmological observational data are actively employed. The research methodology includes quantum field theory in curved spacetime, cosmological perturbation theory, the slow-roll approximation, stochastic inflation formalism, and the Press–Schechter framework for analyzing primordial black hole formation. Numerical simulations are performed using Wolfram Mathematica and Python, allowing for a detailed comparison between analytical approximations and fully numerical solutions.

Research in inflationary cosmology and modified gravity is actively pursued in leading scientific institutions worldwide, including CERN, Sorbonne University, and The University of Tokyo. The work carried out at KazNU is fully embedded within this international context and contributes to strengthening Kazakhstan’s presence in modern theoretical physics.

The project actively involves young researchers, master’s students, and doctoral candidates. Participants acquire expertise in advanced analytical and numerical techniques in cosmology and gravitational physics, present their findings at international conferences, and prepare publications for peer-reviewed journals indexed in Web of Science and Scopus. In this way, the project fulfills not only a scientific mission but also an important educational role, fostering the next generation of specialists in theoretical cosmology.

The project is scheduled for implementation from January 2025 through December 2027, with a total duration of 36 months. The expected outcomes include a series of publications in internationally recognized scientific journals and the development of new research directions at the intersection of cosmology, high-energy physics, and gravitational theory.

Throughout the project, strict adherence to principles of scientific ethics is ensured. Fabrication, falsification, plagiarism, and inappropriate authorship practices are not tolerated. Intellectual property rights are distributed fairly among members of the research team, and publication in open scientific literature serves as a primary mechanism for protecting and disseminating research results.

The investigation of scalar fields interacting with Einstein–Gauss–Bonnet gravity opens new avenues for understanding the physics of the early Universe. By extending the standard inflationary paradigm and exploring gravitational effects beyond General Relativity, the project contributes to one of the central challenges of modern theoretical physics — the reconciliation of quantum field theory and gravity. The research conducted at KazNU represents a systematic and forward-looking effort to advance theoretical cosmology in Kazakhstan and to enhance the country’s scientific standing on the global stage.