В МФТИ выяснили, возможно ли, чтобы космологическая инфляция являлась квантовым эффектом.

The study published in Physics of Particles and Nuclei Letters. In recent years, researchers have been working to unravel the mystery of cosmic inflation—a period of rapid expansion of our Universe in its early moments. The challenge lies in the fact that existing theoretical models do not always align with the observational data we obtain. Furthermore, the origins of the potentials used to describe inflation remain unclear. Recent research, discussed in a new article by Russian physicists, offers a fresh perspective on this issue by examining various models that describe inflation and their correspondence with observational data.

Scientists conducted a numerical analysis of three relatively simple inflation models, each characterized by unique parameters. The results indicated that the first model, which describes inflation using a scalar field with non-zero mass and minimal gravitational interaction, shows agreement with observational data under certain conditions. However, not all parameters in this model can maintain this correspondence.

The studies revealed that parameters below the Planck mass threshold represent the most interesting and promising range. In particular, special attention was given to the area of low mass values and a large initial scalar field value, indicating the need for further research in this domain.

The second model describes a massless scalar field interacting with gravity in a non-minimal way. It attempts to account for contributions solely from gravity. The parameter N (the number of e-foldings, or expansions by a factor of e) has a lower bound around 50–60, which corresponds to inflationary expansion up to the reheating stage of the Universe. The total number of e-foldings could be higher, depending on the model being considered. Therefore, the second model is unsuitable (besides its strong correlation) as it only aligns with observational data at N = 40. This raises doubts about its ability to address the horizon and flatness problems faced by cosmology.

The third model is a generalization of the Coleman-Weinberg model for gravity, which also does not align with observations. Although it employs complex parameters to describe the effective potential and accounts for the self-interaction of the field, the results indicate its misalignment with observational data, highlighting the need for further refinements and its inapplicability in its current form.

“The models we examined are minimal modifications of general relativity, making them the simplest natural candidates for a true theory of cosmic inflation,” said Vladimir Schmidt, assistant professor at the Department of Higher Mathematics at MIPT. “We concluded that the first model aligns well with observations for certain parameter values, while the other two require modifications.”

In the framework of the first model, four cases were considered: inflation during which the universe expanded N = 50, 60, 64, and 70 times by a factor of e (approximately 2.71828).

Initially, the researchers were interested in the parameters ns and r, which play a crucial role in understanding the inflationary process and its impact on the formation of the Universe's structure. The first is known as the spectral index, which measures the frequency of occurrence of structures (density fluctuations in the early universe): denser or less dense. A value of one corresponds to a uniform distribution of structures. If it is less than one, larger structures occur more frequently; if greater, they occur less frequently. This spectral index can be estimated by measuring the temperature of the cosmic microwave background radiation at various points in the sky and comparing these temperatures.

The second parameter is called the tensor-scalar ratio. This is the ratio of the amplitudes of gravitational waves to the densities of matter resulting from inflation. It indicates how strongly the inflationary expansion of the universe generates gravitational waves compared to how much they are produced by matter itself. A large value of this parameter means that cosmic inflation occurred in conditions where gravitational waves arising from inflation played a significant role in the formation of the universe. Conversely, if this parameter is close to zero, the influence of gravitational waves can be neglected.

Both parameters can be estimated using observational data of the cosmic microwave background radiation. Modeling revealed that for N = 70 in the first model, there are parameter values at which the model aligns with observations. The remaining two models showed no alignment at all.

“The models we studied represent interesting examples of inflationary scenarios based on quantum effects. The first model, in particular, demonstrates a promising approach to explaining inflation based on simple assumptions while ensuring agreement with observational data,” said Andrey Arbuzov, the first author of the article and head of Sector No. 5 at the N.N. Bogolyubov Laboratory of Theoretical Physics at JINR (Dubna). “We hope that our findings will contribute to further research efforts in the field of quantum gravity and expand our understanding of cosmological processes.”

_{(published with the support of a grant from the Ministry of Science and Higher Education of Russia as part of the federal project “Popularization of Science and Technology” No. 075-15-2024-571)}