MIPT researchers explored whether cosmic inflation could be a quantum effect.

The study has been published in Physics of Particles and Nuclei Letters. In recent years, scientists have been trying to unravel the mystery of cosmic inflation—a period of rapid expansion of our Universe during its early moments. The issue is that existing theoretical models do not always align with the data we obtain from observations. 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 problem by examining various models that describe inflation and their alignment with observational data.

The researchers 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 are capable of maintaining this consistency.

The studies revealed that parameters below the Planck mass threshold represent the most interesting and promising range. Specifically, particular attention was given to the area of small mass values and a large initial value of the scalar field, 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 the contribution solely from gravity. The parameter N (the number of e-foldings, or expansions by a factor of e) has a lower limit around 50-60, corresponding to inflationary expansion up to the reheating stage of the Universe. The total number of e-foldings could be higher, depending on the model considered. Therefore, the second model is deemed unsuitable (aside from its strong coupling), as it aligns with observational data only at N = 40. This raises doubts about its ability to address the horizon and flatness problems facing cosmology.

The third model is a generalization of the Coleman-Weinberg model for gravity, which also does not match observations. Although it employs complex parameters to describe the effective potential and accounts for the field's self-interaction, the results indicate its misalignment with observational data, suggesting the need for further improvements 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, an assistant professor in the Department of Higher Mathematics at MIPT. “We concluded that the first model aligns excellently with observations at certain parameter values, while the other two require modifications.”

Within the first model, four cases were considered: inflation where 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, known as the spectral index, measures which structures (density fluctuations in the early Universe) occur more frequently: 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 in different parts of 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 that arise from inflation. It indicates how strongly the inflationary expansion of the Universe generates gravitational waves compared to how they are created by matter itself. A large value of this parameter suggests that cosmic inflation occurred under conditions where the gravitational waves generated by inflation play a significant role in the formation of the Universe. Conversely, if this parameter is close to zero, the influence of gravitational waves can be disregarded.

Both parameters can be estimated using observational data on cosmic background radiation. The modeling revealed that for N = 70 in the first model, there are parameter values where the model aligns with observations. The remaining two models did not yield any alignment.

“The models we investigated represent intriguing 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 Andrei 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 Education and Science of Russia within the framework of the federal project “Popularization of Science and Technology” No. 075-15-2024-571)}