Search Results (5)

The problem of mathematical modeling and analysis of stochastic phenomena in population systems with competition is considered. This problem is investigated based on a discrete system of two populations modeled by the Ricker map. We study the dependence of the joint dynamic behavior on the parameters of the growth rate and competition intensity. It is shown that, due to multistability, random perturbations can transfer the population system from one attractor to another, generating stochastic P-bifurcations and transformations of synchronization modes. The effectiveness of a mathematical approach, based on the stochastic sensitivity technique and the confidence domain method, in the parametric analysis of these stochastic effects is demonstrated. For monostability zones, the phenomenon of stochastic generation of the phantom attractor is found, in which the system enters the trigger mode with alternating transitions between states of almost complete extinction of one or the other population. It is shown that the noise-induced effects are accompanied by stochastic D-bifurcations with transitions from order to chaos. Full article

In this work, we focus on two important aspects of modern cosmology: reheating and Hubble constant tension within the framework of a unified cosmic theory, namely the quintessential inflation connecting the early inflationary era and late-time cosmic acceleration. In the context of reheating, we use instant preheating and gravitational reheating, two viable reheating mechanisms when the evolution of the universe is not affected by an oscillating regime. After obtaining the reheating temperature, we analyze the number of e-folds and establish its relationship with the reheating temperature. This allows us to connect, for different quintessential inflation models (in particular for models coming from super-symmetric theories such as $\alpha$-attractors), the reheating temperature with the spectral index of scalar perturbations, thereby enabling us to constrain its values. In the second part of this article, we explore various alternatives to address the $H_0$ tension. From our perspective, this tension suggests that the simple Λ-Cold Dark Matter model, used as the baseline by the Planck team, needs to be refined in order to reconcile its results with the late-time measurements of the Hubble constant. Initially, we establish that quintessential inflation alone cannot mitigate the Hubble tension by solely deviating from the concordance model at low redshifts. The introduction of a phantom fluid, capable of increasing the Hubble rate at the present time, becomes a crucial element in alleviating the Hubble tension, resulting in a deviation from the Λ-Cold Dark Matter model only at low redshifts. On a different note, by utilizing quintessential inflation as a source of early dark energy, thereby diminishing the physical size of the sound horizon close to the baryon–photon decoupling redshift, we observe a reduction in the Hubble tension. This alternative avenue, which has the same effect of a cosmological constant changing its scale close to the recombination, sheds light on the nuanced interplay between the quintessential inflation and the Hubble tension, offering a distinct perspective on addressing this cosmological challenge. Full article

We studied the following scalar field ϕCDM models: ten quintessence models and seven phantom models. We reconstructed these models using the phenomenological method developed by our group. For each potential, the following ranges were found: (i) model parameters; (ii) EoS parameters; and (iii) the initial conditions for differential equations, which describe the dynamics of the universe. Using MCMC analysis, we obtained the constraints of scalar field models by comparing observations for the expansion rate of the universe, the angular diameter distance and the growth rate function, with corresponding data generated for the fiducial ΛCDM model. We applied Bayes statistical criteria to compare scalar field models. To this end, we calculated the Bayes factor, as well as the AIC and BIC information criteria. The results of this analysis show that we could not uniquely identify the preferable scalar field ϕCDM models compared to the fiducial ΛCDM model based on the predicted DESI data, and that the ΛCDM model is a true dark energy model. We investigated scalar field ϕCDM models in the w₀–w_a phase spaces of the CPL-ΛCDM contours. We identified subclasses of quintessence and phantom scalar field models that, in the present epoch: (i) can be distinguished from the ΛCDM model; (ii) cannot be distinguished from the ΛCDM model; and (iii) can be either distinguished or undistinguished from the ΛCDM model. We found that all the studied models can be divided into two classes: models that have attractor solutions and models whose evolution depends on initial conditions. Full article

We investigate the phase space of a scalar field theory obtained by minisuperspace deformation. We consider quintessence or phantom scalar fields in the action that arises from minisuperspace deformation on the Einstein–Hilbert action. We use a modified Poisson algebra where Poisson brackets are the $\alpha$-deformed ones and are related to the Moyal–Weyl star product. We discuss early- and late-time attractors and reconstruct the cosmological evolution. We show that the model can have the $\mathrm{\Lambda CDM}$ model as a future attractor if we initially consider a massless scalar field without a cosmological constant term. Full article

A problem of the noise-induced generation and shifts of phantom attractors in nonlinear dynamical systems is considered. On the basis of the model describing interaction of the climate and vegetation we study the probabilistic mechanisms of noise-induced systematic shifts in global temperature both upward (“warming”) and downward (“freezing”). These shifts are associated with changes in the area of Earth covered by vegetation. The mathematical study of these noise-induced phenomena is performed within the framework of the stochastic theory of phantom attractors in slow-fast systems. We give a theoretical description of stochastic generation and shifts of phantom attractors based on the method of freezing a slow variable and averaging a fast one. The probabilistic mechanisms of oppositely directed shifts caused by additive and multiplicative noise are discussed. Full article