Asymptotic Solutions of a Generalized Starobinski Model: Kinetic Dominance, Slow Roll and Separatrices

We consider a generalized Starobinski inflationary model. We present a method for computing solutions as generalized asymptotic expansions, both in the kinetic dominance stage (psi series solutions) and in the slow roll stage (asymptotic expansions of the separatrix solutions). These asymptotic expansions are derived in the framework of the Hamilton-Jacobi formalism where the Hubble parameter is written as a function of the inflaton field. They are applied to determine the values of the inflaton field when the inflation period starts and ends as well as to estimate the corresponding amount of inflation. As a consequence, they can be used to select the appropriate initial conditions for determining a solution with a previously fixed amount of inflation.

Inflation from the Symmetry of the Generalized Cosmological Model

It is shown that the inflationary model is the result of the symmetry of the generalized F(R,T,X,φ)-cosmological model using the Noether symmetry. It leads to a solution, a particular case of which is Starobinsky’s cosmological model. It is shown that even in the more particular case of cosmological models F(R,X,φ) and F(T,X,φ) the Monge–Ampère equation is still obtained, one of the solutions including the Starobinsky model. For these models, it is shown that one can obtain both power-law and exponential solutions for the scale factor from the Euler–Lagrange equations. In this case, the scalar field φ has similar time dependences, exponential and exponential. The resulting form of the Lagrangian of the model allows us to consider it as a model with R2 or X2. However, it is also shown that previously less studied models with a non-minimal relationship between R and X are important, as one of the possible models. It is shown that in this case the power-law model can have a limited evolutionary period with a negative value of the kinetic term.

Warm constant-roll inflation in brane-world cosmology

In this paper, we study a constant-roll inflationary model in the context of brane-world cosmology caused by a quintessence scalar field for warm inflation with a constant dissipative parameter [Formula: see text]. We determine the analytical solution for the Friedmann equation coupled to the equation of motion of the scalar field. The evolution of the primordial scalar and tensor perturbations is also studied using the modified Langevin equation. To check the viability of the model, we use numerical approaches and plot some figures. Our results for the scalar spectral index and the tensor-to-scalar ratio show good consistency with observations.

Formation of a New Economic Model in the Post-Stalinist Soviet Union

Introduction. The article is devoted to the change of economic model in the post-Stalinist USSR. It considers measures through which this model was implemented, its consequences, features and social results are distinguished. Materials and Methods. The results of research are based on statistic of the USSR State Bank and analytical reports of experts published in the issues of edition “On the pages of archival funds of the Central Bank of the Russian Federation”. The author examines the dynamic and problems of money circulation, the social and economic contradictions generated by them. Results. The transition to the inflationary model began with a political course to reject from limiting population monetary income. In 1953–1970, in various forms, the monetary incomes of citizens, including the rural population, low-income, socially unprotected, were significantly increased. These measures led to negative processes in money circulation, to which experts of the State Bank drew the attention of the country’s leadership for a long period. Among them there were: the monetary growth, outpacing the growth in the production of consumer goods and the possibilities of goods turnover; the growth of public deposits in savings bank reflecting unmet demand for consumer goods; the use of public deposits to maintain the solvency of the country’s budget; increasing of the emission. Discussions. The inflationary economic model, implemented in a centralized planning system, had visible features. First, inflation in this model was not accompanied with price increases; secondly, the emission of money was the base for raising the standard of living of the population; thirdly, in this model the social stratification between ordinary citizens and the elite was intensified; fourthly, with transit to the inflationary model the shadow economy got the development. Conclusion. The transition in the USSR to an inflationary economic model improved standards of living in the USSR but predetermined the inevitable economic crisis in the foreseeable future with a high probability of the destruction of socialism.

Primordial black holes formation in the inflationary model with field-dependent kinetic term for quartic and natural potentials

Within the framework of inflationary model with field-dependent kinetic term for quartic and natural potentials, we investigate generation of the primordial black holes (PBHs) and induced gravitational waves (GWs). In this setup, we consider a kinetic function as $$G(\phi )=g_I(\phi )\big (1+g_{II}(\phi )\big )$$ G ( ϕ ) = g I ( ϕ ) ( 1 + g II ( ϕ ) ) and show that in the presence of first term $$g_I(\phi )$$ g I ( ϕ ) both quartic and natural potentials, in contrast to the standard model of inflation, can be consistent, with the 68% CL of Planck observations. Besides, the second term $$g_{II}(\phi )$$ g II ( ϕ ) can cause a significant enhancement in the primordial curvature perturbations at the small scales which results the PBHs formation. For the both potentials, we obtain an enhancement in the scalar power spectrum at the scales $$k\sim 10^{12}~{\mathrm{Mpc}}^{-1}$$ k ∼ 10 12 Mpc - 1 , $$10^{8}~{\mathrm{Mpc}}^{-1}$$ 10 8 Mpc - 1 , and $$10^{5}~{\mathrm{Mpc}}^{-1}$$ 10 5 Mpc - 1 , which causes PBHs production in mass scales around $$10^{-13}M_{\odot }$$ 10 - 13 M ⊙ , $$10^{-5}M_{\odot }$$ 10 - 5 M ⊙ , and $$10 M_{\odot }$$ 10 M ⊙ , respectively. Observational constraints confirm that PBHs with a mass scale of $$10^{-13}M_{\odot }$$ 10 - 13 M ⊙ can constitute the total of dark matter in the universe. Furthermore, we estimate the energy density parameter of induced GWs which can be examined by the observation. Also we conclude that it can be parametrized as a power-law function $$\Omega _{\mathrm{GW}}\sim (f/f_c)^n$$ Ω GW ∼ ( f / f c ) n , where the power index equals $$n=3-2/\ln (f_c/f)$$ n = 3 - 2 / ln ( f c / f ) in the infrared limit $$f\ll f_{c}$$ f ≪ f c .

Favored Inflationary Models by Scalar Field Condensate Baryogenesis

We calculate the baryon asymmetry value generated in the Scalar Field Condensate (SCF) baryogenesis model obtained in several inflationary scenarios and different reheating models. We provide analysis of the baryon asymmetry value obtained for more than 70 sets of parameters of the SCF model and the following inflationary scenarios, namely: new inflation, chaotic inflation, Starobinsky inflation, MSSM inflation, quintessential inflation. We considered both cases of efficient thermalization after inflation and delayed thermalization. We have found that the SFC baryogenesis model produces baryon asymmetry orders of magnitude bigger than the observed one for the following inflationary models: new inflation, new inflation model by Shafi and Vilenkin, MSSM inflation, chaotic inflation with high reheating temperature and the simplest Shafi–Vilenkin chaotic inflationary model. Strong diluting mechanisms are needed for these models to reduce the resultant baryon excess at low energies to its observational value today. We have found that a successful generation of the observed baryon asymmetry is possible by the SCF baryogenesis model in Modified Starobinsky inflation, chaotic inflation with low reheating temperature, chaotic inflation in SUGRA, and Quintessential inflation.