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.

Wave-Like Exact Models with Symmetry of Spatial Homogeneity in the Quadratic Theory of Gravity with a Scalar Field

Exact solutions are obtained in the quadratic theory of gravity with a scalar field for wave-like models of space–time with spatial homogeneity symmetry and allowing the integration of the equations of motion of test particles in the Hamilton–Jacobi formalism by the method of separation of variables with separation of wave variables (Shapovalov spaces of type II). The form of the scalar field and the scalar field functions included in the Lagrangian of the theory is found. The obtained exact solutions can describe the primary gravitational wave disturbances in the Universe (primary gravitational waves).

Hamilton-Jacobi Equation of Time Dependent Hamiltonians

In this work, we apply the geometric Hamilton-Jacobi theory to obtain solution of Hamiltonian systems in classical mechanics that are either compatible with two structures: the first structure plays a central role in the theory of time- dependent Hamiltonians, whilst the second is used to treat classical Hamiltonians including dissipation terms. It is proved that the generalization of problems from the calculus of variation methods in the nonstationary case can be obtained naturally in Hamilton-Jacobi formalism.

Nonlinear dynamics of a charged particle in a strong non-null knot wave background

In this paper, we study the dynamics of a charged particle interacting with the non-null electromagnetic knot wave background. We analyze the classical system in the Hamilton–Jacobi formalism and find the action, the linear momentum and the trajectory of the particle. Also, we calculate the effective mass and the emitted radiation along the knot wave. Next, we quantize the system in the classical strong knot wave background by using the strong-field QED canonical formalism. We explicitly construct the Furry picture and calculate the Volkov solutions of the Dirac equation. As an application, we discuss the one-photon Compton effect where we determine the general form of the S-matrix. Also, we discuss in detail the first partial amplitudes in the transition matrix in two simple backgrounds and show that there is a pair of states for which these amplitudes are identical.

Hubble inflation in Randall–Sundrum type II model

We study a braneworld Randall–Sundrum type II (RSII) model using the Hamilton–Jacobi formalism. We extend the standard inflationary parameters and the flow equations for this braneworld scenario. We investigate the conditions that reduce the infinite number of flow equations into a finite number and confirm that by considering one of the inflationary parameters that vanishes, the Hubble expansion rate gets a polynomial form in both General Relativity (GR) and in the high-energy regime of RSII. We also show that if one sets this inflationary parameter to a constant value, the model features a nonpolynomial form of the Hubble expansion rate. The form of the Hubble parameter in this case is different in GR and RSII. Next, we consider a single-scalar field model with a Hubble expansion rate behaving as [Formula: see text] and show that compared to GR, the RSII model has a smaller tensor-to-scalar ratio and larger spectral index for [Formula: see text]. Therefore, RSII model leads to better predictions than GR.