Exact Scalar Field Inflationary Solution in Rainbow Universe

Abstract

Using the Friedmann equation in rainbow Universe, we obtain an exact scalar field Inflationary Solution, which is a modification of the exact scalar field with negative potential −V 0 + m 2 ϕ 2 /2. Because the rainbow metric is Finsler metric, the result in this paper implies that the research of Finsler geometry in Cosmology should lead to several new physics theories.

Non-Minimally Conformally Coupling Cosmology with Multiple Vacua Potential with Cubic-Quintic-Septic Duffing Oscillator Properties

“…As the scalar field evolves with time, one can therefore express the Hubble parameter or the scale factor (depending on the ansatz considered) as a function of the scalar field instead of as a function of time [46]. This method is used in different cosmological scenarios [33][34][35][36][37][38][39][40][41][42] and in constructing exact inflationary solution in non-minimally chaotic inflation model [47] as well as many exact inflationary models [48,49]. This method is commendable, as all field equations are expressed in terms of the scalar field, and therefore, depending on the model under study, there is no need to neglect frictions terms in the field equations for example or assume that that they are dominant with respect to the kinetic energy of the scalar field.…”

Quantum Corrections to Hawking Radiation for Rainbow Universe

“…So we are in urgent need of a new geometry-Finsler geometry to overcome this difficult. Resulting from this reason, some persons have pointed out that the explaining of rainbow gravitational theory lies on Finsler geometry [47][48][49][50]. In this aspect, some achievements have been got.…”

An Exact Inflationary Solution to Non-Minimally Coupling

“…This method is creditable because it allows the full dynamical behavior of field to be investigated in terms of the function H (ϕ) thus does not have to assume that friction terms in the field equations dominate or that the field kinetic energy is negligible. This approach can be used to solve some exact inflationary solutions, see [11][12][13][14][15] for example.…”