Effect of e-business strategy on performance of selected supermarkets in kisumu city, kenya

Abstract

Inflation is a period of an accelerated expansion of the universe. Cosmological perturbations are created by the amplification of quantum vacuum fluctuations of matter and metric perturbations during inflation. The equation of dynamics governing the evolution of cosmological perturbations within the cosmological model in a single field inflationary scenario takes the form of a standard non-linear second-order differential equation, whose exact analytical solution has not been obtained to date. The various methods of approximation that have been used in solving this equation of dynamics have varied limitations that include: inadequate error control; difficulty in improving the accuracy beyond the leading order (are not systematically extendable); complicated/tedious mathematical formulations; and series expansions that may be also divergent at some order. This study provides a systematically extendable method of approximation for the study of single field cosmological perturbations during inflation, which removes the divergence in the Wentzel-Kramers-Brillouin (WKB) approximation, based on a factorization and boost transformation procedures up to zeroth-order. The equation of dynamic is factorized and then converted into a matrix equation with its corresponding Hamiltonian. By using appropriately defined boost transformation operator, the resultant matrix equation undergoes successive boost transformations along suitable axes to new dynamical frames of high accuracy levels, characterized by an approximation parameter that becomes smaller with increasing number of boost transformations and is safely neglected at the highest level of approximation (accuracy). Diagonalization of the boost frame Hamiltonian leads to a simple analytical solution of the boost frame matrix equation through direct