Mahgoub Salih

A Canonical Quantization Formalism of Curvature Squared Action: Curvature Squared Action in Cosmology Mahgoub Salih

We have seen that the canonical quantization formalism adopted in this work has brought interesting results. We have solved the Wheeler-De Witt equation and obtained the wave function of the universe. We found that density parameter is related to probability. Moreover, we have found that the scale factor is imaginary. From Stefan's law we have found the cosmic microwave background radiation (CMBR) temperature.when the universe radius is large, the expansion rate is slow, equation (2-26) which is the expression for the density reduces to that of GR, the density of universe decreases with time as radius increases in conformity with observations. When the radius is assumed to be very small with high expansion rate i.e. a?0 ,a ???, as happens at early universe, the pressure becomes negative. This also agrees with inflation assumption. We constructed the generalized wave-function in interval of -1?n?1 . and obtained the energy states of the universe . We found E=0 ,when n=a/(2a-1) . This leads to E=0 at radiation era. We calculated the Curvature density parameter ? and the Curvature energy density?. At early universe we found a new Phantom energy, increasing with time.