The Investigation Of Initial Spectrum Of The Early Universe Model

The problem of quadrupole anomaly in the cosmic microwave background temperature anisotropy spectrum is treated in many works. Most of them provide scenarios different from the one of standard inflation and point to a cutoff of power in the primordial power spectrum at large scales. We study the scenario of the early universe with a pre-inflation matter era, and make an ab initio calculation to check the existence of the infrared cutoff.To understand the effects of the pre-inflation matter era from a more solid theoretical standing, we decide to find the primordial power spectrum in an ab initio way. First we adopt a massive scalar field responsible for the inflation, and discard the "cosmological constant" formulation. We solve the complete perturbed Einstein equations, with the perturbations to the scalar field and the metric both included, and obtain the initial conditions to the differential equations by quantizing the scalar field. The quantization is performed under some approximations; the conditions for these approximations to be valid are carefully analyzed. As for the primordial power spectrum, we use the conservative gauge-invariant variable and examine the time-evolutions of various quantities to make sure that the primordial power spectrum is not affected by the details at the end of inflation. Finally, to gain a full control to the evolution of the modes, so as to determine the suitable parameters of the scalar field and the value of k’s we are going to study, we solve both the scale factors in ACDM model and inflation era numerically, and connect them to obtain the entire expansion history of the universe.This enables us to have a better understanding on the behavior of the modes, when they are crossing out or in the Hubble radius, and the physical intuition about how the pre-inflation matter era affect the evolution of the modes. We then compare the results of the pure inflation case and the case with pre-inflation matter era at the end.