# Quantum cosmological correlations in inflating universe: effect of gravitational fluctuation due to fermion, gauge, and others [sic] loops

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Quantum theory of cosmological fluctuations with other matters is studied to higher order to understand the origin of the universe during the time of inflation. This study also links gravitational and all matter fluctuations with the observed cosmic microwave background (CMB) anisotropy. It is important to keep in mind that what is tested observationally is the paradigm that the primordial spectrum of inhomogeneities was nearly scale invariant and predominantly adiabatic. Therefore, if other matters such as fermion and gauge fields which do not drive inflation predict the scale invariant spectrums, their existence during inflation cannot be ruled out. We therefore extend the calculation of quantum corrections to the cosmological correlation hζζi, which has been done by Weinberg for a loop of minimally coupled scalars, to other types of matters loops and a general and realistic potential. This dissertation shows that departures from scale invariance are never large even when Dirac, vector, and conformal scalar fields are present during inflation and even when the two-loop spectrum is calculated. No fine tuning is needed, in the sense that effective masses can be arbitrary values. Although the loop power spectrum was generally expected to be smaller than the classical one by a factor of GH2 , I find that the quantum effect could be in the order of the classical value at the two loop level. The momentum dependence of the quantum spectrum goes as q −3 ln q for all massless matters at one-loop and goes as q −3 ln2 q at two-loop. For massive matters, the momentum dependence goes as q −3+η(m) , where |η| ¿ 1 regardless of the value of m. Thus scale free correlations are consistent with natural reheating. These results imply that we and the things around us did not come from nothing or an unknown scalar field as in conventional beliefs. Rather it points to the fact that we originated from quantum fluctuations due to the interactions between gravity and various matters during the time of Big Bang inflation.