In this thesis the Big Bang and inflation theory are reviewed. The success of inflation is largely due to the predicted generation of inhomogeneities. We review the dynamical equations of motion for an accelerating expansion of the Universe and the flow equations which describe the evolution of the Hubble slow-roll parameters. We use cosmological perturbation theory to find a new expression relating comoving curvature perturbations generated during inflation to density perturbations responsible for structure formation. Primordial black holes (PBHs) may form from primordial perturbations. We compile and update constraints on the abundance of PBHs. We then use our new relationship to translate these abundance limits into constraints on the power spectrum of primordial curvature perturbation. In addition we investigate the possible formation of ultracompact dark matter minihalos (UCMHs) which may also form from primordial pertubations. If dark matter is in the form of weakly interacting massive particles (WIMPs) then WIMP annihilation may produce a detectable gamma-ray signature. We calculate the potential constraints which would arise from a detection by the Fermi satellite. Finally, we investigate single field models of inflation using a stochastic technique to generate a large ensemble of models. Using a numerical approach along with a modified flow algorithm we find models of inflation compatible with all cosmological data which have large perturbations on small scales. Significant PBH formation occurs in models in which inflation can continue indefinitely and is ended via a secondary mechanism. We use our PBH constraints to eliminate such models which overproduce PBHs. In this work we demonstrate that PBH constraints, although weak, are effective at constraining models of inflation. We also demonstrate that a gamma-ray detection from UCMHs could potentially constrain the power spectrum of curvature perturbation on small scales very tightly in the near future.
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