| Summary: | During inflation quantum fluctuations of the field driving
inflation, known as inflaton, were stretched by inflationary
expansion to galactic size scales or even larger. A possible
implication of inflation -- if it is correct -- is that our
observable universe was once of sub-Planckian size. Thus inflation
could act as a magnifier to probe the short distance structure of
space-time. General arguments about the quantum theory of gravity
suggest that the short distance structure of space-time can be
modeled as arising from some corrections to the well-known
uncertainty relation between the position and momentum operators.
Such modifications have been predicted by more fundamental theories
such as string theory. This modified commutation relation has been
implemented at the first quantized level to the theory of
cosmological perturbations. In this thesis, we will show that the
aforementioned scenario of implementing the minimal length to the
action has an ambiguity: total time derivatives that in continuous
space-time could be neglected and do not contribute to the equations
of motion, cease to remain total time derivatives as we implement
minimal length. Such an ambiguity opens up the possibility for
trans-Planckian physics to leave an imprint on the ratio of tensor
to scalar fluctuations. In near de-Sitter space, we obtain the
explicit dependence of the tensor/scalar on the minimal length. Also
the first consistency relation is examined in a power-law
background, where it is found that despite the ambiguity that exists
in choosing the action, Planck scale physics modifies the
consistency relation considerably as it leads to large oscillations
in the scalar spectral index in the observable range of scales. In
the second part of the thesis, I demonstrate how the assumption of
existence of invariant minimal length can assist us to explain the
origin of cosmic magnetic fields. The third part of the thesis is
dedicated to the study of signatures of M-theory Cascade inflation.
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