Reconstructing inflationary potential from BICEP2 and running of tensor
  modes
  In this paper we will analyse the constraints on a sub-Planckian excursion of
a single inflaton field, which would yield a large tensor to scalar ratio,
while explaining the temperature anisotropy of the cosmic microwave background
(CMB) radiation. In particular, our attempt will be to reconstruct the
inflationary potential by constraining, $V(\phi_0), V^{\prime}(\phi_0),
V^{\prime\prime}(\phi_0), V^{\prime\prime\prime}(\phi_0)$ and
$V^{\prime\prime\prime\prime}(\phi_0)$, in the vicinity of the field,
$\phi_0\ll M_p$, and the field displacement, $\Delta \phi \ll M_p$, where $M_p$
is the reduced Planck mass. We will provide, for the first time, a set of new
{\it consistency} relationships for sub-Planckian excursion of the inflaton
field, which would help us to differentiate sub-versus-super Planckian models
of inflation. For a generic single field inflationary potential, we will be
able to put a stringent bound on the potential energy density:
$2.07\times10^{16} {\rm GeV}\leq\sqrt[4]{V_{\star}}\leq 2.40\times 10^{16} {\rm
GeV}$, where inflation can occur on the flat potential within, $0.066
\leq\frac{\left |\Delta\phi\right|}{M_p}\,\leq 0.092$, for the following
observational constraints: (Planck+WMAP-9+high L+BICEP2). We then provide a
prediction for the spectral tilt ($n_{T}$), running ($\alpha_{T}$) and running
of running ($\kappa_{T}$) of the tensor modes within the window,
$-0.019<n_{T}<-0.033$, $-2.97\times 10^{-4}<\alpha_{T}(=dn_{T}/d\ln
k)<2.86\times 10^{-5}$,and $-0.11\times 10^{-4}<\kappa_{T}(=d^{2}n_{T}/d\ln
k^{2})<-3.58\times 10^{-4}$, in a model independent way. We also provide a
simple example of an {\it inflection-point} model of inflation and reconstruct
the potential in a model independent way to match the current observations.
