Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Second-Order Reconstruction of the Inflationary Potential   To first order in the deviation from scale invariance the inflationary
potential and its first two derivatives can be expressed in terms of the
spectral indices of the scalar and tensor perturbations, $n$ and $n_T$, and
their contributions to the variance of the quadrupole CBR temperature
anisotropy, $S$ and $T$. In addition, there is a ``consistency relation''
between these quantities: $n_T= -{1\over 7}{T\over S}$. We discuss the overall
strategy of perturbative reconstruction and derive the second-order expressions
for the inflationary potential and its first two derivatives and the
first-order expression for its third derivative, all in terms of $n$, $n_T$,
$S$, $T$, and $dn/d\ln k$. We also obtain the second-order consistency
relation, $n_T =-{1\over 7}{T\over S}[1+0.11{T\over S} + 0.15 (n-1)]$. As an
example we consider the exponential potential, the only known case where exact
analytic solutions for the perturbation spectra exist. We reconstruct the
potential via Taylor expansion (with coefficients calculated at both first and
second order), and introduce the Pad\'{e} approximant as a greatly improved
alternative.

31
The categories of this paper are: ao-sci
2
The categories of this paper are: math
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg