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Second-order reconstruction of the inflationary potentialTo 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(sub 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(sub T) = (-1/ 7)(T/S). We derive the second-order expressions for the inflationary potential and its first two derivatives and the first-order expression for its third derivative, in terms, of n, n(sub T), S, T, and dn/d ln gamma. We also obtain the second-order consistency relation, n(sub T) = (-1/7)(T/S)(1 + 0.11(T/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 Pade approximate as a greatly improved alternative.
Document ID
19950012615
Acquisition Source
Legacy CDMS
Document Type
Preprint (Draft being sent to journal)
Authors
Liddle, Andrew R. (Sussex Univ. Brighton, United Kingdom)
Turner, Michael S. (Chicago Univ. Chicago, IL., United States)
Date Acquired
September 6, 2013
Publication Date
January 1, 1994
Subject Category
Theoretical Mathematics
Report/Patent Number
NAS 1.26:197629
FERMILAB-PUB-93/399-A
NASA-CR-197629
ASTRO-PH/9402021
SUSSEX-AST-94/2-1
Accession Number
95N19030
Funding Number(s)
CONTRACT_GRANT: NAGW-2381
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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