Open AccessResponse of distance measures to the equation of state
Author(s) -
Deep Saini Tarun,
Padmanabhan T.,
Bridle Sarah
Publication year - 2003
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.2003.06685.x
Subject(s) - physics , dark energy , weighting , function (biology) , polynomial , cosmic microwave background , luminosity distance , constant (computer programming) , heuristic , matrix (chemical analysis) , mathematical analysis , mathematics , quantum mechanics , mathematical optimization , cosmology , materials science , anisotropy , evolutionary biology , acoustics , computer science , composite material , biology , programming language
We show that the distance measures (such as the luminosity and angular diameter distances) are linear function als of the equation of state function w ( z ) of the dark energy to a fair degree of accuracy in the regimes of interest. That is, the distance measures can be expressed as a sum of (i) a constant and (ii) an integral of a weighting function multiplied by the equation of state parameter w ( z ) . The existence of such an accurate linear response approximation has several important implications. (1) Fitting a constant‐ w model to the data drawn from an evolving model has a simple interpretation as a weighted average of w ( z ) . (2) Any polynomial (or other expansion coefficients) can also be expressed as weighted sums of the true w . (3) A replacement for the commonly used heuristic equation for the effective w , as determined by the cosmic microwave background, can be derived and the result is found to be quite close to the heuristic expression commonly used. (4) The reconstruction of w ( z ) by Huterer & Starkman can be expressed as a matrix inversion. In each case the limitations of the linear response approximation are explored and found to be surprisingly small.