100 Years of Relativity Space-Time Structure: Einstein and Beyond ...

188 T. PadmanabhanFig. 1. Different observations of cosmological significance and the length scales andredshift ranges probed by them. The broken (thin) lines in the figure are contoursof ∆(k = 2π/x, a) = (5, 1.69, 1, 10 −2 , 10 −5 ) from bottom to top. Figure courtesy:T. Roy Choudhury.to modulated acoustic oscillations with a characteristic wavelength at thez = 10 3 surface. Regions of high and low baryonic density contrast willlead to anisotropies in the temperature with the same characteristic wavelength(which acts as a standard ruler) leading to a series of peaks in thetemperature anisotropy that have been detected. The angles subtended bythese acoustic peaks will depend on the geometry of the universe and providesa reliable procedure for estimating the cosmological parameters. Detailedcomputations 9 show that: (i) The multipole index l corresponding tothe first acoustic peak has a strong, easily observable, dependence on Ω totand scales as l p ≈ 220Ω −1/2tot if there is no dark energy and Ω tot = Ω NR .(ii) But if both non-relativistic matter and dark energy is present, withΩ NR + Ω DE = 1 and 0.1 Ω NR 1, then the peak has only a very weakdependence on Ω NR and l p ≈ 220Ω 0.1NR . Thus the observed location of thepeak (which is around l ∼ 220) can be used to infer that Ω tot ≃ 1. More