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We report experimental measurements of heat transport in rotating Rayleigh-Bénard convection in a cylindrical convection cell with an aspect ratio of Γ = 1/2. The fluid is helium gas with a Prandtl number Pr = 0.7. The range of control parameters for Rayleigh numbers 4 × 109 < Ra < 4 × 1011 and for Flan an numbers 2 × 10-7 < Ek < 3 × 10-5 (corresponding to Taylor numbers 4 × 109 < Ta < 1 × 1014 and convective Rossby numbers 0.07 < Ro < 5). We determine the transition from weakly rotating turbulent convection to rotation dominated geostrophic convection through experimental measurements of the heat transport Nu. The heat transport, best collapsed using a parameter RaEkβ with 1.65 < β < 1.8, defines two boundaries in the phase diagram of Ra/Rac versus Ek and elucidates properties of the geostrophic turbulence regime of rotating thermal convection. We find Nu ~ (Ra/Rac)γ, with γ ≈ 1 from direct measurement and 1.2 < γ < 1.6 inferred from scaring arguments. [ABSTRACT FROM AUTHOR]