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Parameterizing Dark Energy Z. Huang, R. J. Bond, L. Kofman Canadian Institute of Theoretical Astrophysics w - Dark Energy Equation of State Data: CMB + SN + LSS + WL + Lya Constant w=w0 Code: modified cosmomc w(a)=w0+wa(1-a) Principal components s1=0.12 s2=0.32 s3=0.63 w0 = -0.98 ± 0.05 What we know about w Phenomenologically • w is close to –1 at low redshift • Rich information at z<2, weak information at 2<z<4, almost no information at z>4 • Results depend on parametrization. Need theoretical priors. What if we start from physics? Use physics to solve problems When Canadian plug does not fit UK socket… Dynamics of Quintessence/Phantom simplicity of w(a). we do need assumptions simplicity of V(φ). Dynamics of Quintessence/Phantom define Popular story of quintessence: Fast rolling (large eV) in early universe (scaling regime); Slow rolling (small eV) in late universe. Field equation + Friedmann Equations Simplicity assumptions In the relevant redshift range (e.g. 0<z<4), 1. V(f) is monotonic. 2. Quintessence rolls down (dV/dt<0). Phantom rolls up (dV/dt>0). 3. w is close to -1 at low redshift. Quantitatively, |1+w|<0.4 at 0<z<1. 4. V(f) is a “simple” function. Quantitatively, |hV| is less than or of the same order of either Planck scale or eV. examples, V(f) = V0 exp(-lf) V(f) = V0 + V1 f V(f) = V0 fn (n=0,±1, ±2, ±3,…) 1-parameter parametrization • Additional assumption: slow-roll at 0<z<10 (initial velocity Hubble-damped at low redshift). “average slope” es=<ev> where es>0, quintessence es=0, cosmological constant es<0, phantom CMB + SN + LSS + WL + Lya Initial velocity is damped by Hubble friction Time variation of eV is not important Given solution w(a) and eV(a), define trajectory variables: • es= eV uniformly averaged at 1/3<a<1. • ew = (1+w)/f(a/aeq). (remind: 1-param formula is wfit=-1+ es f(a/aeq)) Constraint Equation • Define w0=w|a=1, wa=-dw/da|a=1 w0 and wa are functions of (es, Ωm). Numerical fitting yields binned SNe samples (192 samples) Some w0-wa mimic cosmological constant 2-parameter parametrization • Assumption: slow-roll at 0<z<2 (with possible non-damped velocity). CMB + SN + LSS + WL + Lya Hubble damping term 2-parameter parametrization - residual velocity at low redshift. 3-parameter parametrization In general eV varies. Assuming no oscillation , we model Other corrections can only be numerically fitted: •redefine aeq. •O(θ3) term numerical fitting. •as- es power suppression (if es and as are both large, the power of Hubble damping term would be suppressed). When all smoke clears 3-parameter parametrization 3-parameter fitting • Perfectly fits slow-to-moderate roll. Fit wild rising trajectories Measuring 3 parameters • Use 3-parameter for 0<z<4. Assume w(z>4)=wh (free parameter). Comparing 1-2-3-parameter 1-parameter: use 1-param formula for all redshift. 2-parameter: use 2-param formula for 0<z<2, assuming w(z>2)=wh (free constant). 3-parameter: use 3-param formula for 0<z<4, assuming w(z>4)=wh (free constant). Conclusion: all the complications are irrelevant, now only can measure es CMB + SN + WL + LSS +Lya Forecast: Planck + JDEM SN + DUNE WL Thawing, freezing or non-monotonic? • Thawing: w monotonically deviate from -1. • Freezing: w monotonically approaches -1. • Our parameterization with flat priors. Roughly 15 percent thawing, 8 percent freezing, most are non-monotonic. With freezing prior: With thawing prior: Conclusions For a wide class of quintessence/phantom models, the functional form V(φ) in the near future is observationally immeasurable. Only a key trajectory parameter es = (1/16πG) <(V’/V)2> can be well measured. The second parameter as can only be constrained to be less than ~0.3. For current observational data, even with (physically motivated) dynamic w(a) parametrization, cosmological constant remains to be the best and simplest model.