Figure 1.
The conformal structure of the CMB is shown. The surface of the cone represents the flight path of photons traveling from the surface of last scattering. The dominant contribution to the temperature anisotropy is due to acoustic oscillations in the baryon-photon plasma on the scale of the sound horizon at recombination. Using the apparent size of this length scale in the CMB sky, the spatial curvature is determined to be small.
Figure 2.
The angular power spectrum from COBE [19, 20], Saskatoon [21], QMAP [22] , TOCO97 [23], and TOCO98 ([3] from which this figure is taken) are shown. The rise and fall in the anisotropy spectrum in the range l ~ 100 - 300 in the TOCO98 data is the strongest evidence to date that the spatial curvature of the Universe is small. The cosmological models are SCDM (dashed line: Wm = 1, Wb = 0.05, h = 0.5) and a L concordance model [24] (solid line: Wm = 0.33, Wb = 0.041, WL = 0.67, and h = 0.65.) The error bars are 1s statistical.
Figure 3.
The magnitude - red shift relationship traced by the type 1a supernovae measured by the SCP [6] and HZS [7] groups is shown. The vertical axis shows the magnitude difference with respect to an open, empty (accelerating) Universe, represented by the curve D(m-M) = 0. The top-most curve is the prediction for a WL = 1 model; the bottom-most curve is for a Wm = 1 model. The weight of the data strongly rules out the Wm = 1 Universe, and favors models with Wm = 0.3 and w = -1, -2/3, -1/3 in decreasing order (the blue dashed, red dashed, and red dot-dashed curves).
Figure 4. Quintessence introduces the equation of state, w, to the space of cosmological parameters. The most important quantities for characterizing a QCDM model is w and the matter density, Wm = 1 - WQ.
Figure 5.
The fluctuations in quintessence are important on large scales. As a demonstration, the CMB anisotropy is computed for a smooth component, where dQ is artificially set to zero in a model with Wm = 0.3 and w = -1/3; the fluctuations dQ which would normally cancel with the strong, late time integrated Sachs-Wolfe terms in the CMB, are absent, leading to a dramatically difference anisotropy spectrum. The fluctuations distinguish Q from L, and provide insight into the microphysical properties of Q.
Figure 6.
The characteristic shape of the potential for tracker and creeper quintessence models is shown; for these runaway scalar fields, the potential is high and steep at small Q and falls off, approaching zero as Q becomes large. Starting from a wide range of initial conditions, an interplay between the Hubble damping and the curvature of the potential drives the field evolution towards a common evolutionary track, in which the equation of state is always more negative than the background. Inevitably, the field comes to dominate the cosmological fluid, driving accelerated expansion. Once the field reaches the freeze-out point, the rolling field is critically damped by the Hubble expansion as w ® -1 and WQ® 1.
Figure 7.
The energy density versus red shift for a tracker field is shown. Starting with initial conditions anywhere in the vertical box at left, including the yellow region which represents equipartition, to the singularly tuned black dot as required for L, the tracker field (black line) rapidly joins the common evolutionary track (orange dashed line). The tracker quintessence rapidly overtakes the radiation (red) and matter (blue) and comes to dominate the Universe by today. The red shift z = 1012 has been arbitrarily chosen as the initial time. (Figure provided by [29].)
Figure 8. The projection of the concordance region on the Wm - h plane, on the basis of the low red shift observational constraints only, is shown. The observations which dominate the location of the boundary are labeled.
Figure 9. The projection of the concordance region on the Wm - w plane, on the basis of the low red shift and COBE observational constraints only, is shown. The observations which dominate the location of the boundary are labelled. If a wider range for the baryon density is allowed, such as 0.006 < Wbh2 < 0.022, the shape of the mass power spectrum (not discussed here: see [24]) and s8 constraint determine the location of the low Wm boundary, and the concordance region extends slightly as shown by the light dashed line.
Figure 10. The 2s maximum likelihood constraints on the Wm - w plane, due to the SCP (solid), HZS MLCS (short dashed), and HZS template fitting methods (dot-dashed). The light, dashed line shows the low red shift concordance region.
Figure 11.
The dark shaded region is the projection of the concordance region on the W
m -
w plane with the low, intermediate, and high red shift observational constraints. The dashed curve shows the 2s boundary as evaluated using maximum likelihood, which is the same as
Fig. 10.
Figure 12. The concordance region (white) resulting if we artificially set Wbh2 = 0.019 and fix the spectral tilt to precisely match the central values of COBE normalization and cluster abundance measurements. The curves represent the constraints imposed by individual measurements. The curves divide the plane into patches which have been numbered (and colored) according to the number of constraints violated by models in that patch.
Figure 13. The concordance region (white) resulting if we artificially set h = 0.65 and Wbh2 = 0.019 precisely and fix the spectral tilt to precisely match the central values of COBE normalization and cluster abundance measurements. The curves represent the constraints imposed by individual measurements. The curves divide the plane into patches which have been numbered (and colored) according to the number of constraints violated by models in that patch.
Figure 14.
The concordance region based on COBE and low red shift tests for tracker quintessence is shown. The thin black swath along w = -1 shows the allowed region for creeper quintessence and L. The equation-of-state is time-varying; the abscissa is the effective (average) w.
Figure 15.
The overall concordance region based low, intermediate, and high red shift tests for tracker quintessence is shown. The thin black swath along w = -1 shows the allowed region for creeper quintessence and L. The equation of state is time-varying; the abscissa is the effective (average) w. The dark shaded region corresponds to the most preferred region (the 2s maximum likelihood region consistent with the tracker constraint), Wm» 0.33 ± 0.05, effective equation-of-state w » -0.65 ± 0.10 and h = 0.65 ± 0.10 and are consistent with spectral index n = 1. The numbers refer to the representative models that appear in Table I of [24] and that are referenced frequently in the text. Model 1 is the best fit LCDM model and Model 2 is the best fit QCDM model.
Figure 16. The differential volume - red shift relationship for a series of models is shown. The DEEP survey [65] will measure the differential volume out to z ~ 1. Given that the Universe is spatially flat, this test will be able to pin down the equation of state, w.
Figure 17. The cross-correlation of the CMB temperature anisotropy with the weak lensing convergence of the temperature field. The difference between the signals for a L and Q model, as shown, gives clues to the behavior of the gravitational potential at late times and on the largest scales.
