"... In PAGE 21: ... Examination of Figure 4 shows that there are plausible model for both an open and a at universe. Cosmological parameters for this models as well as the ratio of 8 at the current epoch to the rms density uctuations on Jeans apos; scale at the decoupling are summarized in Table1 . Amplitudes are selfconsistent in the sense that if 8(t0) is in a range (0.... In PAGE 21: ...ange (0.5{1.0), then J(tREC) gt; 1. The three representative models in Figure 4 designated by a triangle ( at case) and a circle and a diamond (open case) are noted with these symbols in Table1 . They are permitted by the 4He and 2D+3 He observations.... In PAGE 29: ... 6.| a) Jeans apos; mass (solid line) and the mass of nonlinearity (dashed line) as a function of redshift for the model 3 from Table1 . The hatched regions show eras when the Jeans apos; mass is below the mass of nonlinearity.... In PAGE 29: ... 7.| Final (X, ) ray spectrum for the representative model 3 from Table1 (solid line). Also shown the nal radiation spectrum if it were no any absorption at all (dashed line).... ..."

"... In PAGE 7: ... We consider here ve models, standard cold dark matter model (SCDM), open SCDM (OSCDM), the CDM model with cosmolog- ical constant ( CDM), open CDM (O CDM), and open CDM (OCDM). The model values of the cosmological parameters are shown in Table1 . The C2 values in Table 1 are obtained by normalizing all ve models to the COBE four-year data, following Bunn amp; White (1997).... In PAGE 23: ...are known to be that of the SCDM model (with A2 S(k) = 1) listed in Table1 . (a) MAP only.... ..."

"... In PAGE 5: ... Figure 3 sug- gests that the parameters of our cur- rent SPH simulations (643 particles, 11h?1Mpc box) are probably su - cient to give accurate predictions of the ux decrement distribution at these smoothing scales, although a factor of eight decrease in the reso- lution or box volume would change the predictions noticeably. Figure 4 compares the ux decre- ment distributions predicted by SPH simulations of a variety of CDM models (with parameters listed in Table1 ) to measurements from a sample of 28 Keck HIRES spectra. The absorption redshifts in the ob- servational sample range from z = 2:5 to z = 3:7, with mean z = 2:96, and the total path length in this red- shift range is equivalent to 21 full Ly to Ly regions.... In PAGE 6: ... The in uence of mass resolution and simulation box size on calcu- lations of the ux decrement distribution function, in the PM approximation at z = 3. Solid lines show results from an LCDM simulation (see Table1 for cosmological parameters) with 643 particles in an 11h?1Mpc comoving box. In the upper panels, dotted and dashed lines show results from simulations with the same box size but 1283 and 323 particles, respectively.... In PAGE 7: ... Comparison of the ux decrement distribution from SPH simula- tions of ve di erent cosmological models to measurements from a sample of Keck HIRES spectra with mean redshift z = 2:96. Parameters of the models are given in Table1 . The resolution and box size of the simulations corre- spond to the solid lines in Figure 3.... ..."

"... In PAGE 10: ... Figure 9, based on Phillips et al. (1998), shows power spectra of four COBE-normalized CDM models with the in ationary power spectrum index n chosen so that the predicted power spectrum matches the CWPHK result (see model parameters in Table2 ). While all of these models can simultane- ously match COBE-DMR and the Ly forest P(k), the high 8 val- ues of the = 1 models (TCDM2, CHDM2) would imply excessively massive galaxy clusters at z = 0, in agreement with our earlier, more general argument.... In PAGE 11: ... Constraints on the parameters of CDM models obtained by combin- ing the CWPHK P(k) with COBE-DMR normalization. The left panel shows linear mass power spectra of four COBE-normalized CDM models (parame- ters listed in Table2 ), with the in ationary power spectrum index n chosen to give the best match to the measured P(k) ( lled circles). The right panel illus- trates constraints on the parameters of the LCDM model.... ..."

"... In PAGE 5: ...rom Eq. (13) it is clear that this occurs at the maximum attainable value of f( ; ). For any one of our theories, then, the most favored values of the parameters occurs where f is largest; hence the preference for universe dominated by curvature ( = 0) or a cosmological constant ( = 1), at least as far as these data alone.The integral over the posterior needed for setting the odds is given in Table1 , for each combination of experimental result and model; the odds comparing to models for a given set of data are just the ratios of the entries in the table. The \best t quot; model is + = 1 irrespective of the particular experiment considered; the worst is the simplest with = 1.... In PAGE 6: ...) We must also decide on what to use as our prior distribution for and |in the light of which model or combination of models will we consider the data? For example, if we only consider = 1, = 0, the more strongly the data disfavor f = 2=3, the smaller the evidence. In Table1 , we show the evidence for each of our models individually, as well as the combination of models 1 + 2 + 3 + 4 apos;, each weighted equally, all for each possible combination of datasets. Note that combining models inevitably decreases the evidence, because the quadrature combination of datasets decreases the e ective error in the Hubble constant measurement, H, thereby decreasing the width of the step in the likelihood for f.... ..."

"... In PAGE 9: ... At z = 0:5, the comoving volume element in a at universe with = 0:7 is twice that in a at universe with no cosmological constant. Table3 gives the results of the ts for di erent values of M and . For a spatially- at cosmological model with M = 0:28 as measured by the SCP (Perlmutter et al.... In PAGE 10: ... As before, we perform maximum likelihood ts for a choice of cosmological models. The results are reported in Table3 . As expected, the evolution parameter , depends strongly on the assumed cosmology.... ..."

"... In PAGE 14: ... Galaxy luminosity The CFRS galaxy counts are based on data that are well-matched to our survey in magnitude and redshift range, and only minimal extrapolation was required to convert from the I to R band. The associated uncertainty should be small and this is supported by the calculation based on using the observed LFs as discussed in Section 5 ( Table4 ). The di erence in the two calculations serves as our estimate of the systematic uncertainty here and this amounts to 0:05 h2 SNu.... ..."