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\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}}
\@writefile{toc}{\contentsline {section}{\numberline {2}The method}{2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}The datasets}{2}}
\newlabel{ssec:data}{{2.1}{2}}
\newlabel{eq:q+a}{{1}{3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}The parameter space}{3}}
\newlabel{ssec:param}{{2.2}{3}}
\newlabel{eq:param}{{2}{3}}
\newlabel{eq:paramderived}{{3}{3}}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces  The parameter space probed in our analysis. We assume a flat prior in each case. We do not vary the values of all parameters at the same time; the parameter spaces that we consider are set out in Section\nobreakspace  {}2.2\hbox {}. }}{4}}
\newlabel{tab:param}{{2.2}{4}}
\newlabel{eq:param5}{{4}{4}}
\newlabel{eq:paramf5}{{5}{4}}
\newlabel{eq:param6}{{6}{4}}
\newlabel{eq:paramf6}{{7}{4}}
\newlabel{eq:param7a}{{8}{4}}
\newlabel{eq:paramf7a}{{9}{4}}
\newlabel{eq:param7b}{{10}{4}}
\newlabel{eq:paramf7b}{{11}{4}}
\newlabel{eq:param7c}{{12}{4}}
\newlabel{eq:paramf7c}{{13}{4}}
\newlabel{eq:param7d}{{14}{4}}
\newlabel{eq:paramf7d}{{15}{4}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Constraining parameters}{4}}
\newlabel{ssec:mechanics}{{2.3}{4}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Results}{5}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}The simplest case -- five parameters}{5}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Six parameters -- including the scalar spectral index}{5}}
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Marginalized 68\% interval constraints (unless stated otherwise) on cosmological parameters obtained using CMB information only for the different hypothesis and parameter sets analysed. The models are defined in Section\nobreakspace  {}2.2.}}{6}}
\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces Marginalized 68\% interval constraints (unless stated otherwise) on cosmological parameters obtained using information from CMB and the 2dFGRS power spectrum for the different hypothesis and parameter sets analysed. The models are defined in Section\nobreakspace  {}2.2.}}{6}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces  Marginalized posterior likelihoods for the cosmological parameters in the basic-five model determined from CMB information only (dashed lines) and CMB+2dFGRS $P(k)$ (solid lines). The diagonal shows the likelihood for individual parameters; the other panels show the likelihood contours for pairs of parameters, marginalizing over the other parameters. The contours show $-2\Delta \mathop {\mathgroup \symoperators ln}\nolimits (L/L_{\rm  max}) = 2.3$ and $6.17$. }}{7}}
\newlabel{fig:b5-san}{{1}{7}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces  Marginalized posterior likelihoods for the cosmological parameters in the basic-six model determined from CMB information only (dashed lines) and CMB plus 2dFGRS $P(k)$ (solid lines). }}{8}}
\newlabel{fig:b6-san}{{2}{8}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Six parameters plus the mass fraction of massive neutrinos}{8}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces  The marginalized posterior likelihood in the $f_{\nu }-\omega _{\rm  dm}$ plane for the basic-six+$f_{\nu }$ parameter set. The dashed lines show the 68\% and 95\% contours obtained in the CMB only case. The solid contours show the corresponding results obtained in the CMB plus 2dFGRS $P(k)$ case. }}{9}}
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\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces  The marginalized posterior likelihood in the $f_{\nu }-\Omega _{\rm  DE}$ plane for the basic-six+$f_{\nu }$ parameter set. The dashed lines show the 68\% and 95\% contours obtained in the CMB only case. The solid contours show the parameter constraints obtained for combined CMB and 2dFGRS $P(k)$ datasets. }}{9}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {3.4}Six parameters plus the curvature of the universe: non-flat models}{10}}
\newlabel{ssec:omegak}{{3.4}{10}}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces  The one dimensional marginalized posterior likelihood for $\Omega _{k}$ for CMB data only (dashed line), CMB plus 2dFGRS $P(k)$ (solid line), and CMB plus 2dFGRS $P(k)$, with a prior on the optical depth of $\tau <0.3$ (dot-dashed line). Closed models have $\Omega _{k}<0$. }}{10}}
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\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces  The marginalized posterior likelihood in the $\Omega _{k}-\tau $ plane for the basic-six plus $\Omega _{k}$ parameter set. The dashed lines show the 68\% and 95\% contours obtained in the CMB only case. The solid contours correspond to the constraints obtained in the CMB plus 2dFGRS $P(k)$ case. }}{11}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {3.5}Six parameters plus the dark energy equation of state}{11}}
\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces  The marginalized posterior likelihood in the $\Omega _{\rm  m}-\Omega _{\rm  DE}$ plane for the basic-six plus $\Omega _{k}$ parameter set. The dashed lines show the 68\% and 95\% contours obtained in the CMB only case. The solid contours correspond to constraints in the CMB plus 2dFGRS $P(k)$ case. }}{11}}
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\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces  The marginalized posterior likelihood in the $\Omega _{\rm  m}-w_{\rm  DE}$ plane for the basic six plus $w_{\rm  DE}$ parameter set. The dashed lines show the 68\% and 95\% contours obtained in the CMB only case. The solid contours show the corresponding constraints obtained in the CMB+2dFGRS $P(k)$ case. }}{12}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {3.6}Six parameters plus non-zero tensor modes}{12}}
\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces  The marginalized posterior likelihood in the $n_{\rm  s}-r$ plane for the basic-six plus $r$ parameter set. The dashed lines show the 68\% and 95\% contours obtained in the CMB only case. The solid contours show the corresponding results in the CMB plus 2dFGRS $P(k)$ case. }}{12}}
\newlabel{fig:b6r-ns-r}{{9}{12}}
\newlabel{eq:n-r}{{17}{12}}
\newlabel{eq:alfa-n}{{19}{12}}
\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces  The marginalized posterior likelihood in the $\epsilon _1-\epsilon _2$ plane for the basic-six plus $r$ parameter set. The dashed lines show the 68\% and 95\% contours obtained in the CMB only case. The solid contours correspond to the results obtained in the CMB plus 2dFGRS $P(k)$ case. }}{13}}
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\newlabel{eq:power-law}{{21}{13}}
\newlabel{eq:rfijo}{{22}{13}}
\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces  The marginalized posterior likelihood in the $\alpha - N$ plane for the basic-six plus $r$ parameter set. The dashed lines show the 68\% and 95\% contours obtained in the CMB only case. The solid contours show the results in the CMB plus 2dFGRS $P(k)$ case. }}{13}}
\newlabel{fig:b6r-alpha-n}{{11}{13}}
\@writefile{toc}{\contentsline {section}{\numberline {4}The role of priors}{13}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}The baryon density}{13}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2}The dark matter density}{14}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.3}The amplitude of fluctuations}{14}}
\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces  The marginalized posterior likelihood in the $\Omega _{\rm  m}-\sigma _{8}$ plane obtained using CMB plus 2dFGRS information for different parameter sets. The solid lines correspond to the 68\% and 95\% contours obtained for the basic-six parameter set. The dashed lines correspond to the results obtained when the neutrino fraction $f_{\nu }$ is also allowed to vary. The dot-dashed lines show constraints from weak lensing measurements from Hoekstra et\nobreakspace  {}al. (2002). }}{14}}
\newlabel{fig:priors_16_17}{{12}{14}}
\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces  The marginalized posterior likelihood in the $\Omega _{m}-h$ plane obtained using CMB plus 2dFGRS information for different parameter sets. The solid lines correspond to the 68\% and 95\% contours obtained for the basic-six parameter set. The dashed lines show the results obtained when non-flat models are considered (basic-six plus $\Omega _{k}$). The dot-dashed lines show the constraint on $h$ from the HST Key Project (Freedman et\nobreakspace  {}al. 2001). }}{14}}
\newlabel{fig:priors_16_20}{{13}{14}}
\@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces  The marginalized posterior likelihood in the $\Omega _{k}-t_{0}$ plane for the basic-six plus $\Omega _{k}$ parameter set. The dashed lines show the 68\% and 95\% contours obtained in the CMB only case. The solid contours correspond to the constraints obtained in the CMB plus 2dFGRS case. }}{15}}
\newlabel{fig:prior-t0}{{14}{15}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.4}The optical depth}{15}}
\newlabel{ssec:ptau}{{4.4}{15}}
\@writefile{lof}{\contentsline {figure}{\numberline {15}{\ignorespaces  The marginalized posterior likelihood in the $\Omega _{k}-n_{\rm  s}$ plane for the basic six plus $\Omega _{k}$ parameter set. The dashed lines show the 68\% and 95\% contours obtained in the CMB only case. The solid contours correspond to the constraints obtained in the CMB plus 2dFGRS case. }}{15}}
\newlabel{fig:prior-omk}{{15}{15}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.5}The flatness prior}{15}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.6}Tensor modes}{16}}
\@writefile{toc}{\contentsline {section}{\numberline {5}Beyond the simplest model}{16}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}How many parameters should float?}{16}}
\newlabel{eq:aic}{{23}{16}}
\newlabel{eq:bic}{{24}{16}}
\@writefile{lot}{\contentsline {table}{\numberline {4}{\ignorespaces  The number of parameters, the likelihood and the values of the {\tt  AIC} and {\tt  BIC} statistics for the various models analysed in this paper. In all cases, $N_{\rm  data}=1403$.}}{16}}
\newlabel{tab:bic}{{5.1}{16}}
\@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces  Model fits to the CMB datasets (top panels) and 2dFGRS $P(k)$ (bottom panels) in the cases of the basic-five (solid line) and basic-six (dashed line) models, with the best fitting parameter values listed in Table\nobreakspace  {}3. In the right-hand panels, the model curves and datapoints have been divided by the best fitting basic-five model to expand the y-axis. }}{17}}
\newlabel{fig:experiments}{{16}{17}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Details of the evidence for tilt}{17}}
\@writefile{lof}{\contentsline {figure}{\numberline {17}{\ignorespaces  The likelihood ratios of the basic-five model to the basic-six model plotted in Fig.16\hbox {} for the individual datasets used in our analysis. }}{18}}
\newlabel{fig:b6_split}{{17}{18}}
\@writefile{toc}{\contentsline {section}{\numberline {6}Comparison with constraints obtained using the CMB data and the SDSS power spectrum}{18}}
\newlabel{sec:sdss}{{6}{18}}
\@writefile{lof}{\contentsline {figure}{\numberline {18}{\ignorespaces  The marginalized one-dimensional posterior likelihood in the basic-six parameter space obtained for CMB information only (dashed lines), CMB plus the 2dFGRS $P(k)$ (solid lines) and CMB plus the SDSS (dot-dashed lines). }}{19}}
\newlabel{fig:b6_sdss}{{18}{19}}
\@writefile{toc}{\contentsline {section}{\numberline {7}Summary}{19}}
\@writefile{lot}{\contentsline {table}{\numberline {5}{\ignorespaces The marginalized 68\% interval constraints (unless otherwise stated) on cosmological parameters obtained using CMB data and the SDSS galaxy power spectrum for different parameter sets.}}{20}}