All Figures

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig1.eps} \end{figure}$ Figure 1: Diagram of $\xi (s)$ as function of s. It turns out that an attractive gravity requires $s \in (-2~ , ~ ~ -1)$ .
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In the text

$\begin{figure} \par\includegraphics[width=4cm,clip]{7045fig2.eps} \end{figure}$ Figure 2: Behavior of the coupling factor $\xi (s)$ (red curve) and the power-law exponent p(s) (blue curve). We see that with an appropriate choice of s in the range (-1.5 , -1) all the values for the exponents are available.
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In the text

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig3.eps} \end{figure}$ Figure 3: Plot of $\log_{10}~{\rho_{\phi}}$ versus ${\log}_{10}~ a$ (solid black line). The upper and lower dashed lines indicate the log-log plot of a^-3 and a^-4 versus a, respectively. It turns out that $\rho _\phi$ scales as a^-n, with 3<n<4. In this and subsequent plots, we use the mean values for the parameters obtained through fits (see Table 2).
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In the text

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig4.eps} \end{figure}$ Figure 4: $w_\phi$ as a function of $x={\rm Log}_{10}~(1+z)$ , for the averaged mean values provided by our analysis, as shown in Table 2. We observe a transition from a small constant value in the past, $\vert w_\phi \vert \approx 0$ , to $w_\phi = -1$ at present.
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In the text

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig5.eps} \end{figure}$ Figure 5: Rate of change in the equation of state as measured by ${\dot w}_{\phi}$ versus the $w_\phi$ parameter. The values of the parameters correspond to the average values provided by our analysis and shown in Table 2.
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In the text

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig6.eps} \end{figure}$ Figure 6: Plot of $\log_{10}~{\rho_{\phi}}$ versus ${\log}_{10}~ a$ in the Jordan frame. The vertical bar marks ${\log}_{10}~a_0$ . The solid red straight line indicates the log-log plot of $\rho _{\rm m}$ versus a. The matter dominated-era and the transition to the present dark-energy dominated regime are represented.
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In the text

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig7.eps} \end{figure}$ Figure 7: Current limits on the PPN parameters restrict the range of the parameter s. We see that the constraint on $\vert\gamma ^{\rm PPN}_0-1\vert< 2\times 10^{-3}$ leads to $s\in (-1.5,-1.4 )$ , as shown in the inner zoom.
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In the text

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig8.eps} \end{figure}$ Figure 8: Behavior of the Brans-Dicke parameter $\omega _{\rm BD}$ as a function of s. For $s\in (-1.6,-1.3 )$ , $\omega _{\rm BD}$ satisfies limits placed by the solar system experiments ( $\omega_{\rm BD}>40~000$ ) and by current cosmological observations ( $\omega _{\rm BD}>120$ ).
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In the text

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig9.eps} \end{figure}$ Figure 9: Time evolution of the transformed scalar field $\widetilde{\phi}$ .
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In the text

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig10.eps} \end{figure}$ Figure 10: Evolution with the redshift of $\widetilde{w}_{\phi}$ in the Einstein frame.
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In the text

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig11.eps} \end{figure}$ Figure 11: Plot of ${\log}_{10}~\widetilde{\rho}_{\phi}$ versus ${\log}_{10}~\widetilde{ a}$ in the Einstein frame. The vertical bar marks ${\log}_{10}~\widetilde{a}_0$ .
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In the text

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig12.eps} \end{figure}$ Figure 12: Redshift dependence of the second derivative of the scale factor. The transition from a decelerating to an accelerating expansion occurs close to $z\sim 0.5$ , as predicted by recent observations of SNIa $z_t= 0.46\pm 0.13$ (Riess et al. 2004, 2007).
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In the text

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig13.eps} \end{figure}$ Figure 13: Observational data of the SNIa sample compiled by Riess et al. (2007) fitted to our model. The solid curve is the best fit curve, compared with a standard $\Lambda$ CDM model with $\Omega _{\Lambda }=0.71$ (red dashed line).
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In the text

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig14.eps}\end{figure}$ Figure 14: Updated Daly & Djorgovski database (Daly & Djorgovski 2005) fitted to our model. The solid curve is the best fit curve with $\chi _{\rm red}^2=1.1$ for 248 data points, and the best fit values are ${\widehat H}_0=.97^{+0.04}_{-0.03}$ , s=-1.49^+0.02_-0.04.
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In the text

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig15.eps} \end{figure}$ Figure 15: The sensitivity of the ${{\rm d}z \over {\rm d}t}$ relation compared to the values of the parameters in our model. The red line shows $\displaystyle {\delta {{\rm d}z \over {\rm d}t}= {{{\rm d}z \over {\rm d}t}(s=-... ...}z \over {\rm d}t}(s=-1.4,H_0=1)\over {{\rm d}z \over {\rm d}t}(s=-1.4,H_0=1)}}$ , and the blue line shows $\displaystyle {\delta {{\rm d}z \over {\rm d}t}= {{{\rm d}z \over {\rm d}t}(s=-... ...}z \over {\rm d}t}(s=-1.4,H_0=1)\over {{\rm d}z \over {\rm d}t}(s=-1.4,H_0=1)}}$ .
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In the text

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig16.eps} \end{figure}$ Figure 16: The sensitivity of the $\mu =m-M$ relation compared to the values of the parameters in our model in. The red line shows $\displaystyle {\delta {{\rm d}\mu \over {\rm d}t}= {{{\rm d}\mu \over {\rm d}t}... ... \over {\rm d}t}(s=-1.4,H_0=1)\over {{\rm d}\mu \over {\rm d}t}(s=-1.4,H_0=1)}}$ , and the blue line shows $\displaystyle {\delta {{\rm d}\mu \over {\rm d}t}= {{{\rm d}\mu \over {\rm d}t}... ... \over {\rm d}t}(s=-1.4,H_0=1)\over {{\rm d}\mu \over {\rm d}t}(s=-1.4,H_0=1)}}$ .
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In the text

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig17.eps} \end{figure}$ Figure 17: The best-fit curve of the measured values of H(z) corresponding to ${\widehat H}_0=1.01^{+0.01}_{-0.03}$ , s=-1.49^+0.03_-0.09.
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In the text

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig18.eps} \end{figure}$ Figure 18: The best-fit curve to the H(z) data for our nmc model (dark blue line) and for the quintessence QCDM fitted to the new released WMAP- three years + SNLS data (WMAP New Three Year Results 2006) $\Omega _{\Lambda }=0.72\pm 0.04$ , $\Omega _k=-0.010^{+0.0016}_{-0.0009}$ , w=-1.06^+0.13_-0.08 (blue line).
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In the text

$\begin{figure} \par\includegraphics[width=5.5cm,clip]{7045fig19.eps} \end{figure}$ Figure 19: Observational SZE data fitted to our model with the best-fit values ${\widehat H}_0=1^{+0.01}_{-0.03}$ , s=-1.49^+0.03_-0.09, and $h=0.70\pm 0.05$ . The empty boxes indicate distance measurements for a sample of 44 mentioned clusters (see Birkinshaw 1999; Reese et al. 2002),while the filled diamonds indicate the measurement of the angular diameter distances from Chandra X-ray imaging and Sunyaev-Zel'dovich effect mapping of 39 high-redshift clusters (Bonamente et al. 2005).
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In the text

$\begin{figure} \par\includegraphics[width=5.5cm,clip]{7045fig20.eps} \end{figure}$ Figure 20: Observational Hubble diagram for the recent SNIa sample compiled by Riess et al. (2006) (empty lozenges), and the GRBs data by () (empty boxes) fitted to our model. The solid curve is the best-fit curve with, ${\widehat H}_0=~ 0.98^{+0.03}_{-0.03}$ , s=-1.43^+0.02_-0.04. The red dashed line corresponds to the standard $\Lambda$ CDM model with $\Omega _{\Lambda }=0.71$ .
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In the text

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig21.eps} \end{figure}$ Figure 21: The best-fit curve to the $f_{\rm gas}$ data for our nmc model (red thick line) and for the quintessence model (black thick line) considered in Lima et al. (2003). It is interesting to note that, as pointed out also for the model described in Demianski et al. (2006), even if the statistical significance of the best-fit procedure for these two models is comparable, the best fit relative to our nmc model seems to be dominated by smaller redshift data, and the one relative to the Lima et al. model by higher redshift data.
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In the text

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig22.eps} \end{figure}$ Figure 22: The growth index f in different cosmological models. The thick dashed red line corresponds to our non minimally-coupled model. The blue thin dashed curve corresponds to the standard $\Lambda$ CDM model with $\Omega _{\rm m}=0.25$ , and the black solid line corresponds to another quintessence model with an exponential potential (described in Demianski et al. 2005).
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In the text

$\begin{figure} \par\includegraphics[width=5.5cm,clip]{7045fig23.eps} \end{figure}$ Figure 23: The potential V as a function of the redshift z.
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In the text

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig1.eps} \end{figure}$	Figure 1: Diagram of $\xi (s)$ as function of s. It turns out that an attractive gravity requires $s \in (-2~ , ~ ~ -1)$ .
Open with DEXTER

$\begin{figure} \par\includegraphics[width=4cm,clip]{7045fig2.eps} \end{figure}$	Figure 2: Behavior of the coupling factor $\xi (s)$ (red curve) and the power-law exponent p(s) (blue curve). We see that with an appropriate choice of s in the range (-1.5 , -1) all the values for the exponents are available.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig3.eps} \end{figure}$	Figure 3: Plot of $\log_{10}~{\rho_{\phi}}$ versus ${\log}_{10}~ a$ (solid black line). The upper and lower dashed lines indicate the log-log plot of a^-3 and a^-4 versus a, respectively. It turns out that $\rho _\phi$ scales as a^-n, with 3<n<4. In this and subsequent plots, we use the mean values for the parameters obtained through fits (see Table 2).
Open with DEXTER

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig4.eps} \end{figure}$	Figure 4: $w_\phi$ as a function of $x={\rm Log}_{10}~(1+z)$ , for the averaged mean values provided by our analysis, as shown in Table 2. We observe a transition from a small constant value in the past, $\vert w_\phi \vert \approx 0$ , to $w_\phi = -1$ at present.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig5.eps} \end{figure}$	Figure 5: Rate of change in the equation of state as measured by ${\dot w}_{\phi}$ versus the $w_\phi$ parameter. The values of the parameters correspond to the average values provided by our analysis and shown in Table 2.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig6.eps} \end{figure}$	Figure 6: Plot of $\log_{10}~{\rho_{\phi}}$ versus ${\log}_{10}~ a$ in the Jordan frame. The vertical bar marks ${\log}_{10}~a_0$ . The solid red straight line indicates the log-log plot of $\rho _{\rm m}$ versus a. The matter dominated-era and the transition to the present dark-energy dominated regime are represented.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig7.eps} \end{figure}$	Figure 7: Current limits on the PPN parameters restrict the range of the parameter s. We see that the constraint on $\vert\gamma ^{\rm PPN}_0-1\vert< 2\times 10^{-3}$ leads to $s\in (-1.5,-1.4 )$ , as shown in the inner zoom.
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$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig8.eps} \end{figure}$	Figure 8: Behavior of the Brans-Dicke parameter $\omega _{\rm BD}$ as a function of s. For $s\in (-1.6,-1.3 )$ , $\omega _{\rm BD}$ satisfies limits placed by the solar system experiments ( $\omega_{\rm BD}>40~000$ ) and by current cosmological observations ( $\omega _{\rm BD}>120$ ).
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$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig9.eps} \end{figure}$	Figure 9: Time evolution of the transformed scalar field $\widetilde{\phi}$ .
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$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig10.eps} \end{figure}$	Figure 10: Evolution with the redshift of $\widetilde{w}_{\phi}$ in the Einstein frame.
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$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig11.eps} \end{figure}$	Figure 11: Plot of ${\log}_{10}~\widetilde{\rho}_{\phi}$ versus ${\log}_{10}~\widetilde{ a}$ in the Einstein frame. The vertical bar marks ${\log}_{10}~\widetilde{a}_0$ .
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$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig12.eps} \end{figure}$	Figure 12: Redshift dependence of the second derivative of the scale factor. The transition from a decelerating to an accelerating expansion occurs close to $z\sim 0.5$ , as predicted by recent observations of SNIa $z_t= 0.46\pm 0.13$ (Riess et al. 2004, 2007).
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$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig13.eps} \end{figure}$	Figure 13: Observational data of the SNIa sample compiled by Riess et al. (2007) fitted to our model. The solid curve is the best fit curve, compared with a standard $\Lambda$ CDM model with $\Omega _{\Lambda }=0.71$ (red dashed line).
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$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig14.eps}\end{figure}$	Figure 14: Updated Daly & Djorgovski database (Daly & Djorgovski 2005) fitted to our model. The solid curve is the best fit curve with $\chi _{\rm red}^2=1.1$ for 248 data points, and the best fit values are ${\widehat H}_0=.97^{+0.04}_{-0.03}$ , s=-1.49^+0.02_-0.04.
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$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig17.eps} \end{figure}$	Figure 17: The best-fit curve of the measured values of H(z) corresponding to ${\widehat H}_0=1.01^{+0.01}_{-0.03}$ , s=-1.49^+0.03_-0.09.
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$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig18.eps} \end{figure}$	Figure 18: The best-fit curve to the H(z) data for our nmc model (dark blue line) and for the quintessence QCDM fitted to the new released WMAP- three years + SNLS data (WMAP New Three Year Results 2006) $\Omega _{\Lambda }=0.72\pm 0.04$ , $\Omega _k=-0.010^{+0.0016}_{-0.0009}$ , w=-1.06^+0.13_-0.08 (blue line).
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$\begin{figure} \par\includegraphics[width=5.5cm,clip]{7045fig20.eps} \end{figure}$	Figure 20: Observational Hubble diagram for the recent SNIa sample compiled by Riess et al. (2006) (empty lozenges), and the GRBs data by () (empty boxes) fitted to our model. The solid curve is the best-fit curve with, ${\widehat H}_0=~ 0.98^{+0.03}_{-0.03}$ , s=-1.43^+0.02_-0.04. The red dashed line corresponds to the standard $\Lambda$ CDM model with $\Omega _{\Lambda }=0.71$ .
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$\begin{figure} \par\includegraphics[width=5cm,clip]{7045fig22.eps} \end{figure}$	Figure 22: The growth index f in different cosmological models. The thick dashed red line corresponds to our non minimally-coupled model. The blue thin dashed curve corresponds to the standard $\Lambda$ CDM model with $\Omega _{\rm m}=0.25$ , and the black solid line corresponds to another quintessence model with an exponential potential (described in Demianski et al. 2005).
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$\begin{figure} \par\includegraphics[width=5.5cm,clip]{7045fig23.eps} \end{figure}$	Figure 23: The potential V as a function of the redshift z.
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