We use theoretical Period-Luminosity and Period-Luminosity-Color relations in the VI passbands , as based on nonlinear , nonlocal and time-dependent convective pulsating models , to predict the reddening and true distance modulus of distant Cepheids observed with the Hubble Space Telescope .
By relying on the pulsating models with metal content Z =0.008 , we find that the theoretical predictions agree to the values obtained by the Extragalactic Distance Scale Key Project on the basis of empirical Period-Luminosity relations referenced to LMC variables .
In the meantime , from the theoretical relations with Z =0.004 and 0.02 we find that the predicted E ( B - V ) and \mu _ { 0 } decrease as the adopted metal content increases .
This suggests a metallicity correction to LMC-based distances as given by \Delta \mu _ { 0 } / \Delta \log Z \sim - 0.27 mag dex ^ { -1 } , where \Delta \log Z is the difference between the metallicity of the Cepheids whose distance we are estimating and the LMC value Z =0.008 .
Such a theoretical correction appears supported by an existing , although weak , correlation between the Cepheid distance and the [ O/H ] metallicity of galaxies within a given group or cluster , as well as by a similar correlation between the H _ { 0 } estimate and the [ O/H ] metallicity of the galaxies which calibrate the SNIa luminosity .
On the contrary , the metallicity correction earlier suggested on empirical grounds seem to be excluded .
Eventually we suggest that the average value < H _ { 0 } > \sim 67 km s ^ { -1 } Mpc ^ { -1 } provided by the Key Project team should increase at least up to \sim 69 km s ^ { -1 } Mpc ^ { -1 } .
Further observational evidences in support of the predicted scenario are finally presented .