Implications to the CMB from a model independent evolution ofwand a late time phase transition

Abstract

We present model independent determination of the CMB from any kind of fluid that has an equation of state taking four different values. The first region has $w=1/3$, the second $w=1$, the third $w=-1$ while the last one has $-1<w=cte<-2/3$. This kind of dynamical $w$ contains as a limit the cosmological constant and tracker models. We derive the model independent evolution of $\wp$, for scalar fields, and we see that it remains most of the time in either of its three extremal values given by $\wp=1,-1,w_{tr}$. This varying $w$ is the generic behavior of scalar fields, quintessence, and we determine the size of the different regions by solving the dynamical equations in a model independent way. The dynamical $w$ models have a better fit to CMB data then the cosmological constant and the tracker models. We determine the effect of having the first two regions $w=1/3,1$ and depending on the size of these periods they can be observed in the CMB. In general, the CMB spectrum sets a lower limit to $\D N_T$ and to the phase transition scale $\Lm_c$. For smaller $\D N_T$ the CMB peaks are moved to the right of the spectrum and the hight increases considerably. For $\Ompi=0.1$ the CMB sets a lower limit to the phase transition scale $\Lm_c\geq 0.2 eV$.