# Contiguous redshift parameterizations of the growth index - Astrophysics > Cosmology and Nongalactic Astrophysics

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Abstract: The growth rate of matter perturbations can be used to distinguish betweendifferent gravity theories and to distinguish between dark energy and modifiedgravity at cosmological scales as an explanation to the observed cosmicacceleration. We suggest here parameterizations of the growth index asfunctions of the redshift. The first one is given by $\gammaa=\tilde\gammaa\frac{1}{1+a { {ttc}}-a}+\gamma { {early}} \frac{1}{1+a-a { {ttc}}}$ thatinterpolates between a low-intermediate redshift parameterization$\tilde\gammaa=\gamma { {late}}a= \gamma 0 + 1-a \gamma a$ and a highredshift $\gamma { {early}}$ constant value. For example, our interpolated form$\gammaa$ can be used when including the CMB to the rest of the data whilethe form $\gamma { {late}}a$ can be used otherwise. It is found that theparameterizations proposed achieve a fit that is better than 0.004% for thegrowth rate in a $\Lambda$CDM model, better than 0.014% forQuintessence-Cold-Dark-Matter QCDM models, and better than 0.04% for the flatDvali-Gabadadze-Porrati DGP model with $\Omega m^0=0.27$ for the entireredshift range up to $z { {CMB}}$. We find that the growth index parameters$\gamma 0,\gamma a$ take distinctive values for dark energy models andmodified gravity models, e.g. $0.5655,-0.02718$ for the $\Lambda$CDM modeland $0.6418,0.06261$ for the flat DGP model. This provides a means for futureobservational data to distinguish between the models.

Author: ** Mustapha Ishak, Jason Dossett The University of Texas at Dallas**

Source: https://arxiv.org/