Growth factor parametrization in curved space

Abstract

The growth rate of matter perturbation and the expansion rate of the Universe can be used to distinguish modified gravity and dark energy models in explaining cosmic acceleration. We explore here the inclusion of spatial curvature into the growth factor. We expand previous results using the approximation ${\Omega }_m^{\gamma }$ and then suggest a new form, $f_a={\Omega }_m^{\gamma }+(\gamma -4/7){\Omega }_k$, as an approximation for the growth factor when the curvature ${\Omega }_k$ is not negligible, and where the growth index $\gamma$ is usually model dependent. The expression recovers the standard results for the curved and flat $\Lambda$CDM and Dvali-Gabadadze-Porrati models. Using the best fit values of ${\Omega }_{m0}$ and ${\Omega }_{k0}$ to the expansion/distance measurements from Type Ia supernovae, baryon acoustic oscillation, WMAP5, and $H(z)$ data, we fit the growth index parameter to current growth factor data and obtain ${\gamma }_{\Lambda }({\Omega }_k\ne 0)=0.65_{-0.15}^{+0.17}$ and ${\gamma }_{DGP}({\Omega }_k\ne 0)=0.53_{-0.12}^{+0.14}$. For the $\Lambda$CDM model, the 1-$\sigma$ observational bounds are found consistent with theoretical value, unlike the case for the Dvali-Gabadadze-Porrati model. We also find that the current data we used is not enough to put significant constraints when the 3 parameters in $f_a$ are fit simultaneously. Importantly, we find that, in the presence of curvature, the analytical expression proposed for $f_a$ provides a better fit to the growth factor than other forms and should be useful for future high precision missions and studies.

latex, 8 figures

References in corpus (18)

• New Hubble Space Telescope Discoveries of Type Ia Supernovae at z > 1: Narrowing Constraints on the Early Behavior of Dark Energy
• Observational Constraints on the Nature of the Dark Energy: First Cosmological Results from the ESSENCE Supernova Survey
• Measuring the Baryon Acoustic Oscillation scale using the SDSS and 2dFGRS
• Two new diagnostics of dark energy
• WMAP constraints on low redshift evolution of dark energy
• Large Scale Structure as a Probe of Gravitational Slip
• Distinguishing Modified Gravity from Dark Energy
• Dark Energy versus Modified Gravity
• Testing LCDM with the Growth Function δ(a): Current Constraints
• On the growth of linear perturbations
• Differentiating dark energy and modified gravity with galaxy redshift surveys
• Observational constraints on the linear fluctuation growth rate
• Next Generation Redshift Surveys and the Origin of Cosmic Acceleration
• Growth Index of DGP Model and Current Growth Rate Data
• Nonlinear growth in modified gravity theories of dark energy
• Neutrino Mass, Dark Energy, and the Linear Growth Factor
• Constraints on alternative models to dark energy
• The cosmological constant in the brane world of string theory on $S^1/Z_2$

Cited by in corpus (1)

• Dispersion in the growth of matter perturbations