Phantom boundary crossing and anomalous growth index of fluctuations in viable f(R) models of cosmic acceleration

TL;DR

The paper investigates whether viable $f(R)$ gravity can explain cosmic acceleration while remaining consistent with structure formation. It numerically evolves the background expansion and sub-horizon density perturbations for a Starobinsky-type $f(R)$ model that includes an $R^2$ term to tame high-curvature behavior, under stability requirements. The results show a phantom crossing of the equation of state parameter $w_DE$ at $z \lesssim 1$ and a non-monotonic growth index caused by a time-varying effective gravitational constant $G_{eff}$, with density perturbations exhibiting a scale-dependent enhancement for large wavenumbers. These findings constrain the model parameters via deviations in the growth of structure (e.g., $\sigma_8$) and suggest that future measurements of the growth index $\gamma(z)$ and scale-dependent clustering can distinguish viable $f(R)$ scenarios from LCDM. Overall, the study provides concrete, testable predictions for upcoming large-scale structure surveys.

Abstract

Evolution of a background space-time metric and sub-horizon matter density perturbations in the Universe is numerically analyzed in viable $f(R)$ models of present dark energy and cosmic acceleration. It is found that viable models generically exhibit recent crossing of the phantom boundary $w_{\rm DE}=-1$. Furthermore, it is shown that, as a consequence of the anomalous growth of density perturbations during the end of the matter-dominated stage, their growth index evolves non-monotonically with time and may even become negative temporarily.

Figures (7)

• Figure 1: Evolution of the equation-of-state parameter of effective dark energy.
• Figure 2: The ratio of linear density perturbations $\delta_{{\rm fRG}}/\delta_{{\rm \Lambda CDM}}$ at present as a function of $k$ for three different values of $\lambda$ with $n=2$.
• Figure 3: The ratio of linear density perturbations $\delta_{\rm fRG}/\delta_{{\rm \Lambda CDM}} (k=0.174h{\rm Mpc}^{-1}$) as a function of redshift for three different values of $\lambda$ with $n=2$.
• Figure 4: The present ratio $(\delta_{{\rm fRG}}/\delta_{{\rm \Lambda CDM}})^2(k=0.174h{\rm Mpc}^{-1})$ as a function of $\lambda$ together with two fitting functions.
• Figure 5: Constraints for parameter space.