http://arxiv.org/abs/1310.6986
We study the late-time Integrated Sachs-Wolfe (ISW) effect in $f(R)$ modified gravity using N-body simulations. In the $f(R)$ model under study, the linear growth rate is larger than that in general relativity (GR) due to the enhancement of gravity. This counters the effect of cosmic acceleration at late times, thus slowing down the decay of the cosmic potential and induces a smaller ISW effect on large scales. Therefore, the $\dot\Phi$ (time derivative of the potential) power spectrum at the Fourier $k$ range of $k<0.1 h$/Mpc is suppressed relative to that in GR. In the non-linear regime, the enhanced gravity in $f(R)$ speeds up structure formation, boosting the non-linear ISW effect over GR. The $\dot\Phi$ power spectrum at $k>0.1h$/Mpc is increased. The difference between the $\dot\Phi$ power spectrum in $f(R)$ and GR reaches 100% on small scales at z=0. In contrast, the differences in the density power spectrum is only 50%. We explore the detectability of the ISW signal via stacking supervoids and superclusters in simulations. For relatively large ISW cold spots, they are less cold in $f(R)$ than in GR, while small cold spots are colder. ISW hot spots corresponding to the stacking of superclusters in $f(R)$ are not as hot as in GR, due to the stronger non-linearity that counteracts the ISW. The differences in cold or hot spots are about 20% for structures of ~100Mpc/$h$. Such differences are much greater for smaller structures, but the amplitude of the stacked signal is much lower. It is challenging to distinguish these differences given the weakness of the signal. We identify one type of strong non-linear phenomenon related to the transverse bulk motion of dark matter, where the difference between $f(R)$ and GR seems to be maximized, and suggest that it might be detectable via the relative frequency shifts of photons from multiple lensed images using high-resolution spectra lines.
Date added: Mon, 28 Oct 13
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