Testing Oscillating Primordial Spectrum and Oscillating Dark Energy with Astronomical Observations

In this paper we revisit the issue of determining the oscillating primordial scalar power spectrum and oscillating equation of state of dark energy from the astronomical observations. By performing a global analysis with the Markov Chain Monte Carlo method, we find that the current observations from five-year WMAP and SDSS-LRG matter power spectrum, as well as the "union" supernovae sample, constrain the oscillating index of primordial spectrum and oscillating equation of state of dark energy with the amplitude less than $|n_{\rm amp}|<0.116$ and $|w_{\rm amp}|<0.232$ at 95% confidence level, respectively. This result shows that the oscillatory structures on the primordial scalar spectrum and the equation of state of dark energy are still allowed by the current data. Furthermore, we point out that these kinds of modulation effects will be detectable (or gotten a stronger constraint) in the near future astronomical observations, such as the PLANCK satellite, LAMOST telescope and the currently ongoing supernovae projects SNLS.