CMB angular power spectrum from correlated primordial fluctuation

The usual inflationary scenario predicts a Gaussian random primordial density fluctuation, different Fourier modes of which do not correlate with each other. In this paper we propose a correlation between these different modes. A simple case is that these different Fourier modes correlate with each other following a Gaussian function. For such a primordial density fluctuation we calculate the cosmic microwave background angular power spectrum and find that its amplitude decreases but the decrease is different for different l. This feature can be used to constrain the correlation strength from the real data.