Bursts of particle production during inflation provide a well-motivated mechanism for creating bump like features in the primordial power spectrum. Current data constrains these features to be less than about 5% the size of the featureless primordial
power spectrum at wavenumbers of about 0.1 h Mpc^{-1}. We forecast that the Planck cosmic microwave background experiment will be able to strengthen this constraint to the 0.5% level. We also predict that adding data from a square kilometer array (SKA) galaxy redshift survey would improve the constraint to about the 0.1% level. For features at larger wave-numbers, Planck will be limited by Silk damping and foregrounds. While, SKA will be limited by non-linear effects. We forecast for a Cosmic Inflation Probe (CIP) galaxy redshift survey, similar constraints can be achieved up to about a wavenumber of 1 h Mpc^{-1}.
A compensated isocurvature perturbation consists of an overdensity (or underdensity) in the cold dark matter which is completely cancelled out by a corresponding underdensity (or overdensity) in the baryons. Such a configuration may be generated by a
curvaton model of inflation if the cold dark matter is created before curvaton decay and the baryon number is created by the curvaton decay (or vice-versa). Compensated isocurvature perturbations, at the level producible by the curvaton model, have no observable effect on cosmic microwave background anisotropies or on galaxy surveys. They can be detected through their effect on the distribution of neutral hydrogen between redshifts 30 to 300 using 21 cm absorption observations. However, to obtain a good signal to noise ratio, very large observing arrays are needed. We estimate that a fast Fourier transform telescope would need a total collecting area of about 20 square kilometers to detect a curvaton generated compensated isocurvature perturbation at more than 5 sigma significance.
We estimate the solar system motion relative to the cosmic microwave background using type Ia supernovae (SNe) measurements. We take into account the correlations in the error bars of the SNe measurements arising from correlated peculiar velocities.
Without accounting for correlations in the peculiar velocities, the SNe data we use appear to detect the peculiar velocity of the solar system at about the 3.5 sigma level. However, when the correlations are correctly accounted for, the SNe data only detects the solar system peculiar velocity at about the 2.5 sigma level. We forecast that the solar system peculiar velocity will be detected at the 9 sigma level by GAIA and the 11 sigma level by the LSST. For these surveys we find the correlations are much less important as most of the signal comes from higher redshifts where the number density of SNe is insufficient for the correlations to be important.
