Cold Dark Matter Isocurvature Perturbations: Cosmological Constraints
  and Applications
  In this paper we present the constraints on cold dark matter (CDM)
isocurvature contributions to the cosmological perturbations. By employing
Markov Chain Monte Carlo method (MCMC), we perform a global analysis for
cosmological parameters using the latest astronomical data, such as 7-year
Wilkinson Microwave Anisotropy Probe (WMAP7) observations, matter power
spectrum from the Sloan Digital Sky Survey (SDSS) luminous red galaxies (LRG),
and "Union2" type Ia Supernovae (SNIa) sample. We find that the correlated
mixture of adiabatic and isocurvature modes are mildly better fitting to the
current data than the pure adiabatic ones, with the minimal $\chi^2$ given by
the likelihood analysis being reduced by 3.5. We also obtain a tight limit on
the fraction of the CDM isocurvature contributions, which should be less than
14.6% at 95% confidence level. With the presence of the isocurvature modes, the
adiabatic spectral index becomes slightly bigger, n_s^{\rm
adi}=0.972\pm0.014~(1\,\sigma), and the tilt for isocurvature spectrum could be
large, namely, the best fit value is n_s^{\rm iso}=3.020. Finally, we discuss
the effect on WMAP normalization priors, shift parameter R, acoustic scale l_A
and z_{*}, from the CDM isocurvaure perturbation. By fitting the mixed initial
condition to the combined data, we find the mean values of R, l_A and z_{*} can
be changed about 2.9\sigma, 2.8\sigma and 1.5\sigma respectively, comparing
with those obtained in the pure adiabatic condition.
