The exact analytical solution of the linear structure growth rate in
  LCDM cosmology and its cosmological applications
  We derive the exact analytical solution of the linear structure growth rate
in LCDM cosmology with flat or curved geometry, under the Newtonian gauge.
Unlike the well known solution under the Newtonian limit (Heath 1977), our
solution takes all general relativistic corrections into account and is hence
valid at both the sub- and super-horizon scales. With this exact solution, we
evaluate cosmological impacts induced by these relativistic corrections. (1)
General relativistic corrections alter the density growth from z=100 to z=0 by
10% at k=0.01h/Mpc and the impact becomes stronger toward larger scales. We
caution the readers that the overdensity is not gauge invariant and the above
statement is restrained to the Newtonian gauge. (2) Relativistic corrections
introduce a k^{-2} scale dependence in the density fluctuation. It mimics a
primordial non-Gaussianity of the local type with $f^{\rm local}_{\rm NL}\sim
1$. This systematical error may become non-negligible for future all sky deep
galaxy surveys. (3) Cosmological simulations with box size greater than 1Gpc
are also affected by these relativistic corrections. We provide a
post-processing recipe to correct for these effects. (4) These relativistic
corrections affect the redshift distortion. However, at redshifts and scales
relevant to redshift distortion measurements, such effect is negligible.
