Non-linear matter power spectrum from Time Renormalisation Group:
  efficient computation and comparison with one-loop
  We address the issue of computing the non-linear matter power spectrum on
mildly non-linear scales with efficient semi-analytic methods. We implemented
M. Pietroni's Time Renormalization Group (TRG) method and its Dynamical 1-Loop
(D1L) limit in a numerical module for the new Boltzmann code CLASS. Our
publicly released module is valid for LCDM models, and optimized in such a way
to run in less than a minute for D1L, or in one hour (divided by number of
nodes) for TRG. A careful comparison of the D1L, TRG and Standard 1-Loop
approaches reveals that results depend crucially on the assumed initial
bispectrum at high redshift. When starting from a common assumption, the three
methods give roughly the same results, showing that the partial resumation of
diagrams beyond one loop in the TRG method improves one-loop results by a
negligible amount. A comparison with highly accurate simulations by M. Sato &
T. Matsubara shows that all three methods tend to over-predict non-linear
corrections by the same amount on small wavelengths. Percent precision is
achieved until k~0.2 h/Mpc for z>2, or until k~0.14 h/Mpc at z=1.
