Breaking CMB degeneracy in dark energy through LSS

Abstract

The cosmic microwave background (CMB) and large-scale structure (LSS) are complementary probes in the investigatation of the early and late time Universe. After the current accomplishment of the high accuracies of CMB measurements, accompanying precision cosmology from LSS data is emphasized. We investigate the dynamical dark energy (DE) models which can produce the same CMB angular power spectra as that of the (Formula presented.) CDM model with less than a sub-percent level accuracy. If one adopts the dynamical DE models using the so-called Chevallier–Polarski–Linder (CPL) parametrization, (Formula presented.) , then one obtains models (Formula presented.) named M8, M9, M11, and M12, respectively. The differences of the growth rate, f, which is related to the redshift-space distortions (RSD) between different DE models and the (Formula presented.) CDM model are about 0.2 % only at z = 0. The difference of f between M8 (M9, M11, M12) and the (Formula presented.) CDM model becomes maximum at (Formula presented.) with (Formula presented.)  %. This is a scale-independent quantity. One can investigate the one-loop correction of the matter power spectrum of each model using the standard perturbation theory in order to probe the scale-dependent quantity in the quasi-linear regime (i.e. (Formula presented.)). The differences in the matter power spectra including the one-loop correction between M8 (M9, M11, M12) and the (Formula presented.) CDM model for the (Formula presented.) scale are 1.8 (0.9, 1.2, 3.0) % at (Formula presented.) , 3.0 (1.6, 1.9, 4.2) % at (Formula presented.) , and 3.2 (1.7, 2.0, 4.5) % at (Formula presented.). The larger departure from (Formula presented.) of (Formula presented.) , the larger the difference in the power spectrum. Thus, one should use both the RSD and the quasi-linear observable in order to discriminate a viable DE model among a slew of the models which are degenerate in CMB. Also we obtain the lower limit on (Formula presented.) from the CMB acoustic peaks and this will provide a useful limitation on phantom models.