Improved cosmological model fitting of Planck data with a dark energy spike

Abstract

The $\mathrm{\ensuremath{\Lambda}}$ cold dark matter ($\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$) model is currently known as the simplest cosmology model that best describes observations with a minimal number of parameters. Here we introduce a cosmology model that is preferred over the conventional $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ one by constructing dark energy as the sum of the cosmological constant $\mathrm{\ensuremath{\Lambda}}$ and an additional fluid that is designed to have an extremely short transient spike in energy density during the radiation-matter equality era and an early scaling behavior with radiation and matter densities. The density parameter of the additional fluid is defined as a Gaussian function plus a constant in logarithmic scale-factor space. Searching for the best-fit cosmological parameters in the presence of such a dark energy spike gives a far smaller chi-square value by about 5 times the number of additional parameters introduced and narrower constraints on the matter density and Hubble constant compared with the best-fit $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. The significant improvement in reducing the chi square mainly comes from the better fitting of the Planck temperature power spectrum around the third ($\ensuremath{\ell}\ensuremath{\approx}800$) and sixth ($\ensuremath{\ell}\ensuremath{\approx}1800$) acoustic peaks. The likelihood ratio test and the Akaike information criterion suggest that the model of a dark energy spike is strongly favored by the current cosmological observations over the conventional $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. However, based on the Bayesian information criterion which penalizes models with more parameters, the strong evidence supporting the presence of a dark energy spike disappears. Our result emphasizes that the alternative cosmological parameter estimation with even better fitting of the same observational data is allowed in Einstein's gravity.