An improved cosmological model fitting of Planck data with a dark energy
  spike
  The $\Lambda$ cold dark matter ($\Lambda\textrm{CDM}$) model is currently
known as the simplest cosmology model that best describes observations with
minimal number of parameters. Here we introduce a cosmology model that is
preferred over the conventional $\Lambda\textrm{CDM}$ one by constructing dark
energy as the sum of the cosmological constant $\Lambda$ and the additional
fluid that is designed to have an extremely short transient spike in energy
density during the radiation-matter equality era and the 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 five times the number of additional parameters introduced and narrower
constraints on matter density and Hubble constant compared with the best-fit
$\Lambda\textrm{CDM}$ model. The significant improvement in reducing chi-square
mainly comes from the better fitting of Planck temperature power spectrum
around the third ($\ell \approx 800$) and sixth ($\ell \approx 1800$) acoustic
peaks. The likelihood ratio test and the Akaike information criterion suggest
that the model of dark energy spike is strongly favored by the current
cosmological observations over the conventional $\Lambda\textrm{CDM}$ model.
However, based on the Bayesian information criterion which penalizes models
with more parameters, the strong evidence supporting the presence of 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 the Einstein's gravity.
