Variable Cosmological Constant model: the reconstruction equations and constraints from current observational data

In this paper we first give a brief review of the variable cosmological constant model and its scalar field description. We mainly discuss two types of variable cosmological constant models: $a$ power law and $H$ power law models. A method to obtain all of the equivalent scalar field potentials and the effective equation of state of the two models is presented. In addition, the dynamics of such scalar field potentials and effective equation of state are discussed in detail. The parameters of the two models are constrained by current 307 high-quality "Union" SN Ia data set, baryon acoustic oscillation (BAO) measurement from the Sloan Digital Sky Survey (SDSS), 9 observational \textrm{H(z)} data derived from the Gemini Deep Deep Survey (GDDS) and the shift parameter of the cosmic microwave background (CMB) given by the three-year Wilkinson Microwave Anisotropy Probe (\textrm{WMAP}) observations. We also calculate and draw the picture of the Hubble parameter, the deceleration parameter and the matter density of the two models. Then, we show that the indices $m$ and $n$ in the two models have specific meaning in determining properties of the models. Moreover, The reasons that indices $m$ and $n$ may also influence the behavior of effective equation of state and scalar field potentials are presented.Comment: 1 Latex, 14 pages, 11 figures, revised versio

Constraining the ionized gas evolution with CMB-spectroscopic survey cross-correlation

We forecast the prospective constraints on the ionized gas model $f_{\rm gas}(z)$ at different evolutionary epochs via the tomographic cross-correlation between kinetic Sunyaev-Zeldovich (kSZ) effect and the reconstructed momentum field at different redshifts. The experiments we consider are the Planck and CMB Stage-4 survey for CMB and the SDSS-III for the galaxy spectroscopic survey. We calculate the tomographic cross-correlation power spectrum, and use the Fisher matrix to forecast the detectability of different $f_{\rm gas}(z)$ models. We find that for constant $f_{\rm gas}$ model, Planck can constrain the error of $f_{\rm gas}$ ($\sigma_{f_{\rm gas}}$) at each redshift bin to $\sim 0.2$, whereas four cases of CMB-S4 can achieve $\sigma_{f_{\rm gas}} \sim 10^{-3}$. For $f_{\rm gas}(z)=f_{\rm gas,0}/(1+z)$ model the error budget will be slightly broadened. We also investigate the model $f_{\rm gas}(z)=f_{\rm gas,0}/(1+z)^{\alpha}$. Planck is unable to constrain the index of redshift evolution, but the CMB-S4 experiments can constrain the index $\alpha$ to the level of $\sigma_{\alpha} \sim 0.01$--$0.1$. The tomographic cross-correlation method will provide an accurate measurement of the ionized gas evolution at different epochs of the Universe.Comment: 11 pages, 5 figures, 5 table

CMB Cold Spot from Inflationary Feature Scattering

We propose a "feature-scattering" mechanism to explain the cosmic microwave background cold spot seen from WMAP and Planck maps. If there are hidden features in the potential of multi-field inflation, the inflationary trajectory can be scattered by such features. The scattering is controlled by the amount of isocurvature fluctuations, and thus can be considered as a mechanism to convert isocurvature fluctuations into curvature fluctuations. This mechanism predicts localized cold spots (instead of hot ones) on the CMB. In addition, it may also bridge a connection between the cold spot and a dip on the CMB power spectrum at $\ell \sim 20$.Comment: 17 pages, 17 figures, Nuclear Physics B in pres

Reconstructing the Local Potential of Inflation with BICEP2 data

We locally reconstruct the inflationary potential by using the current constraints on $r$ and $n_{\rm s}$ from BICEP2 data. Assuming small and negligible $\alpha_{\rm s}$, the inflationary potential is approximately linear in $\Delta\phi\sim M_{\rm pl}$ range but becomes non-linear in $\Delta\phi\sim 10 M_{\rm pl}$ range. However if we vary the value of $\alpha_{\rm s}$ within the range given by constraints from {\it Planck} measurement, the local reconstruction is only valid in the range of $\Delta\phi\sim 0.4 M_{\rm pl}$, which challenges the inflationary background from the point of view of effective field theory. We show that, within the range of $\Delta \phi \sim 0.4 M_{\rm pl}$, the inflation potential can be precisely reconstructed. With the current reconstruction, we show that $V(\phi) \sim \phi^{2}$ and $\phi^{3}$ are consistent, while $\phi$ model is ruled out by $95\%$ confidence level of the reconstructed range of potential. This sets up a strong limit of large-field inflation models.Comment: 11 pages, 10 figure