A novel mechanism for the primordial black hole (PBH) production is proposed as a natural and inevitable consequence of general first-order phase transitions without reference to specific underlying particle physics models. We obtain mutual predictions and constraints between primordial black holes and gravitational waves from phase transitions in the general case. For particular interest, our PBHs generated during a PeV-scale phase transition could make up all the dark matter, while PBHs generated during a MeV-scale phase transition could simultaneously account for LIGO-Virgo coalescence events and NANOGrav 12.5-yr result for the corresponding gravitational waves.

The newly released Planck cosmic microwave background data place tight constraints on slow-roll inflationary models. Some commonly discussed inflationary potentials are disfavored due mainly to the large tensor-to-scalar ratio. In this paper we show that these potentials may be in good agreement with the Planck data when the inflaton has a nonminimal coupling to the Gauss-Bonnet term. Moreover, such a coupling violates the consistency relation between the tensor spectral index and tensor-to-scalar ratio. If the tensor spectral index is allowed to vary freely, the Planck constraints on the tensor-to-scalar ratio are slightly improved.

We introduce a model-independent approach to the null test of the cosmic curvature, which is geometrically related to the Hubble parameter $H(z)$ and luminosity distance $d_L(z)$. Combining the independent observations of $H(z)$ and $d_L(z)$, we use the model-independent smoothing technique, Gaussian processes, to reconstruct them and determine the cosmic curvature ${\mathrm{\Omega }}_K^{(0)}$ in the null test relation. The null test is totally geometrical and does not assume any cosmological model. We show that the cosmic curvature ${\mathrm{\Omega }}_K^{(0)}=0$ is consistent with current observational data sets, falling within the $1\sigma$ limit. To demonstrate the effect on the precision of the null test, we produce a series of simulated data of the models with different ${\mathrm{\Omega }}_K^{(0)}$. Future observations in better quality can provide a greater improvement to constrain or refute the flat universe with ${\mathrm{\Omega }}_K^{(0)}=0$.

Recent Planck data show the anomalies of cosmic microwave background (CMB) fluctuations on large angular scales, which confirms the early observations by WMAP. We continue studying an inflationary model, in which before the slow-roll inflation the universe is in a contracting phase, and fit the model with the Planck data. We show that this model may generate not only the power deficit at low $l$, but also a large hemispherical power asymmetry in the CMB. We also discuss the implication of the result to the eternal inflation scenario.

We propose a double inflection points inflationary model in supergravity with a single chiral superfield. Such a model allows for the generation of primordial black holes (PBHs) at small scales, which can account for a significant fraction of dark matter. Moreover, in vacuum it is possible to give a small and adjustable supersymmetry breaking with a tiny cosmological constant.