We study in this paper the perturbations of the quintom dark energy model and the effects of quintom perturbations on the current observations. Quintom describes a scenario of dark energy where the equation of state gets across the cosmological constant boundary $w=-1$ during evolution. We present a new method to show that the conventional dark energy models based on a single $k$-essence field and perfect fluid cannot act as the quintom due to the singularities and classical instabilities of perturbations around $w=-1$. One needs to add extra degrees of freedom for successful quintom model building. There are no singularities or classical instabilities in perturbations of realistic quintom models and they are potentially distinguishable from the cosmological constant. Basing on the realistic quintom models in this paper we provide one way to include the perturbations for dark energy models with parametrized equation of state across $-1$. Compared with those assuming no dark energy perturbations, we find that the parameter space which allows the equation of state to get across $-1$ will be enlarged, in general, when including the perturbations.

We search for signatures of Lorentz and $CPT$ violations in the cosmic microwave background (CMB) temperature and polarization anisotropies by using the Wilkinson Microwave Anisotropy Probe (WMAP) and the 2003 flight of BOOMERANG (B03) data. We note that if the Lorentz and $CPT$ symmetries are broken by a Chern-Simons term in the effective Lagrangian, which couples the dual electromagnetic field strength tensor to an external four-vector, the polarization vectors of propagating CMB photons will get rotated. Using the WMAP data alone, one could put an interesting constraint on the size of such a term. Combined with the B03 data, we found that a nonzero rotation angle of the photons is mildly favored: $\Delta \alpha =-6.0\genfrac{}{}{0ex}{}{+4.0}{-4.0}\genfrac{}{}{0ex}{}{+3.9}{-3.7}\mathrm{deg}(1,2\sigma )$.

We use a suite of N-body simulations that incorporate massive neutrinos as an extra-set of particles to investigate their effect on the halo mass function. We show that for cosmologies with massive neutrinos the mass function of dark matter haloes selected using the spherical overdensity (SO) criterion is well reproduced by the fitting formula of Tinker et al. (2008) once the cold dark matter power spectrum is considered instead of the total matter power, as it is usually done. The differences between the two implementations, i.e. using Pcdm(k) instead of Pm(k), are more pronounced for large values of the neutrino masses and in the high end of the halo mass function: in particular, the number of massive haloes is higher when Pcdm(k) is considered rather than Pm(k). As a quantitative application of our findings we consider a Planck-like SZ-clusters survey and show that the differences in predicted number counts can be as large as 30% for ∑mν = 0.4 eV. Finally, we use the Planck-SZ clusters sample, with an approximate likelihood calculation, to derive Planck-like constraints on cosmological parameters. We find that, in a massive neutrino cosmology, our correction to the halo mass function produces a shift in the σ8(Ωm/0.27)γ relation which can be quantified as Δγ ~ 0.05 and Δγ ~ 0.14 assuming one (Nν = 1) or three (Nν = 3) degenerate massive neutrino, respectively. The shift results in a lower mean value of σ8 with Δσ8 = 0.01 for Nν = 1 and Δσ8 = 0.02 for Nν = 3, respectively. Such difference, in a cosmology with massive neutrinos, would increase the tension between cluster abundance and Planck CMB measurements.

In this paper, we consider a model of inflationary cosmology with inflation preceded by a bounce and study its primordial curvature perturbations. Our model gives rise to a primordial power spectrum with a feature of oscillation on large scales compared with the nearly scale-invariant spectrum generated by the traditional slow-rolling inflation model. This effect changes the cosmic microwave background temperature power spectrum and the large scale structure matter power spectrum. Further, with a detailed simulation we will show that in some detailed models this signal might be detectable in forthcoming observations, such as PLANCK and LAMOST.