119266840
Modified Lyth bound and implications of BICEP2 results
To reconcile the BICEP2 measurement on the tensor-to-scalar ratio $r$ with Planck constraint, a large negative running of scalar spectral index $n_s$ is needed. So the inflationary observable such as $n_s$ should be expanded at least to the second-order slow-roll parameters for single-field inflationary models. The large value of $r$ and the Lyth bound indicate that it is impossible to obtain the sub-Planckian excursion for the inflaton. However, we derive an absolutely minimal bound $\Delta\phi/M_{\rm Pl}>\sqrt{r/2}$ on the inflaton excursion for single-field inflationary models, which can be applied to non-slow-roll inflationary models as well. This bound excludes the possibility of the small-field inflation with $\Delta\phi<0.1 M_{\rm Pl}$ if the BICEP2 result on $r$ stands and it opens the window of sub-Planckian excursion with $\Delta\phi<M_{\rm Pl}$ even if $r$ is as large as $0.1$. To get the sub-Planckian excursion with $\Delta\phi<0.1 M_{\rm Pl}$, our modified bound requires $r<0.02$. Using a fifth-order polynomial potential as an explicit example, we show that it not only agrees with the observational results, but also violates the Lyth bound.
124732020
On the effect of the degeneracy among dark energy parameters
The dynamics of scalar fields as dark energy is well approximated by some general relations between the equation of state parameter $$w(z)$$w(z) and the fractional energy density $$\varOmega _\phi $$Ωϕ. Based on the approximation, for slowly rolling scalar fields, we derived the analytical expressions of $$w(z)$$w(z) which reduce to the popular Chevallier–Polarski–Linder parametrization with an explicit degeneracy relation between $$w_0$$w0 and $$w_a$$wa. The models approximate the dynamics of scalar fields well and help eliminate the degeneracies among $$w_a$$wa, $$w_0$$w0, and $$\varOmega _{m0}$$Ωm0. With the explicit degeneracy relations, we test their effects on the constraints of the cosmological parameters. We find that: (1) The analytical relations between $$w_0$$w0 and $$w_a$$wa for the two models are consistent with observational data. (2) The degeneracies have little effect on $$\varOmega _{m0}$$Ωm0. (3) The $$1\sigma $$1σ error of $$w_0$$w0 was reduced about 30 % with the degeneracy relations.
119181212
The tension on the cosmological parameters from different observational data
Planck measurements of the cosmic microwave background power spectra find a lower value of the Hubble constant H-0 and a higher value of the fractional matter energy density Omega(m0) for the concordance Lambda CDMmodel, and these results are in tension with other measurements. The Planck group argued that the tension came either from some sources of unknown systematic errors in some astrophysical measurements or the wrong Lambda CDM model applied in fitting the data. We studied the reason for the tension on H-0 from different measurements by considering two dynamical dark energy models. We found that there is no tension between different data, the constraint on H-0 is almost unchanged for different dark energy models and the tension with the local measurements remains when the error bar on H-0 is tightened to be around 1. We argue that the tension on H-0 is not caused by the fitting model.
118683947
The challenge for single field inflation with BICEP2 result
The detection of B-mode power spectrum by the BICEP2 collaboration constrains the tensor-to-scalar ratio r = 0.20(-0.05)(+0.07) for the lensed-Lambda CDM model. The consistency of this big value with the Planck results requires a large running of the spectral index. The large values of the tensor-to-scalar ratio and the running of the spectral index put a challenge to single field inflation. For the chaotic inflation, the larger the value of the tensor-to-scalar ratio is, the smaller the value of the running of the spectral index is. For the natural inflation, the absolute value of the running of the spectral index has an upper limit. (C) 2014 The Authors. Published by Elsevier B.V.
182546364
ANALYSIS OF QUASI - DELTA (33) DOORWAY STATE MODEL IN PI NUCLEUS SCATTERING. (IN CHINESE)