Probing the primordial Universe from the low-multipole CMB data

Since the temperature fluctuations in cosmic microwave background (CMB) on large-angular scales probe length scales that were super-horizon sized at photon decoupling and hence insensitive to microphysical processes, the low-multipole CMB data are supposed to be a good probe to the physics of the primordial Universe. In this letter we will constrain the cosmological parameters in the base $\Lambda$CDM model with tensor perturbations by only using low-multipole CMB data, including Background Imaging of Cosmic Extragalactic Polarization (B2), Planck released in 2013 (P13) and Wilkinson Microwaves Anisotropy Probe 9-year data (W9). We find that a red tilted power spectrum of relic gravitational waves is compatible with the data, but a blue tilted power spectrum of scalar perturbations on the large scales is preferred at around $2\sigma$ confidence level.Comment: 5 pages, 2 tables, 2 figure

Constraints on the cosmological parameters from BICEP2, Planck and WMAP

In this paper we constrain the cosmological parameters, in particular the tilt of tensor power spectrum, by adopting Background Imaging of Cosmic Extragalactic Polarization (B2), Planck released in 2013 (P13) and Wilkinson Microwaves Anisotropy Probe 9-year Polarization (WP) data. We find that a blue tilted tensor power spectrum is preferred at more than $3\sigma$ confidence level if the data from B2 are assumed to be totally interpreted as the relic gravitational waves, but a scale invariant tensor power spectrum is consistent with the data once the polarized dust is taken into account. The recent Planck 353 GHz HFI dust polarization data imply that the B2 data are perfectly consistent with there being no gravitational wave signal.Comment: 4 pages, 3 figures and 1 table; major revision, dust added for solving the tension between Planck13 and BICEP2, version accepted for publication in EPJ

An Electroweak-like Theory from Four Fermion Interactions

An electroweak-like theory of a broken chiral symmetry that is constructed by the collective modes of fermion pairs from four fermion interactions of one lepton generation is presented. The products of Dirac spinors lead to the separation of the two chiral fermions to couple respectively with two different kinds of polarization states. Because of a broken vacuum, a fermion and an anti-fermion out of the four pair up to form vector bosons, which behave like gauge bosons, such as $W^\pm$, $Z$ and $\gamma$ in a group structure of $SU(2)_L\times U(1)_Y$. The pairing of spinors only allows left-handed fermions to interact with charged bosons to secure the gauge invariance, while, as desired, $Z$-like bosons mediate different weak forces for two chiral fermions and $\gamma$-like bosons interact freely with fermions.Comment: 15 page

A Route toward Quantum Gravity through the Imaginary-Time Field Theory

A possible way toward the quantization of a weak gravitational field inspired by the imaginary-time field theory is discussed. The analogies of the general relativity in the canonical formulation with the thermodynamic geometry and superfluids are also pointed out. The proposed regularization method in the imaginary-time formalism of field theory shows a good chance removing theoretical obstacles and constructing a perturbative theory of quantum gravity.Comment: 13 pages, 3 figures, some corrections have been mad