Degrees of freedom of f(T)f(T) gravity

We investigate the Hamiltonian formulation of $f(T)$ gravity and find that there are five degrees of freedom. The six first class constraints corresponding to the local Lorentz transformation in Teleparallel gravity become second class constraints in $f(T)$ gravity, which leads to the appearance of three extra degrees of freedom and the violation of the local Lorentz invariance in $f(T)$ gravity. In general, there are $D-1$ extra degrees of freedom for $f(T)$ gravity in $D$ dimensions, and this implies that the extra degrees of freedom correspond to one massive vector field or one massless vector field with one scalar field.Comment: 18 pages, some references added, minor revision to appear in JHE

Metamaterials Mimicking Dynamic Spacetime, D-brane and Noncommutativity in String Theory

We propose an executable scheme to mimic the expanding cosmos in 1+2 dimensions in laboratory. Furthermore, we develop a general procedure to use nonlinear metamaterials to mimic D-brane and noncommutativity in string theory.Comment: 15 pages, 2 figure

Planck Constraints on Holographic Dark Energy

We perform a detailed investigation on the cosmological constraints on the holographic dark energy (HDE) model by using the Planck data. HDE can provide a good fit to Planck high-l (l>40) temperature power spectrum, while the discrepancy at l=20-40 found in LCDM remains unsolved in HDE. The Planck data alone can lead to strong and reliable constraint on the HDE parameter c. At 68% CL, we get c=0.508+-0.207 with Planck+WP+lensing, favoring the present phantom HDE at > 2sigma CL. Comparably, by using WMAP9 alone we cannot get interesting constraint on c. By combining Planck+WP with the BAO measurements from 6dFGS+SDSS DR7(R)+BOSS DR9, the H0 measurement from HST, the SNLS3 and Union2.1 SNIa data sets, we get 68% CL constraints c=0.484+-0.070, 0.474+-0.049, 0.594+-0.051 and 0.642+-0.066. Constraints can be improved by 2%-15% if we further add the Planck lensing data. Compared with the WMAP9 results, the Planck results reduce the error by 30%-60%, and prefer a phantom-like HDE at higher CL. We find no evident tension between Planck and BAO/HST. Especially, the strong correlation between Omegam h^3 and dark energy parameters is helpful in relieving the tension between Planck and HST. The residual chi^2_{Planck+WP+HST}-chi^2_{Planck+WP} is 7.8 in LCDM, and is reduced to 1.0 or 0.3 if we switch dark energy to the w model or the holographic model. We find SNLS3 is in tension with all other data sets; for Planck+WP, WMAP9 and BAO+HST, the corresponding Delta chi^2 is 6.4, 3.5 and 4.1, respectively. Comparably, Union2.1 is consistent with these data sets, but the combination Union2.1+BAO+HST is in tension with Planck+WP+lensing, corresponding to a Delta chi^2 8.6 (1.4% probability). Thus, it is not reasonable to perform an all-combined (CMB+SNIa+BAO+HST) analysis for HDE when using the Planck data. Our tightest self-consistent constraint is c=0.495+-0.039 obtained from Planck+WP+BAO+HST+lensing.Comment: 29 pages, 11 figures, 3 tables; version accepted for publication in JCA

Dark Energy and Fate of the Universe

We explore the ultimate fate of the Universe by using a divergence-free parametrization for dark energy $w(z)=w_0+w_a({\ln (2+z)\over 1+z}-\ln2)$. Unlike the CPL parametrization, this parametrization has well behaved, bounded behavior for both high redshifts and negative redshifts, and thus can genuinely cover many theoretical dark energy models. After constraining the parameter space of this parametrization by using the current cosmological observations, we find that, at the 95.4% confidence level, our Universe can still exist at least 16.7 Gyr before it ends in a big rip. Moreover, for the phantom energy dominated Universe, we find that a gravitationally bound system will be destroyed at a time $t \simeq P\sqrt{2|1+3w(-1)|}/[6\pi |1+w(-1)|]$, where $P$ is the period of a circular orbit around this system, before the big rip.Comment: 5 pages, 3 figures; typos corrected, publication version, Sci China-Phys Mech Astron, doi: 10.1007/s11433-012-4748-