We derive the primordial power spectra and spectral indexes of the density fluctuations and gravitational waves in the framework of loop quantum cosmology (LQC) with holonomy and inverse-volume corrections, by using the uniform asymptotic approximation method to its third-order, at which the upper error bounds are $lesssim 0.15%$, and accurate enough for the current and forthcoming cosmological observations. Then, using the Planck, BAO and SN data we obtain the tightest constraints on quantum gravitational effects from LQC corrections, and find that such effects could be well within the detection of the current and forthcoming cosmological observations.
We use the Monte-Carlo Markov Chain method to explore the dark energy property and the cosmic curvature by fitting two popular dark energy parameterizations to the observational data. The new 182 gold supernova Ia data and the ESSENCE data both give good constraint on the DE parameters and the cosmic curvature for the dark energy model $w_0+w_a z/(1+z)$. The cosmic curvature is found to be $|Omega_k|la 0.03$. For the dark energy model $w_0+w_a z/(1+z)^2$, the ESSENCE data gives better constraint on the cosmic curvature and we get $|Omega_k|leq 0.02$.
Orbifold branes are studied in the framework of the 11-dimensional Horava-Witten heterotic M-Theory. It is found that the effective cosmological constant can be easily lowered to its current observational value by the mechanism of large extra dimensions. The domination of this constant over the evolution of the universe is only temporarily. Due to the interaction of the bulk and the branes, the universe will be in its decelerating expansion phase again in the future, whereby all problems connected with a far future de Sitter universe are resolved.
With the help of a masslike function which has dimension of energy and equals to the Misner-Sharp mass at the apparent horizon, we show that the first law of thermodynamics of the apparent horizon $dE=T_AdS_A$ can be derived from the Friedmann equation in various theories of gravity, including the Einstein, Lovelock, nonlinear, and scalar-tensor theories. This result strongly suggests that the relationship between the first law of thermodynamics of the apparent horizon and the Friedmann equation is not just a simple coincidence, but rather a more profound physical connection.
