We show that the recently proposed weak gravity conjecture\cite{AMNV0601} can be extended to a class of scalar field theories. Taking gravity into account, we find an upper bound on the gravity interaction strength, expressed in terms of scalar coupling parameters. This conjecture is supported by some two-dimensional models and noncommutative field theories.

We quantize a string in the de Sitter background, and we find that the mass spectrum is modified by a term which is quadratic in oscillating numbers, and also proportional to the square of the Hubble constant.

We compute the string production rate at the end of inflation, using the string spectrum obtained in [M. Li, W. Song, Y. Song, Quantizing strings in de Sitter space, JHEP 0704 (2007) 042, hep-th/0701258] in a near-de Sitter space. Our result shows that highly excited strings are hardly produced, thus the simple slow-roll inflation alone does not offer a cosmic string production mechanism.

Three dimensional Einstein gravity with negative cosmological constant -1/\ell^2 deformed by a gravitational Chern-Simons action with coefficient 1/\mu is studied in an asymptotically AdS_3 spacetime. It is argued to violate unitary or positivity for generic \mu due to negative-energy massive gravitons. However at the critical value \mu\ell=1, the massive gravitons disappear and BTZ black holes all have mass and angular momentum related by \ell M=J. The corresponding chiral quantum theory of gravity is conjectured to exist and be dual to a purely right-moving boundary CFT with central charges (c_L,c_R)=(0,3\ell /G).

In a recent paper (arXiv: ) it was shown that all global energy eigenstates of asymptotically $AdS_3$ chiral gravity have non-negative energy at the linearized level. This result was questioned (arXiv: ) by Carlip, Deser, Waldron and Wise (CDWW), who work on the Poincare patch. They exhibit a linearized solution of chiral gravity and claim that it has negative energy and is smooth at the boundary. We show that the solution of CDWW is smooth only on that part of the boundary of $AdS_3$ included in the Poincare patch. Extended to global $AdS_3$, it is divergent at the boundary point not included in the Poincare patch. Hence it is consistent with the results of (arXiv: 0801.4566).