Friction in Gravitational Waves: a test for early-time modified gravity

Modified gravity theories predict in general a non standard equation for the propagation of gravitational waves. Here we discuss the impact of modified friction and speed of tensor modes on cosmic microwave polarization B modes. We show that the non standard friction term, parametrized by $\alpha_{M}$, is degenerate with the tensor-to-scalar ratio $r$, so that small values of $r$ can be compensated by negative constant values of $\alpha_M$. We quantify this degeneracy and its dependence on the epoch at which $\alpha_{M}$ is different from the standard, zero, value and on the speed of gravitational waves $c_{T}$. In the particular case of scalar-tensor theories, $\alpha_{M}$ is constant and strongly constrained by background and scalar perturbations, $0\le \alpha_{M}< 0.01$ and the degeneracy with $r$ is removed. In more general cases however such tight bounds are weakened and the B modes can provide useful constraints on early-time modified gravity.Comment: Minor changes after published version. One new figur

On boosted space-times with cosmological constant and their ultrarelativistic limit

The problem of deriving a shock-wave geometry with cosmological constant by boosting a Schwarzschild-de Sitter (or anti-de Sitter) black hole is re-examined. Unlike previous work in the literature, we deal with the exact Schwarzschild-de Sitter (or anti-de Sitter) metric. By virtue of peculiar cancellations in this exact calculation, where the metric does not depend linearly on the mass parameter, we find a singularity of distributional nature on a null hypersurface, which corresponds to a shock-wave geometry derived in a fully non-perturbative way. The result agrees with previous calculations, where the metric had been linearized in the mass parameter.Comment: 13 pages, Latex file. In the final version, the presentation has been improved, and two references have been adde

Constraints on coupled dark energy using CMB data from WMAP and SPT

We consider the case of a coupling in the dark cosmological sector, where a dark energy scalar field modifies the gravitational attraction between dark matter particles. We find that the strength of the coupling {\beta} is constrained using current Cosmic Microwave Background (CMB) data, including WMAP7 and SPT, to be less than 0.063 (0.11) at 68% (95%) confidence level. Further, we consider the additional effect of the CMB-lensing amplitude, curvature, effective number of relativistic species and massive neutrinos and show that the bound from current data on {\beta} is already strong enough to be rather stable with respect to any of these variables. The strongest effect is obtained when we allow for massive neutrinos, in which case the bound becomes slightly weaker, {\beta} < 0.084(0.14). A larger value of the effective number of relativistic degrees of freedom favors larger couplings between dark matter and dark energy as well as values of the spectral index closer to 1. Adding the present constraints on the Hubble constant, as well as from baryon acoustic oscillations and supernovae Ia, we find {\beta} < 0.050(0.074). In this case we also find an interesting likelihood peak for {\beta} = 0.041 (still compatible with 0 at 1{\sigma}). This peak comes mostly from a slight difference between the Hubble parameter HST result and the WMAP7+SPT best fit. Finally, we show that forecasts of Planck+SPT mock data can pin down the coupling to a precision of better than 1% and detect whether the marginal peak we find at small non zero coupling is a real effect.Comment: 22 pages, 17 figure

Prescriptions for Off-Shell Bosonic String Amplitudes

We give, in the framework of the bosonic string theory, simple prescriptions for computing, at tree and one-loop levels, off-shell string amplitudes for open and closed string massless states. In particular we obtain a tree amplitude for three open strings that in the field theory limit coincides with the three-gluon vertex in the usual covariant gauge and two-string one-loop amplitudes satisfying the property of transversality.Comment: 11 pages, LaTeX, to appear in the proceedings of the workshop "Quantum Aspects of Gauge Theories, Supersymmetry and Unification", Corfu (Greece), 20-26 September 1998. Eq. (12) and numerical factors in eqs. (13) and (16) corrected; some minor changes and references adde