Scalaron from R2-gravity as a heavy field

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of \(1.0 \times 10^{-21}\). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203 000 years, equivalent to a significance greater than 5.1 {\sigma}. The source lies at a luminosity distance of \(410^{+160}_{-180}\) Mpc corresponding to a redshift \(z = 0.09^{+0.03}_{-0.04}\). In the source frame, the initial black hole masses are \(36^{+5}_{-4} M_\odot\) and \(29^{+4}_{-4} M_\odot\), and the final black hole mass is \(62^{+4}_{-4} M_\odot\), with \(3.0^{+0.5}_{-0.5} M_\odot c^2\) radiated in gravitational waves. All uncertainties define 90% credible intervals.These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

In the DGP model, the ``self-accelerating'' solution is plagued by a ghost instability, which makes the solution untenable. This fact as well as all interesting departures from GR are fully captured by a four-dimensional effective Lagrangian, valid at distances smaller than the present Hubble scale. The 4D effective theory involves a relativistic scalar \pi, universally coupled to matter and with peculiar derivative self-interactions. In this paper, we study the connection between self-acceleration and the presence of ghosts for a quite generic class of theories that modify gravity in the infrared. These theories are defined as those that at distances shorter than cosmological, reduce to a certain generalization of the DGP 4D effective theory. We argue that for infrared modifications of GR locally due to a universally coupled scalar, our generalization is the only one that allows for a robust implementation of the Vainshtein effect--the decoupling of the scalar from matter in gravitationally bound systems--necessary to recover agreement with solar system tests. Our generalization involves an internal ``galilean'' invariance, under which \pi's gradient shifts by a constant. This symmetry constrains the structure of the \pi Lagrangian so much so that in 4D there exist only five terms that can yield sizable non-linearities without introducing ghosts. We show that for such theories in fact there are ``self-accelerating'' deSitter solutions with no ghost-like instabilities. In the presence of compact sources, these solutions can support spherically symmetric, Vainshtein-like non-linear perturbations that are also stable against small fluctuations. [Short version for arxiv]

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.