Effective field theory methods to model compact binaries

In this short review we present a self-contained exposition of the effective field theory method approach to model the dynamics of gravitationally bound compact binary systems within the post-Newtonian approximation to General Relativity. Applications of this approach to the conservative sector, as well as to the radiation emission by the binary system are discussed in their salient features. Most important results are discussed in a pedagogical way, as in-depths and details can be found in the referenced papers.Comment: 37 pages, 22 figure

Cosmological dynamics and dark energy from non-local infrared modifications of gravity

We perform a detailed study of the cosmological dynamics of a recently proposed infrared modification of the Einstein equations, based on the introduction of a non-local term constructed with $m^2g_{\mu\nu}\Box^{-1} R$, where $m$ is a mass parameter. The theory generates automatically a dynamical dark energy component, that can reproduce the observed value of the dark energy density without introducing a cosmological constant. Fixing $m$ so to reproduce the observed value $\Omega_{\rm DE}\simeq 0.68$, and writing $w(a)=w_0+(1-a) w_a$, the model provides a neat prediction for the equation of state parameters of dark energy, $w_0\simeq -1.042$ and $w_a\simeq -0.020$. We show that, because of some freedom in the definition of $\Box^{-1}$, one can extend the construction so to define a more general family of non-local models. However, in a first approximation this turns out to be equivalent to adding an explicit cosmological constant term on top of the dynamical dark energy component. This leads to an extended model with two parameters, $\Omega_{\Lambda}$ and $m$. Even in this extension the EOS parameter $w_0$ is always on the phantom side, in the range $-1.33 < w_0\leq -1$, and there is a prediction for the relation between $w_0$ and $w_a$.Comment: 30 pages, 15 figures; v2: cross-reference to 1311.3421 adde

A braneworld puzzle about entropy bounds and a maximal temperature

Entropy bounds applied to a system of N species of light quantum fields in thermal equilibrium at temperature T are saturated in four dimensions at a maximal temperature T_max=M_Planck/N^1/2. We show that the correct setup for understanding the reason for the saturation is a cosmological setup, and that a possible explanation is the copious production of black holes at this maximal temperature. The proposed explanation implies, if correct, that N light fields cannot be in thermal equilibrium at temperatures T above T_max. However, we have been unable to identify a concrete mechanism that is efficient and quick enough to prevent the universe from exceeding this limiting temperature. The same issues can be studied in the framework of AdS/CFT by using a brane moving in a five dimensional AdS-Schwarzschild space to model a radiation dominated universe. In this case we show that T_max is the temperature at which the brane just reaches the horizon of the black hole, and that entropy bounds and the generalized second law of thermodynamics seem to be violated when the brane continues to fall into the black hole. We find, again, that the known physical mechanisms, including black hole production, are not efficient enough to prevent the brane from falling into the black hole. We propose several possible explanations for the apparent violation of entropy bounds, but none is a conclusive one.Comment: 16 page

Supersymmetric Vacuum Configurations in String Cosmology

We examine in a cosmological context the conditions for unbroken supersymmetry in N=1 supergravity in D=10 dimensions. We show that the cosmological solutions of the equations of motion obtained considering only the bosonic sector correspond to vacuum states with spontaneous supersymmetry breaking. With a non vanishing gravitino-dilatino condensate we find a solution of the equations of motion that satisfies necessary conditions for unbroken supersymmetry and that smoothly interpolates between Minkowski space and DeSitter space with a linearly growing dilaton, thus providing a possible example of a supersymmetric and non-singular pre-big-bang cosmology.Comment: 4 pages, Latex, 2 figure

Effective field theory calculation of conservative binary dynamics at third post-Newtonian order

We reproduce the two-body gravitational conservative dynamics at third post-Newtonian order for spin-less sources by using the effective field theory methods for the gravitationally bound two-body system, proposed by Goldberger and Rothstein. This result has been obtained by automatizing the computation of Feynman amplitudes within a Mathematica algorithm, paving the way for higher-order computations not yet performed by traditional methods.Comment: 24 pages, 6 figures. Typos corrected and references added in v2. Typos corrected in v

Modified gravitational-wave propagation and standard sirens

Studies of dark energy at advanced gravitational-wave (GW) interferometers normally focus on the dark energy equation of state $w_{\rm DE}(z)$. However, modified gravity theories that predict a non-trivial dark energy equation of state generically also predict deviations from general relativity in the propagation of GWs across cosmological distances, even in theories where the speed of gravity is equal to $c$. We find that, in generic modified gravity models, the effect of modified GW propagation dominates over that of $w_{\rm DE}(z)$, making modified GW propagation a crucial observable for dark energy studies with standard sirens. We present a convenient parametrization of the effect in terms of two parameters $(\Xi_0,n)$, analogue to the $(w_0,w_a)$ parametrization of the dark energy equation of state, and we give a limit from the LIGO/Virgo measurement of $H_0$ with the neutron star binary GW170817. We then perform a Markov Chain Monte Carlo analysis to estimate the sensitivity of the Einstein Telescope (ET) to the cosmological parameters, including $(\Xi_0,n)$, both using only standard sirens, and combining them with other cosmological datasets. In particular, the Hubble parameter can be measured with an accuracy better than $1\%$ already using only standard sirens while, when combining ET with current CMB+BAO+SNe data, $\Xi_0$ can be measured to $0.8\%$ . We discuss the predictions for modified GW propagation of a specific nonlocal modification of gravity, recently developed by our group, and we show that they are within the reach of ET. Modified GW propagation also affects the GW transfer function, and therefore the tensor contribution to the ISW effect.Comment: 25 pages, 23 figures: v3: several significant improvement

The gravitational-wave luminosity distance in modified gravity theories

In modified gravity the propagation of gravitational waves (GWs) is in general different from that in general relativity. As a result, the luminosity distance for GWs can differ from that for electromagnetic signals, and is affected both by the dark energy equation of state $w_{\rm DE}(z)$ and by a function $\delta(z)$ describing modified propagation. We show that the effect of modified propagation in general dominates over the effect of the dark energy equation of state, making it easier to distinguish a modified gravity model from $\Lambda$CDM. We illustrate this using a nonlocal modification of gravity, that has been shown to fit remarkably well CMB, SNe, BAO and structure formation data, and we discuss the prospects for distinguishing nonlocal gravity from $\Lambda$CDM with the Einstein Telescope. We find that, depending on the exact sensitivity, a few tens of standard sirens with measured redshift at $z\sim 0.4$, or a few hundreds at $1 < z < 2$, could suffice.Comment: 6 pages, 3 figures; v4: minor modifications; the version to appear in PR

Conformal symmetry and nonlinear extensions of nonlocal gravity

We study two nonlinear extensions of the nonlocal $R\,\Box^{-2}R$ gravity theory. We extend this theory in two different ways suggested by conformal symmetry, either replacing $\Box^{-2}$ with $(-\Box + R/6)^{-2}$, which is the operator that enters the action for a conformally-coupled scalar field, or replacing $\Box^{-2}$ with the inverse of the Paneitz operator, which is a four-derivative operator that enters in the effective action induced by the conformal anomaly. We show that the former modification gives an interesting and viable cosmological model, with a dark energy equation of state today $w_{\rm DE}\simeq -1.01$, which very closely mimics $\Lambda$CDM and evolves asymptotically into a de Sitter solution. The model based on the Paneitz operator seems instead excluded by the comparison with observations. We also review some issues about the causality of nonlocal theories, and we point out that these nonlocal models can be modified so to nicely interpolate between Starobinski inflation in the primordial universe and accelerated expansion in the recent epoch.Comment: 27 pages, 4 figure

Symmetry breaking aspects of the effective Lagrangian for quantum black holes

The physical excitations entering the effective Lagrangian for quantum black holes are related to a Goldstone boson which is present in the Rindler limit and is due to the spontaneous breaking of the translation symmetry of the underlying Minkowski space. This physical interpretation, which closely parallels similar well-known results for the effective stringlike description of flux tubes in QCD, gives a physical insight into the problem of describing the quantum degrees of freedom of black holes. It also suggests that the recently suggested concept of 'black hole complementarity' emerges at the effective Lagrangian level rather than at the fundamental level.Comment: 11 pages, Latex,1 figur