Gravitational-wave experiments with interferometers and with resonant masses can search for stochastic backgrounds of gravitational waves of cosmological origin. We review both experimental and theoretical aspects of the search for these backgrounds. We give a pedagogical derivation of the various relations that characterize the response of a detector to a stochastic background. We discuss the sensitivities of the large interferometers under constructions (LIGO, VIRGO, GEO600, TAMA300, AIGO) or planned (Avdanced LIGO, LISA) and of the presently operating resonant bars, and we give the sensitivities for various two-detectors correlations. We examine the existing limits on the energy density in gravitational waves from nucleosynthesis, COBE and pulsars, and their effects on theoretical predictions. We discuss general theoretical principles for order-of-magnitude estimates of cosmological production mechanisms, and then we turn to specific theoretical predictions from inflation, string cosmology, phase transitions, cosmic strings and other mechanisms. We finally compare with the stochastic backgrounds of astrophysical origin.

ABSTRACT. We discuss a Gedanken experiment for the measurement of the area of the apparent horizon of a black hole in quantum gravity. Using rather general and model-independent considerations we find a generalized uncertainty principle which agrees with a similar result obtained in the framework of string theories. The result indicates that a minimum length of the order of the Planck length emerges naturally from any quantum theory of gravity, and that the concept of black hole is not operationally defined if the mass is smaller than the Planck mass.

The Einstein Telescope (ET), a proposed European ground-based gravitationalwave detector of third-generation, is an evolution of second-generation detectors such as Advanced LIGO, Advanced Virgo, and KAGRA which could be operating in the mid 2030s. ET will explore the universe with gravitational waves up to cosmological distances. We discuss its main scientific objectives and its potential for discoveries in astrophysics, cosmology and fundamental physics. 1 1 Prepared for submission to the ESFRI Roadmap, on behalf of the ET steering committee.

When a classical black hole is perturbed, its relaxation is governed by a set of quasinormal modes with complex frequencies ω=ωR+iωI. We show that this behavior is the same as that of damped harmonic oscillators whose real frequencies are (ω2R+ω2I)1/2, rather than simply ωR. Since, for highly excited modes, ωI≫ωR, this observation changes drastically the physical understanding of the black hole spectrum and forces a reexamination of various results in the literature. In particular, adapting a derivation by Hod, we find that the area of the horizon of a Schwarzschild black hole is quantized in units ΔA=8πl2Pl, in contrast with the original result ΔA=4log(3)l2P

We show that a deformation of the Heisenberg algebra which depends on a dimensionful parameter $\kappa$ is the algebraic structure which underlies the generalized uncertainty principle in quantum gravity. The deformed algebra and therefore the form of the generalized uncertainty principle are fixed uniquely by rather simple assumptions. The string theory result is reproduced expanding our result at first order in $\Delta p/M_{\rm PL}$. We also briefly comment on possible implications for Lorentz invariance at the Planck scale.Comment: 6 pages, IFUP-TH 38/9

A comprehensive and detailed account of the physics of gravitational waves and their role in astrophysics and cosmology. The part on astrophysical sources of gravitational waves includes chapters on GWs from supernovae, neutron stars (neutron star normal modes, CFS instability, r-modes), black-hole perturbation theory (Regge-Wheeler and Zerilli equations, Teukoslky equation for rotating BHs, quasi-normal modes) coalescing compact binaries (effective one-body formalism, numerical relativity), discovery of gravitational waves at the advanced LIGO interferometers (discoveries of GW150914, GW151226, tests of general relativity, astrophysical implications), supermassive black holes (supermassive black-hole binaries, EMRI, relevance for LISA and pulsar timing arrays). The part on gravitational waves and cosmology include discussions of FRW cosmology, cosmological perturbation theory (helicity decomposition, scalar and tensor perturbations, Bardeen variables, power spectra, transfer functions for scalar and tensor modes), the effects of GWs on the Cosmic Microwave Background (ISW effect, CMB polarization, E and B modes), inflation (amplification of vacuum fluctuations, quantum fields in curved space, generation of scalar and tensor perturbations, Mukhanov-Sasaki equation,reheating, preheating), stochastic backgrounds of cosmological origin (phase transitions, cosmic strings, alternatives to inflation, bounds on primordial GWs) and search of stochastic backgrounds with Pulsar Timing Arrays (PTA).

We investigate the relationship between the generalized uncertainty principle in quantum gravity and the quantum deformation of the Poincaré algebra. We find that a deformed Newton-Wigner position operator and the generators of spatial translations and rotations of the deformed Poincaré algebra obey a deformed Heisenberg algebra from which the generalized uncertainty principle follows. The result indicates that in the κdeformed Poincaré algebra a minimal observable length emerges naturally.

Studies of dark energy at advanced gravitational-wave (GW) interferometers normally focus on the dark energy equation of state wDE(z). However, modified gravity theories that predict a nontrivial 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 wDE(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 (Ξ0, n), analogue to the (w0, wa) parametrization of the dark energy equation of state, and we give a limit from the LIGO/Virgo measurement of H0 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 (Ξ0, 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, Ξ0 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.arXiv:1805.08731v3 [gr-qc]