Antonio De Felice

Testing general relativity with present and future astrophysical observations

One century after its formulation, Einsteins general relativity (GR) has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that GR should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of GR. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einsteins theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.

Effective gravitational couplings for cosmological perturbations in the most general scalar-tensor theories with second-order field equations

Abstract In the Horndeskiʼs most general scalar–tensor theories the equations of scalar density perturbations are derived in the presence of non-relativistic matter minimally coupled to gravity. Under a quasi-static approximation on sub-horizon scales we obtain the effective gravitational coupling G eff associated with the growth rate of matter perturbations as well as the effective gravitational potential Φ eff relevant to the deviation of light rays. We then apply our formulas to a number of modified gravitational models of dark energy – such as those based on f ( R ) theories, Brans–Dicke theories, kinetic gravity braidings, covariant Galileons, and field derivative couplings with the Einstein tensor. Our results are useful to test the large-distance modification of gravity from the future high-precision observations of large-scale structure, weak lensing, and cosmic microwave background.

Nonlinear stability of cosmological solutions in massive gravity

We investigate nonlinear stability of two classes of cosmological solutions in massive gravity: isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) solutions and anisotropic FLRW solutions. For this purpose we construct the linear cosmological perturbation theory around axisymmetric Bianchi type-I backgrounds. We then expand the background around the two classes of solutions, which are fixed points of the background evolution equation, and analyze linear perturbations on top of it. This provides a consistent truncation of nonlinear perturbations around these fixed point solutions and allows us to analyze nonlinear stability in a simple way. In particular, it is shown that isotropic FLRW solutions exhibit nonlinear ghost instability. On the other hand, anisotropic FLRW solutions are shown to be ghost-free for a range of parameters and initial conditions.

Conditions for the cosmological viability of the most general scalar-tensor theories and their applications to extended Galileon dark energy models

In the Horndeskis most general scalar-tensor theories with second-order field equations, we derive the conditions for the avoidance of ghosts and Laplacian instabilities associated with scalar, tensor, and vector perturbations in the presence of two perfect fluids on the flat Friedmann-Lemaitre-Robertson-Walker (FLRW) background. Our general results are useful for the construction of theoretically consistent models of dark energy. We apply our formulas to extended Galileon models in which a tracker solution with an equation of state smaller than -1 is present. We clarify the allowed parameter space in which the ghosts and Laplacian instabilities are absent and we numerically confirm that such models are indeed cosmologically viable.

Towards consistent extension of quasidilaton massive gravity

Abstract We present the first example of a unitary theory of Lorentz-invariant massive gravity, with all degrees of freedom propagating on a strictly homogeneous and isotropic, self-accelerating de Sitter background. The theory is a simple extension of the quasidilaton theory, respecting the symmetry of the original theory but allowing for a new type of coupling between the massive graviton and the quasidilaton scalar.

On the cosmology of massive gravity

We present a review of cosmological solutions in nonlinear massive gravity, focusing on the stability of perturbations. Although homogeneous and isotropic solutions have been found, these are now known to suffer from either the Higuchi ghost or a new nonlinear ghost instability. We discuss two approaches to alleviate this issue. By relaxing the symmetry of the background by e.g. breaking isotropy in the hidden sector, it is possible to accommodate a stable cosmological solution. Alternatively, extending the theory to allow for new dynamical degrees of freedom can also remove the conditions which lead to the instability. As examples for this case, we study the stability of self-accelerating solutions in the quasi-dilatonic extension and generic cosmological solutions in the varying mass extension. While the quasi-dilaton case turns out to be unstable, the varying mass case allows stable regimes of parameters. Viable self-accelerating solutions in the varying mass theory yet remain to be found.

Observational constraints on quintessence: Thawing, tracker, and scaling models

For two types of quintessence models having thawing and tracking properties, there exist analytic solutions for the dark energy equation of state

Vainshtein mechanism in second-order scalar-tensor theories

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Possible existence of viable models of bi-gravity with detectable graviton oscillations by gravitational wave detectors

expressed in terms of several free parameters. We put observational bounds on the parameters in such scenarios by using the recent type Ia supernovae, cosmic microwave background, and baryon acoustic oscillations data. The observational constraints are quite different depending on whether or not the recent baryon acoustic oscillations data from BOSS are taken into account. With the BOSS data the upper bounds of todays values of

Shapes of primordial non-Gaussianities in the Horndeski's most general scalar-tensor theories

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