Antonio De Felice

We study the cosmology of a covariant scalar field respecting a Galilean symmetry in flat space-time. We show the existence of a tracker solution that finally approaches a de Sitter fixed point responsible for cosmic acceleration today. The viable region of model parameters is clarified by deriving conditions under which ghosts and Laplacian instabilities of scalar and tensor perturbations are absent. The field equation of state exhibits a peculiar phantomlike behavior along the tracker, which a

We argue that all homogeneous and isotropic solutions in nonlinear massive gravity are unstable. For this purpose, we study the propagating modes on a Bianchi type-I manifold. We analyze their kinetic terms and dispersion relations as the background manifold approaches the homogeneous and isotropic limit. We show that in this limit, at least one ghost always exists and that its frequency tends to vanish for large scales, meaning that it cannot be integrated out from the low energy effective theo

In the Horndeski's 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 tra

We consider a massive vector field with derivative interactions that propagates only the 3 desired polarizations (besides two tensor polarizations from gravity) with second-order equations of motion in curved space-time. The cosmological implications of such generalized Proca theories are investigated for both the background and the linear perturbation by taking into account the Lagrangian up to quintic order. In the presence of a matter fluid with a temporal component of the vector field, we de

For very general scalar-field theories in which the equations of motion are at second order, we evaluate the three-point correlation function of primordial scalar perturbations generated during inflation. We show that the shape of non-Gaussianities is well approximated by the equilateral type. The equilateral nonlinear parameter ${f}_{\mathrm{NL}}^{\mathrm{equil}}$ is derived on the quasi-de Sitter background, where the slow-variation parameters are much smaller than unity. We apply our formula

We study the cosmology of a generalized Galileon field $\ensuremath{\phi}$ with five covariant Lagrangians in which $\ensuremath{\phi}$ is replaced by general scalar functions ${f}_{i}(\ensuremath{\phi})$ ($i=1,\dots{},5$). For these theories, the equations of motion remain at second order in time derivatives. We constrain the forms of the functions ${f}_{i}(\ensuremath{\phi})$ from the requirement to possess de Sitter solutions responsible for dark energy. There are two possible choices for pow

We consider Modified Gravity models involving inverse powers of fourth-order curvature invariants. Using these models' equivalence to the theory of a scalar field coupled to a linear combination of the invariants, we investigate the properties of the propagating modes. Even in the case for which the fourth derivative terms in the field equations vanish, we find that the second derivative terms can give rise to ghosts, instabilities, and superluminal propagation speeds. We establish the condition

We discuss solar system constraints on $f(\mathcal{G})$ gravity models, where $f$ is a function of the Gauss-Bonnet term $\mathcal{G}$. We focus on cosmologically viable $f(\mathcal{G})$ models that can be responsible for late-time cosmic acceleration. These models generally give rise to corrections of the form $ϵ(r/{r}_{s}{)}^{p}$ to the vacuum Schwarzschild solution, where $\ensuremath{\epsilon}={H}_{*}^{2}{r}_{s}^{2}\ensuremath{\ll}1$, ${r}_{s}$ is the Schwarzschild radius of the Sun, and ${H

We study the evolution of matter density perturbations in Galileon cosmology where the late-time cosmic acceleration can be realized by a field kinetic energy. We obtain full perturbation equations at linear order in the presence of five covariant Lagrangians ${\mathcal{L}}_{i}$ ($i=1,\ensuremath{\cdots},5$) satisfying the Galileon symmetry ${\ensuremath{\partial}}_{\ensuremath{\mu}}\ensuremath{\phi}\ensuremath{\rightarrow}{\ensuremath{\partial}}_{\ensuremath{\mu}}\ensuremath{\phi}+{b}_{\ensurem

We consider the finite interactions of the generalized Proca theory including the sixth-order Lagrangian and derive the full linear perturbation equations of motion on the flat Friedmann-Lema\^{\i}tre-Robertson-Walker background in the presence of a matter perfect fluid. By construction, the propagating degrees of freedom (besides the matter perfect fluid) are two transverse vector perturbations, one longitudinal scalar, and two tensor polarizations. The Lagrangians associated with intrinsic vec

We derive the equations of linear cosmological perturbations for the general Lagrangian density $f(R,\ensuremath{\phi},X)/2+{\mathcal{L}}_{c}$, where $R$ is a Ricci scalar, $\ensuremath{\phi}$ is a scalar field, and $X=\ensuremath{-}{\ensuremath{\partial}}^{\ensuremath{\mu}}\ensuremath{\phi}{\ensuremath{\partial}}_{\ensuremath{\mu}}\ensuremath{\phi}/2$ is a field kinetic energy. We take into account a nonlinear self-interaction term ${\mathcal{L}}_{c}=\ensuremath{\xi}(\ensuremath{\phi})\ensurema

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 provid

We study linear metric perturbations around a spherically symmetric static spacetime for general $f(R,\mathcal{G})$ theories, where $R$ is the Ricci scalar and $\mathcal{G}$ is the Gauss-Bonnet term. We find that, unless the determinant of the Hessian of $f(R,\mathcal{G})$ is zero, even-type perturbations have a ghost for any multipole mode. In order for these theories to be plausible alternatives to general relativity, the theory should satisfy the condition that the ghost is massive enough to

We consider higher-order, scalar-tensor theories which appear degenerate when restricted to the unitary gauge but are not degenerate in an arbitrary gauge. We dub them U-degenerate theories. We provide a full classification of theories that are either DHOST or U-degenerate and that are quadratic in second derivatives of the scalar field and discuss its extension to cubic and higher-order theories. Working with a simple example of U-degenerate theory, we find that, for configurations in which the