Gauge invariant formulation of metric f (R) gravity for gravitational waves

We analyze the propagation of gravitational waves in metric f(R) theories of gravity, on the special setting of flat background geometry (Minkowski spacetime). In particular, adopting a gauge invariant formalism, we clearly establish that the exact number of propagating degrees of freedom is three, consisting of the standard tensorial modes along with an additional massive scalar field. Then, investigating their effects on test masses via the geodesic deviation equation, we show that the additional dynamical degree contained in such extended formulations is actually detectable as a superposition of longitudinal and breathing stresses, which even though in principle correspond to distinct pure polarizations turn out to be never separable in the wave dynamics and cannot be interpreted as a proper independent excitations

Torsional birefringence in metric-affine Chern-Simons gravity: gravitational waves in late-time cosmology

In the context of the metric-affine Chern-Simons gravity endowed with projective invariance, we derive analytical solutions for torsion and nonmetricity in the homogeneous and isotropic cosmological case, described by a flat Friedmann-Robertson-Walker metric. We describe in some details the general properties of the cosmological solutions in the presence of a perfect fluid, such as dynamical stability and the settling of big bounce points, and we discuss the structure of some specific solutions reproducing de Sitter and power law behaviours for the scale factor. Then, we focus on first-order perturbations in the de Sitter scenario, and we study the propagation of gravitational waves in the adiabatic limit, looking at tensor and scalar polarizations. In particular, we find that metric tensor modes couple to torsion tensor components, leading to the appearance, as in the metric version of Chern-Simons gravity, of birefringence, described by different dispersion relations for the left and right circularized polarization states. As a result, the purely tensor part of torsion propagates like a wave, while nonmetricity decouples and behaves like a harmonic oscillator. Finally, we discuss scalar modes, outlining as they decay exponentially in time and do not propagate.Comment: References adde

Gravitational Landau damping for massive scalar modes

We establish the possibility of Landau damping for gravitational scalar waves which propagate in a non-collisional gas of particles. In particular, under the hypothesis of homogeneity and isotropy, we describe the medium at the equilibrium with a Jüttner–Maxwell distribution, and we analytically determine the damping rate from the Vlasov equation. We find that damping occurs only if the phase velocity of the wave is subluminal throughout the propagation within the medium. Finally, we investigate relativistic media in cosmological settings by adopting numerical techniques.The work of F. B. is supported by the Fondazione Angelo della Riccia grant for the year 202

Gravitational Landau damping for massive scalar modes

We establish the possibility of Landau damping for gravitational scalar waves which propagate in a non-collisional gas of particles. In particular, under the hypothesis of homogeneity and isotropy, we describe the medium at the equilibrium with a Jüttner–Maxwell distribution, and we analytically determine the damping rate from the Vlasov equation. We find that damping occurs only if the phase velocity of the wave is subluminal throughout the propagation within the medium. Finally, we investigate relativistic media in cosmological settings by adopting numerical techniques

Semiclassical and quantum analysis of the isotropic Universe in the polymer paradigm

We analyze the semiclassical and quantum dynamics of the isotropic universe in the framework of the polymer quantum mechanics in order to implement a cutoff physics on the initial singularity. We first identify in the Universe cubed scale factor (i.e., the spatial volume) the suitable configuration variable, providing a constant critical energy density, such that the bounce arises as intrinsic geometric feature. We then investigate the obtained semiclassical bounce dynamics for the primordial Universe, and we outline its impact on the resolution of cosmological paradoxes, as soon as the semi-classical evolution is extended (in the spirit of the Ehrenfest theorem) to the collapsing prebounce Universe. Finally, we validate the use of the semiclassical effective dynamics by investigating the behaviour of the expectation values of a proper semiclassical states. The present analysis has the merit to enforce the equivalence between the polymer quantization paradigm in the minisuperspace and the loop quantum cosmology approach. In fact, our study allows to define a precise correspondence between the polymer cutoff scale and the discrete geometric structure of LQG