Giuseppe Gaetano Luciano

In this paper we quantify the ability of the Laser Interferometer Space Antenna (LISA) to test the presence of non-tensorial polarizations as well as modifications to the tensor ones in gravitational waves emitted from massive black hole binaries. We employ the Parametrized Post-Einsteinian (PPE) formalism to model deviations from General Relativity (GR) for tensor, vector, and scalar polarizations. Our PPE parametrization is inspired by post-Newtonian waveforms from four modified gravity theories: Horndeski, Einstein-æther, Rosen's bimetric, and Lightman-Lee. We consistently implement these modifications during the inspiral, ensuring proper waveform alignment and tapering at merger. Subsequently, we perform Fisher forecasts to derive expected constraints on deviations from General Relativity and map these constraints to the parameter spaces of the four gravity theories. For tensor polarizations, LISA achieves constraints on amplitude modifications ranging between ∼ 10 ^-4 - 10 ^-2 precision level, depending on the frequency evolution of the modifications, for systems with 10 ⁵ - 10 ⁷ M _⊙ at z = 1. We find that LISA can distinguish breathing and longitudinal scalar polarizations, a capability that current ground-based detectors do not possess, only for relatively light binaries with M ≲ 10 ⁴ M _⊙ , beyond which these modes become degenerate in the detector response. Importantly, constraints on vector polarizations are approximately 2–3 times more precise than for scalar polarizations. For both vector and scalar modes, amplitude measurements reach precisions ranging between ∼ 10 ^-8 - 10 ^-2 , depending on the frequency evolution of the modifications, for systems with 10 ⁵ - 10 ⁷ M _⊙ at z = 1. These results demonstrate LISA's potential to probe gravity in the emission process of gravitational waves.

We develop a thermodynamic formulation of Cotton gravity in the Codazzi parametrization, providing a general framework in which the gravitational dynamics can be interpreted in terms of horizon thermodynamics. As paradigmatic examples, we apply the formalism to Friedmann–Robertson–Walker (FRW) and static spherically symmetric spacetimes. By implementing the first law of thermodynamics on the apparent cosmological and event horizons, we derive a modified holographic entropy consisting of the standard Bekenstein–Hawking term supplemented by a correction induced by the Codazzi tensor. In the cosmological setting, this correction is governed by the temporal component of the Codazzi tensor, while in static configurations it is controlled by its anisotropic sector. Remarkably, the sign of this contribution may provide a potential diagnostic of the underlying matter content, allowing one to distinguish between ordinary matter, a cosmological constant and phantom-like components. These results establish horizon thermodynamics as a sensitive probe of Cotton gravity, offering a complementary perspective beyond background kinematics and enabling a characterization of the statistical and thermodynamic properties of spacetime within the Codazzi formulation.

We develop new modified cosmological scenarios by applying the first law of thermodynamics at the Universe horizon, utilizing a new entropic functional that generalizes the standard Boltzmann-Gibbs-Shannon entropy. In particular, starting from the general theory of entropy in terms of the probability distribution over the accessible microstates, and by imposing violation of the separability requirement and thus considering a generalized microstate scaling, we result to a generalized entropy expression, which applied in systems with boundaries yields a generalized holographic-like area-law scaling with two exponents. Hence, incorporating it within the gravity-thermodynamics framework, we result to a modified cosmological scenario with additional terms, which eventually give rise to an effective dark energy sector. We extract analytical expressions for the dark energy density and equation-of-state parameters, and we show that the Universe experiences the usual thermal history, with the sequence of matter and dark-energy eras. Additionally, depending on the values of the entropic exponents, the dark energy can be quintessence-like, phantom-like or experience the phantom-divide crossing during its evolution, ultimately stabilizing at the cosmological constant value in the asymptotic far future, a behavior richer than other entropic modified cosmologies.