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We have previously presented a reconstruction of Horndeski scalar-tensor theories from linear cosmological observables. It includes free nonlinear terms which can be added onto the reconstructed covariant theory without affecting the…

This article is intended to review the recent developments in the Horndeski theory and its generalization, which provide us with a systematic understanding of scalar-tensor theories of gravity as well as a powerful tool to explore…

In order to have singularity-free solutions at the beginning of the Universe, we need to violate the null energy condition. In the general class of Horndeski gravity, there are healthy NEC-violating solutions, which however are plagued with…

Recently we have derived a set of mapping relations that enables the reconstruction of the family of Horndeski scalar-tensor theories which reproduce the background dynamics and linear perturbations of a given set of effective field theory…

In this paper, we investigate a class of Horndeski scalar-tensor theory of gravity for warm inflation. We present some models where the early-time acceleration is realized in the weak and in the strong dissipation regime. Cosmological…

Linear cosmological perturbations of a large class of modified gravity and dark energy models can be unified in the effective field theory of cosmic acceleration, encompassing Horndeski scalar-tensor theories and beyond. The fully available…

Teleparallel gravity is a modified theory of gravity for which the Ricci scalar $R$ of the underlying geometry in the action is replaced by an arbitrary functional form of torsion scalar $T$. In doing so, cosmology in $% f(T)$ gravity…

When faced with two nigh intractable problems in cosmology -- how to remove the original cosmological constant problem and how to parametrize modified gravity to explain current cosmic acceleration -- we can make progress by counterposing…

A decoupled system of hyperbolic partial differential equations for linear perturbations around any spatially flat FRW universe is obtained for a wide class of perturbations. The considered perturbing energy momentum-tensors can be…

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…

Determining the active screening mechanism from a general scalar-tensor Lagrangian remains a challenging problem. As a diagnostic tool, we present a systematic study of nonlinear cosmological perturbations in luminal Horndeski theories.…

Horndeski gravity is the most general scalar-tensor theory with one scalar field leading to second-order Euler-Lagrange field equations for the metric and scalar field, and it is based on Riemannian geometry. In this paper, we formulate an…

In this paper, we show how the proper choice of gauge is critical in analyzing the stability of non-singular cosmological bounce solutions based on Horndeski theories. We show that it is possible to construct non-singular cosmological…

We study how the Vainshtein mechanism operates in the most general scalar-tensor theories with second-order equations of motion. The field equations of motion, which can be also applicable to most of other screening scenarios proposed in…

Teleparallel geometry offers a platform on which to build up theories of gravity where torsion rather than curvature mediates gravitational interaction. The teleparallel analogue of Horndeski gravity is an approach to teleparallel geometry…

We extend to the Horndeski realm the irreversible thermodynamics description of gravity previously studied in "first generation" scalar-tensor theories. We identify a subclass of Horndeski theories as an out-of--equilibrium state, while…

This thesis investigates modified teleparallel gravity models with a scalar field and teleparallel boundary terms, focusing on their cosmological implications for late-time cosmic acceleration. Teleparallel gravity, is an alternative to…

In scalar-tensor Horndeski theories, nonsingular cosmological models - bounce and genesis - are problematic because of potential ghost and/or gradient instabilities. One way to get around this obstacle is to send the effective Planck mass…

The galilean genesis scenario is an alternative to inflation in which the universe starts expanding from Minkowski in the asymptotic past by violating the null energy condition stably. Several concrete models of galilean genesis have been…

This thesis investigates the characteristics of modified teleparallel gravity models that incorporate a scalar field and a trace of the energy-momentum tensor, with particular attention to their cosmological effects, especially regarding…