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We show how the scalar field, a candidate of quintessence, in a proposed model of the scalar-tensor theories of gravity provides a way to understand a small but nonzero cosmological constant as indicated by recent observations. A particular…

We present a class of modified-gravity theories which we call ultra-local models. We add a scalar field, with negligible kinetic terms, to the Einstein-Hilbert action. We also introduce a conformal coupling to matter. This gives rise to a…

In this work we present a brief discussion about modified and extended cosmological models using current observational tests. We show that according to these astrophysical samples based in late universe measurements, theories like $f(R)$…

The motivations for investigating a theory of gravitation based on a concept of "ether" are discussed-- a crucial point is the existence of an alternative interpretation of special relativity, named the Lorentz-Poincar\'e ether theory. The…

We present a novel solution to the cosmological constant (CC) problem that requires no fine-tunings nor anthropic reasoning. In pre-geometric gravity (PGG), spacetime emerges from the spontaneous breaking of a fundamental gauge symmetry.…

We review recent progress in the construction of modified gravity models as alternatives to dark energy as well as the development of cosmological tests of gravity. Einstein's theory of General Relativity (GR) has been tested accurately…

We discuss some of the issues which we encounter when we try to invoke the scalar-tensor theories of gravitation as a theoretical basis of quintessence. One of the advantages of appealing to these theories is that they allow us to implement…

In this review we present a thoroughly comprehensive survey of recent work on modified theories of gravity and their cosmological consequences. Amongst other things, we cover General Relativity, Scalar-Tensor, Einstein-Aether, and Bimetric…

We present an extension to the gauge-invariant formulation of the parameterized post-Newtonian (PPN) formalism, which allows its application to symmetric teleparallel gravity theories. In its original formulation, the gauge-invariant PPN…

In this work, we construct the logical framework of the Poincar\'e gauge gravity cosmology based on five postulations, and introduce the modified redshift relation within this framework. Then we solve a system with quadratic action and some…

We describe scalar-bimetric theories where the dynamics of the Universe are governed by two separate metrics, each with an Einstein-Hilbert term. In this setting, the baryonic and dark matter components of the Universe couple to metrics…

The next generation of large scale surveys will not only measure cosmological parameters within the framework of General Relativity, but will also allow for precision tests of the framework itself. At the order of linear perturbations,…

The tests of the constancy of the fundamental constants are tests of the local position invariance and thus of the equivalence principle. We summarize the various constraints that have been obtained and then describe the connection between…

Teleparallel gravity has significantly increased in popularity in recent decades, bringing attention to Einstein's other theory of gravity. In this Review, we relate this form of geometry to the broader metric-affine approach to forming…

One of the main technical obstacles in constructing a consistent theory of quantum gravity is that the metric itself defines the causal structure required for quantization. This motivates implementing quantum aspects of gravity through an…

Within the framework of scalar-non-metricity gravity, we introduce a steep potential together with a power-law coupling function and investigate whether the acceleration phases of the universe can be consistently described by this model. In…

Starting from generic quantum effects at the Planck scale M_P, we find that the renormalization group running of the cosmological constant (CC) at low energies is possible if there is a smooth decoupling of all massive particles from M_P to…

We study a Newtonian cosmological model in the context of a noncommutative space. It is shown that the trajectories of a test particle undergo modifications such that it no longer satisfies the cosmological principle. For the case of a…

We consider the cosmologies that arise in a subclass of f(R) gravity with f(R)=R+\mu ^{2n+2}/(-R)^{n} and -1<n<0 in the metric (as opposed to the Palatini) variational approach to deriving the gravitational field equations. The calculations…

We study the imprint of a massive scalar particle on cosmological correlation functions, and suggest the way to determine the mass of the newly introduced particle, which is expected to be around 10^14 GeV. After reviewing the basic theory…