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In the present article, which is the first part of a work in three parts, we build an equation of quantum gravity. This equation is tensorial, is equivalent to general relativity in vacuum, but differs completely from general relativity…
Maxwell equations and the equations of General Relativity are scale invariant in empty space. The presence of charge or currents in electromagnetism or the presence of matter in cosmology are preventing scale invariance. The question arises…
The dipole anomaly in the power spectrum of CMB may indicate that the Lorentz boost invarianc is violated at cosmic scale. We assume that the Lorentz symmetry is violated partly from the scale of galaxy. We employ the symmetry of very…
We showed that the principle of nongravitating vacuum energy, when formulated in the first order formalism, solves the cosmological constant problem. The most appealing formulation of the theory displays a local symmetry associated with the…
We revisit the evolution of the scale factor in a flat FRW spacetime with a new generalized decay rule for the dynamic $\Lambda$-term under modified theories of gravity. It analyses certain cosmological parameters and examines their…
We examine some Weyl invariant cosmological models in the framework of generalized dilaton gravity, in which the action is made of a set of $N$ conformally coupled scalar fields. It will be shown that when the FRW ansatz for the spacetime…
We generalize the scale invariant gravity by allowing a negative kinetic energy term for the classical scalar field. This gives birth to a new scalar-tensor theory of gravity, in which the scalar field is in fact an auxiliary field. For a…
We introduce a new model of background independent physics in which the degrees of freedom live on a complete graph and the physics is invariant under the permutations of all the points. We argue that the model has a low energy phase in…
Thermodynamics provides a useful interpretation of scalar-tensor gravity, in which the effective imperfect fluid admitted by the nonminimal coupling features a temperature that is associated with the departure from general relativity.…
This article explores the cosmological scenario of the universe in the context of the $f(T)$ power law model, where $T$ represent the torsion scalar. To obtain the deterministic solution of the field equations we parametrized the effective…
We examine the relation between the dynamics of Lema\^{\i}tre-Tolman-Bondi (LTB) dust models (with and without $\Lambda$) and the dynamics of dust perturbations in two of the more familiar formalisms used in cosmology: the metric based…
We investigate the phase-space of a flat FRW universe including both a scalar field, $\phi,$ coupled to matter, and radiation. The model is inspired in scalar-tensor theories of gravity, and thus, related with $F(R)$ theories through…
This study investigates the cosmological dynamics of an accelerating universe within the framework of teleparallel gravity using an exponential f(T) functional form. To obtain exact cosmological solutions, a hybrid scale factor is employed…
We investigate consequences of an ultraviolet fixed point in quantum gravity for the cosmological constant. For this purpose we perform dimensional reduction of a general dilatation symmetric effective action $\Gamma$ in dimension $d>4$ to…
The cosmological scalar perturbations of standard matter are investigated in the context of extended teleparallel $f(T)$ gravity theories using the $1+3$ covariant formalism. After a review of the background, gravitational field equations…
We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in…
We investigate whether the extra scalar degree of freedom that arises in the second connection class of scalar-tensor non-metricity gravity can accurately replicate and potentially enrich the cosmic expansion history. Focusing on a…
We present a broad and simple class of scalar-tensor scenarios that successfully realize dynamical damping of the effective cosmological constant, therefore providing a viable dynamical solution to the fine-tuning or "old" cosmological…
A scalar-tensor theory of gravity is formulated in which $G$ and particle masses are allowed to vary. The theory yields a globally static cosmological model with no evolutionary timescales, no cosmological coincidences, and no flatness and…
A genuine dilaton $\sigma$ allows scales to exist even in the limit of exact conformal invariance. In gauge theories, these may occur at an infrared fixed point (IRFP) $\alpha_{\text{IR}}$ through dimensional transmutation. These large…