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The status of multifractional theories is reviewed using comparative tables. Theoretical foundations, classical matter and gravity dynamics, cosmology and experimental constraints are summarized and the application of the multifractional…
Using the singularity analysis, we investigate the integrability properties and existence of analytic solutions in $f\left( R\right)$-cosmology. Specifically, for some power-law $f\left( R\right) $-theories of particular interest, we apply…
We study four-dimensional gravity theories that are rendered renormalisable by the inclusion of curvature-squared terms to the usual Einstein action with cosmological constant. By choosing the parameters appropriately, the massive scalar…
We use a dynamical system approach to study the cosmological viability of $f(R,\mathcal{G})$ gravity theories. The method consists of formulating the evolution equations as an autonomous system of ODEs, using suitable variables. The…
There are several approaches to extend General Relativity in order to explain the phenomena related to the Dark Matter and Dark Energy. These theories, generally called Extended Theories of Gravity, can be tested using observations coming…
General relativity becomes vastly simpler in three spacetime dimensions: all vacuum solutions have constant curvature, and the moduli space of solutions can be almost completely characterized. As a result, this lower dimensional setting…
It is argued that the solution space of the equation determining the class of $f(R)$ theories which admit an Einstein static universe should be broadened by including the algebraic roots.
We consider perturbative modifications of the Friedmann equations in terms of energy density corresponding to modified theories of gravity proposed as an alternative route to comply with the observed accelerated expansion of the universe.…
A bouncing universe is a viable candidate to solve the initial singularity problem. Here we consider bouncing solutions in the context of $f(R,\mathcal{G})$ gravity by using an order reduction technique which allows one to find solutions…
The issues of quintessence and cosmic acceleration can be discussed in the framework of higher order curvature and torsion theories of gravity. We can define effective pressure and energy density directly connected to the curvature or to…
We review the recent literature on modified theories of gravity in the Palatini approach. After discussing the motivations that lead to consider alternatives to Einstein's theory and to treat the metric and the connection as independent…
Modifications of general relativity provide an alternative explanation to dark energy for the observed acceleration of the universe. We review recent developments in modified gravity theories, focusing on higher dimensional approaches and…
This study explores the gravitational collapse of a massless scalar field within Quadratic Gravity treated as a dimension-four operator Effective Field Theory extension to General Relativity. The additional degrees of freedom associated…
Gravitation governs the expansion and fate of the universe, and the growth of large scale structure within it, but has not been tested in detail on these cosmic scales. The observed acceleration of the expansion may provide signs of…
A general approach to find out exact cosmological solutions in f(R)-gravity is discussed. Instead of taking into account phenomenological models, we assume, as a physical criterium, the existence of Noether symmetries in the cosmological…
Cosmological perturbation theory is a key tool to study the universe. The linear or first order theory is well understood, however, developing and applying the theory beyond linear order is at the cutting edge of current research in…
Modifications of Einstein's theory of gravitation have been extensively considered in the past years, in connection to both cosmology and quantum gravity. Higher-curvature and higher-derivative gravity theories constitute the main examples…
We establish a well-posedness theory for the f(R) theory of modified gravity, which is a generalization of Einstein's theory of gravitation. The scalar curvature R of the spacetime, which arises in the integrand of the Einstein-Hilbert…
We investigate the f(R) theory of gravity with broken diffeomorphism due to the change of the coefficient in front of the total divergence term in the (3+1)-decomposition of the scalar curvature. We perform the canonical analysis of this…
{\em Quantum Fourier analysis} is a new subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum…