There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Modified gravity theories have received increased attention lately due to combined motivation coming from high-energy physics, cosmology, and astrophysics. Among numerous alternatives to Einstein's theory of gravity, theories that include higher-order curvature invariants, and specifically the particular class of $f(R)$ theories, have a long history. In the last five years there has been a new stimulus for their study, leading to a number of interesting results. Here $f(R)$ theories of gravity are reviewed in an attempt to comprehensively present their most important aspects and cover the largest possible portion of the relevant literature. All known formalisms are presented---metric, Palatini, and metric affine---and the following topics are discussed: motivation; actions, field equations, and theoretical aspects; equivalence with other theories; cosmological aspects and constraints; viability criteria; and astrophysical applications.

f ( R ) theories of gravity

The task of quantizing general relativity raises serious questions about the meaning of the present formulation and interpretation of quantum mechanics when applied to so fundamental a structure as the space-time geometry itself. This paper seeks to clarify the foundations of quantum mechanics. It presents a reformulation of quantum theory in a form believed suitable for application to general relativity. The aim is not to deny or contradict the conventional formulation of quantum theory, which has demonstrated its usefulness in an overwhelming variety of problems, but rather to supply a new, more general and complete formulation, from which the conventional interpretation can be deduced. The relationship of this new formulation to the older formulation is therefore that of a metatheory to a theory, that is, it is an underlying theory in which the nature and consistency, as well as the realm of applicability, of the older theory can be investigated and clarified.

"relative State" Formulation of Quantum Mechanics

Modified gravity theories on a nutshell: Inflation, bounce and late-time evolution

Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics

We review the general features of nonsingular universes ({\em ie} those that go from an era of accelerated collapse to an expanding era without displaying a singularity) as well as cyclic universes We discuss the mechanisms behind the bounce, and analyze examples of solutions that implement these mechanisms Observational consequences of such regular cosmologies are also considered, with emphasis in the behavior of the perturbations

Bouncing Cosmologies

We analyze the propagation of light in the context of nonlinear electrodynamics, as it occurs in modified QED vacua. We show that the corresponding characteristic equation can be described in terms of a modification of the effective geometry of the underlying spacetime structure. We present the general form for this effective geometry and exhibit some new consequences that result from such an approach.

Geometrical aspects of light propagation in nonlinear electrodynamics

It is shown that the addition of a nonlinear term to the Lagrangian of the electromagnetic field yields a fluid with an asymptotically super-negative equation of state, causing an accelerated expansion of the Universe. Some general properties of nonlinear electromagnetism in cosmology are also discussed.

https://arxiv.org/pdf/astro-ph/0312093.pdf

Nonlinear electrodynamics and the acceleration of the Universe

Maxwell electrodynamics, considered as a source of the classical Einstein field equations, leads to the singular isotropic Friedmann solutions. We show that this singular behavior does not occur for a class of nonlinear generalizations of the electromagnetic theory. A mathematical toy model is proposed for which the analytical nonsingular extension of FRW solutions is obtained.

Mario Novello

Papers

Bouncing Cosmologies

Geometrical aspects of light propagation in nonlinear electrodynamics

Nonlinear electrodynamics and the acceleration of the Universe

Nonlinear electrodynamics and FRW cosmology

Light propagation in non-linear electrodynamics