Accelerated expansion as manifestation of gravity: when Dark Energy belongs to the left

TL;DR

This thesis explores geometrical modifications of gravity as alternative explanations for the Universe's accelerated expansion, proposing new models involving nonlocal operators and the anticurvature tensor, with potential observational tests.

Contribution

It introduces a novel class of modified gravity theories based on the anticurvature tensor and analyzes their potential as sources of Dark Energy, expanding the landscape of cosmological models.

Findings

Nonlocal gravity models with $ox^{-1} R$ exhibit late-time acceleration behaviors.

Anticurvature-based gravity theories can mimic Dark Energy effects.

Predicted drift effects in gravitational lensing can test these theories.

Abstract

In order to explain the Late-times accelerated expansion of the Universe we must appeal to some form of Dark Energy. In the standard model of cosmology, the latter is interpreted as a Cosmological Constant $\Lambda$. However, for a number of reasons, a Cosmological Constant is not completely satisfactory. In this thesis we study Dark Energy models of geometrical nature, and thus a manifestation of the underlying gravitational theory. In the first part of the thesis we will review the $\Lambda$CDM model and give a brief classification of the landscape of alternative Dark Energy candidates based on the Lovelock theorem. The second part of the thesis is instead devoted to the presentation of our main results on the topic of Dark Energy. To begin with, we will report our studies about nonlocal modifications of gravity involving the differential operator $\Box^{-1}R$, with emphasis on a specific model and on the common behavior shared by this and similar theories in the late stages of the evolution of the Universe. Then we introduce a novel class of modified gravity theories based on the anticurvature tensor $A^{\mu\nu}$ (the inverse of the Ricci tensor), and assess their capability as source of Dark Energy. Finally, we will discuss a type of drift effects which we predicted in the contest of Strong Gravitational Lensing, which could be employed both to study the effective equation of state of the Universe and to constrain violations of the Equivalence Principle.