Alex Giacomini

We investigate the evolution of anisotropies in Bianchi I spacetimes within the framework of the 4D Einstein-Gauss-Bonnet scalar field theory. The field equations are formulated using dimensionless variables, and the asymptotic dynamics are studied through a combination of analytical and numerical techniques. For the locally rotationally symmetric case, we analytically explore the stationary points of the field equations. The analysis reveals the existence of accelerating solutions in which the scalar field and the Gauss-Bonnet scalar effectively play the role of a cosmological constant. As a result, both anisotropic and isotropic expanding solutions are recovered, along with the Minkowski spacetime. No scaling solutions are supported by the gravitational model. For the general anisotropic Bianchi I geometry with three distinct scale factors, we find that a class of compactified Kasner-like solutions is obtained. In addition, a new family of solutions follows, describing a two-dimensional splitting of the background geometry. This behavior is similar to the previously observed pure Einstein-Gauss-Bonnet theory in higher-dimensional spacetimes.

We investigate the evolution of cosmological anisotropies within the framework of $f\left(G\right)$-gravity. Specifically, we consider a locally rotationally symmetric geometry in four-dimensional spacetime that describes the Bianchi I, Bianchi III, and the Kantowski-Sachs spacetimes. Within this context, we introduce a Lagrange multiplier which allows us to reformulate the geometric degrees of freedom in terms of a scalar field. The resulting theory is dynamically equivalent to an Einstein-Gauss-Bonnet scalar field model. We normalize the field equations by introducing dimensionless variables. The dynamics of our system is then explored by solving the resulting nonlinear differential equations numerically for various sets of initial conditions. Our analysis reveals the existence of two finite attractors: the Minkowski universe and an isotropic, spatially flat solution capable of describing accelerated expansion. Although de Sitter expansion may be recovered, it appears only as an unstable solution. In addition, the theory suffers from the existence of Big Rip singularities.

We investigate the evolution of anisotropies in Einstein-Gauss-Bonnet theory with a scalar field coupled to the Gauss-Bonnet term. Specifically, we examine the simplest scenario in which the scalar field lacks a kinetic term, and its kinetic contribution arises from an integration by parts of the Gauss-Bonnet scalar. We consider four- and five-dimensional anisotropic spacetimes, focusing on Bianchi I and extended Bianchi I geometries. Our study reveals that the asymptotic solutions correspond to locally symmetric spacetimes where at least two scale factors exhibit analogous behavior or, alternatively, to isotropic configurations where all scale factors evolve identically. Additionally, we discuss the effects of a cosmological constant, finding that the presence of the cosmological constant does not lead to an isotropic universe.

We investigate the evolution of anisotropies in Einstein-Gauss-Bonnet theory with a scalar field coupled to the Gauss-Bonnet term. Specifically, we examine the simplest scenario in which the scalar field lacks a kinetic term, and its kinetic contribution arises from an integration by parts of the Gauss-Bonnet scalar. We consider four- and five-dimensional anisotropic spacetimes, focusing on Bianchi I and extended Bianchi I geometries. Our study reveals that the asymptotic solutions correspond to locally symmetric spacetimes where at least two scale factors exhibit analogous behavior or, alternatively, to isotropic configurations where all scale factors evolve identically. Additionally, we discuss the effects of a cosmological constant, finding that the presence of the cosmological constant does not lead to an isotropic universe.

We explore the phase-space of homogeneous and anisotropic spacetimes within symmetric teleparallel $f(Q)$-gravity. Specifically, we consider the Kantowski-Sachs and locally rotational Bianchi III geometries to describe the physical space. By analyzing the phase-space, we reconstruct the cosmological history dictated by $f(Q)$-gravity and comment about the theory's viability. Our findings suggest that the free parameters of the connection must be constrained to eliminate nonlinear terms in the field equations. Consequently, new stationary points emerge, rendering the theory cosmologically viable. We identify the existence of anisotropic accelerated universes, which may correspond to the pre-inflationary epoch.

We investigate the impact of conformal transformations on the physical properties of solution trajectories in nonmetricity gravity. Specifically, we explore the phase-space and reconstruct the cosmological history of a spatially flat Friedmann-Lemaître-Robertson-Walker universe within scalar-nonmetricity theory in both the Jordan and Einstein frames. A detailed analysis is conducted for three different connections defined in both the coincident and non-coincident gauges. Our findings reveal the existence of a unique one-to-one correspondence for equilibrium points in the two frames. Furthermore, we demonstrate that solutions describing accelerated universes remain invariant under the transformation that relates these conformally equivalent theories.