Cosmological models in Weyl geometrical scalar-tensor theory

Abstract

We investigate cosmological models in a recently proposed geometrical theory of gravity, in which the scalar field appears as part of the space-time geometry. We extend the previous theory to include a scalar potential in the action. We solve the vacuum field equations for different choices of the scalar potential and give a detailed analysis of the solutions. We show that in some cases a cosmological scenario is found that seems to suggest the appearance of a geometric phase transition. We build a toy model, in which the accelerated expansion of the early universe is driven by pure geometry.

16 pages, 19 figures

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• An Invariant Approach to Weyl's unified field theory
• On the Cauchy Problem for Weyl-Geometric Scalar-Tensor Theories of Gravity
• Quantum cosmology in an anisotropic n-dimensional universe
• Dynamical analysis and cosmological evolution in Weyl integrable gravity
• The unexpected resurgence of Weyl geometry in late 20-th century physics
• On the physical interpretation of non-metricity in Brans-Dicke gravity
• Weyl frames and canonical transformations in geometrical scalar-tensor theories of gravity
• Gravitational Waves Emission in Quadratic Gravity: longitudinal modes, angular momentum emission, and positivity of the radiated power
• A brief note on the limit $\omega \to \infty$ in Weyl geometrical scalar-tensor theory
• Probing Primordial Symmetry Breaking with Cosmic Microwave Background Anisotropy
• Cosmological Solutions for the Geometrical Scalar-Tensor with the Potential Determined by the Noether Symmetry Approach
• Dark energy from a geometrical gauge scalar-tensor theory of gravity
• Homogeneous Cosmological Models in Weyl's Geometrical Scalar-Tensor Theory
• $f(R)$ gravity with broken Weyl gauge symmetry, cosmological backreaction, and its effects on CMB anisotropy
• Geometric formulation of $k$-essence and late-time acceleration