Quintessential Inflation: A Tale of Emergent and Broken Symmetries

Quintessential inflation provides a unified description of inflation and dark energy in terms of a single scalar degree of freedom, the cosmon. We present here a comprehensive overview of this appealing paradigm, highlighting its key ingredients and keeping a reasonable and homogeneous level of details. After summarizing the cosmological evolution in a simple canonical case, we discuss how quintessential inflation can be embedded in a more general scalar-tensor formulation and its relation to variable gravity scenarios. Particular emphasis is placed on the role played by symmetries. In particular, we discuss the evolution of the cosmon field in terms of ultraviolet and infrared fixed points potentially appearing in quantum gravity formulations and leading to the emergence of scale invariance in the early and late Universe. The second part of the review is devoted to the exploration of the phenomenological consequences of the paradigm. First, we discuss how direct couplings of the cosmon field to matter may affect neutrinos masses and primordial structure formation. Second, we describe how Ricci-mediated couplings to spectator fields can trigger the spontaneous symmetry breaking of internal symmetries such as, but not limited to, global U(1) or Z2 symmetries, and affect a large variety of physical processes in the early Universe.

Dark Energy and Dark Matter Interaction: Kernels of Volterra Type and Coincidence Problem

We study a new exactly solvable model of coupling of the Dark Energy and Dark Matter, in the framework of which the kernel of non-gravitational interaction is presented by the integral Volterra-type operator well-known in the classical theory of fading memory. Exact solutions of this isotropic homogeneous cosmological model were classified with respect to the sign of the discriminant of the cubic characteristic polynomial associated with the key equation of the model. Energy-density scalars of the Dark Energy and Dark Matter, the Hubble function and acceleration parameter are presented explicitly; the scale factor is found in quadratures. Asymptotic analysis of the exact solutions has shown that the Big Rip, Little Rip, Pseudo Rip regimes can be realized with the specific choice of guiding parameters of the model. We show that the Coincidence problem can be solved if we consider the memory effect associated with the interactions in the Dark Sector of the universe.

Dark matter and dark energy interactions: theoretical challenges, cosmological implications and observational signatures

Models where dark matter and dark energy interact with each other have been proposed to solve the coincidence problem. We review the motivations underlying the need to introduce such interaction, its influence on the background dynamics and how it modifies the evolution of linear perturbations. We test models using the most recent observational data and we find that the interaction is compatible with the current astronomical and cosmological data. Finally, we describe the forthcoming data sets from current and future facilities that are being constructed or designed that will allow a clearer understanding of the physics of the dark sector.