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Register a new userClassical, quantum, and phenomenological aspects of dark energy models
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Houri Ziaeepour
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The origin of accelerating expansion of the Universe is one the biggest conundrum of fundamental physics. In this paper we review vacuum energy issues as the origin of accelerating expansion - generally called dark energy - and give an overview of alternatives, which a large number of them can be classified as interacting scalar field models. We review properties of these models both as classical field and as quantum condensates in the framework of non-equilibrium quantum field theory. Finally, we review phenomenology of models with the goal of discriminating between them.
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We describe a new class of dark energy (DE) models which behave like cosmological trackers at early times. These models are based on the $alpha$-attractor set of potentials, originally discussed in the context of inflation. The new models allow the current acceleration of the universe to be reached from a wide class of initial conditions. Prominent examples of this class of models are the potentials $cothvarphi$ and $coshvarphi$. A remarkable feature of this new class of models is that they lead to large enough negative values of the equation of state at the present epoch, consistent with the observations of accelerated expansion of the universe, from a very large initial basin of attraction. They therefore avoid the fine tuning problem which afflicts many models of DE.
The thermal history of a large class of running vacuum models in which the effective cosmological term is described by a truncated power series of the Hubble rate, whose dominant term is $Lambda (H) propto H^{n+2}$, is discussed in detail. Specifically, by assuming that the ultra-relativistic particles produced by the vacuum decay emerge into space-time in such a way that its energy density $rho_r propto T^{4}$, the temperature evolution law and the increasing entropy function are analytically calculated. For the whole class of vacuum models explored here we findthat the primeval value of the comoving radiation entropy density (associated to effectively massless particles) starts from zero and evolves extremely fast until reaching a maximum near the end of the vacuum decay phase, where it saturates. The late time conservation of the radiation entropy during the adiabatic FRW phase also guarantees that the whole class of running vacuum models predicts thesame correct value of the present day entropy, $S_{0} sim 10^{87-88}$ (in natural units), independently of the initial conditions. In addition, by assuming Gibbons-Hawking temperature as an initial condition, we find that the ratio between the late time and primordial vacuum energy densities is in agreement with naive estimates from quantum field theory, namely, $rho_{Lambda 0}/rho_{Lambda I} sim10^{-123}$. Such results are independent on the power $n$ and suggests that the observed Universe may evolve smoothly between two extreme, unstable, nonsingular de Sitter phases.
We consider cosmological models with a dynamical dark energy field, and study the presence of three types of commonly found instabilities, namely ghost (when fields have negative kinetic energy), gradient (negative momentum squared) and tachyon (negative mass squared). In particular, we study the linear scalar perturbations of theories with two interacting scalar fields as a proxy for a dark energy and matter fields, and explicitly show how canonical transformations relate these three types of instabilities with each other. We generically show that low-energy ghosts are equivalent to tachyonic instabilities, and that high-energy ghosts are equivalent to gradient instabilities. Via examples we make evident the fact that whenever one of these fields exhibits an instability then the entire physical system becomes unstable, with an unbounded Hamiltonian. Finally, we discuss the role of interactions between the two fields, and show that whereas most of the time interactions will not determine whether an instability is present or not, they may affect the timescale of the instability. We also find exceptional cases in which the two fields are ghosts and hence the physical system is seemingly unstable, but the presence of interactions actually lead to stable solutions. These results are very important for assessing the viability of dark energy models that may exhibit ghost, gradient or tachyonic modes.
Recently, Kallosh and Linde have drawn attention to a new family of superconformal inflationary potentials, subsequently called $alpha$-attractors. The $alpha$-attractor family can interpolate between a large class of inflationary models. It also has an important theoretical underpinning within the framework of supergravity. We demonstrate that the $alpha$-attractors have an even wider appeal since they may describe dark matter and perhaps even dark energy. The dark matter associated with the $alpha$-attractors, which we call $alpha$-dark matter ($alpha$DM), shares many of the attractive features of fuzzy dark matter, with $V(varphi) = frac{1}{2}m^2varphi^2$, while having none of its drawbacks. Like fuzzy dark matter, $alpha$DM can have a large Jeans length which could resolve the cusp-core and substructure problems faced by standard cold dark matter. $alpha$DM also has an appealing tracker property which enables it to converge to the late-time dark matter asymptote, $langle wrangle simeq 0$, from a wide range of initial conditions. It thus avoids the enormous fine-tuning problems faced by the $m^2varphi^2$ potential in describing dark matter.
Studying the effects of dark energy and modified gravity on cosmological scales has led to a great number of physical models being developed. The effective field theory (EFT) of cosmic acceleration allows an efficient exploration of this large model space, usually carried out on a phenomenological basis. However, constraints on such parametrized EFT coefficients cannot be trivially connected to fundamental covariant theories. In this paper we reconstruct the class of covariant Horndeski scalar-tensor theories that reproduce the same background dynamics and linear perturbations as a given EFT action. One can use this reconstruction to interpret constraints on parametrized EFT coefficients in terms of viable covariant Horndeski theories. We demonstrate this method with a number of well-known models and discuss a range of future applications.
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