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Register a new userDark energy, $alpha$-attractors, and large-scale structure surveys
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Over the last few years, a large family of cosmological attractor models has been discovered, which can successfully match the latest inflation-related observational data. Many of these models can also describe a small cosmological constant $Lambda$, which provides the most natural description of the present stage of the cosmological acceleration. In this paper, we study $alpha$-attractor models with dynamical dark energy, including the cosmological constant $Lambda$ as a free parameter. Predominantly, the models with $Lambda > 0$ converge to the asymptotic regime with the equation of state $w=-1$. However, there are some models with $w eq -1$, which are compatible with the current observations. In the simplest models with $Lambda = 0$, one has the tensor to scalar ratio $r=frac{12alpha}{N^2}$ and the asymptotic equation of state $w=-1+frac{2}{9alpha}$ (which in general differs from its present value). For example, in the seven disk M-theory related model with $alpha = 7/3$ one finds $r sim 10^{-2}$ and the asymptotic equation of state is $w sim -0.9$. Future observations, including large-scale structure surveys as well as B-mode detectors will test these, as well as more general models presented here. We also discuss gravitational reheating in models of quintessential inflation and argue that its investigation may be interesting from the point of view of inflationary cosmology. Such models require a much greater number of $e$-folds, and therefore predict a spectral index $n_{s}$ that can exceed the value in more conventional models by about $0.006$. This suggests a way to distinguish the conventional inflationary models from the models of quintessential inflation, even if they predict $w = -1$.
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The Planck value of the spectral index can be interpreted as $n_s = 1 - 2/N$ in terms of the number of e-foldings $N$. An appealing explanation for this phenomenological observation is provided by $alpha$-attractors: the inflationary predictions of these supergravity models are fully determined by the curvature of the Kahler manifold. We provide a novel formulation of $alpha$-attractors which only involves a single chiral superfield. Our construction involves a natural deformation of no-scale models, and employs these to construct a De Sitter plateau with an exponential fall-off. Finally, we show how analogous structures with a flat Kahler geometry arise as a singular limit of such $alpha$-scale models.
We provide a unified description of cosmological $alpha$-attractors and late-time acceleration, in excellent agreement with the latest Planck data. Our construction involves two superfields playing distinctive roles: one is the dynamical field and its evolution determines inflation and dark energy, the other is nilpotent and responsible for a landscape of vacua and supersymmetry breaking. We prove that the attractor nature of the theory is enhanced when combining the two sectors: cosmological attractors are very stable with respect to any possible value of the cosmological constant and, interestingly, to any generic coupling of the inflationary sector with the field responsible for uplifting. Finally, as related result, we show how specific couplings generate an arbitrary inflaton potential in a supergravity framework with varying Kahler curvature.
In a series of recent papers Kallosh, Linde, and collaborators have provided a unified description of single-field inflation with several types of potentials, ranging from power law to supergravity, in terms of just one parameter $alpha$. These so-called $alpha$-attractors predict a spectral index $n_{s}$ and a tensor-to-scalar ratio $r$, which are fully compatible with the latest Planck data. The only common feature of all $alpha$-attractors is a non-canonical kinetic term with a pole, and a potential analytic around the pole. In this paper, starting from the same Einstein frame with a non-canonical scalar kinetic energy, we explore the case of non-analytic potentials. We find the functional form that corresponds to quasi-scale invariant gravitational models in the Jordan frame, characterised by a universal relation between $r$ and $n_{s}$ that fits the observational data but is clearly distinct from the one of the $alpha$-attractors. It is known that the breaking of the exact classical scale-invariance in the Jordan frame can be attributed to one-loop corrections. Therefore we conclude that there exists a class of non-analytic potentials in the non-canonical Einstein frame that are physically equivalent to a class of models in the Jordan frame, with scale-invariance softly broken by one-loop quantum corrections.
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.
In this PhD thesis, we investigate generic features of inflation which are strictly related to fundamental aspects of UV-physics scenarios, such as string theory or supergravity. After a short introduction to standard and inflationary cosmology, we present our research findings. On the one hand, we show that focusing on universality properties of inflation can yield surprisingly stringent bounds on its dynamics. This approach allows us to identify the regime where the inflationary field range is uniquely determined by both the tensor-to-scalar ratio and the spectral index. Then, we derive a novel field-range bound, which is two orders of magnitude stronger than the original one derived by Lyth. On the other hand, we discuss the embedding of inflation in supergravity and prove that non-trivial hyperbolic Kahler geometries induce an attractor for the inflationary observables: the spectral tilt tends automatically to the center of the Planck dome whereas the amount of primordial gravitational waves is directly controlled by curvature of the internal manifold. We identify the origin of this attractor mechanism in the so-called $alpha$-scale supergravity model. Finally, we show how the inclusion of a nilpotent sector, allowing for a unified description of inflation and dark energy, implies an enhancement of the attractor nature of the theory. The main results of this thesis have been already published elsewhere. However, here we pay special attention to present them in a comprehensive way and provide the reader with the necessary background.
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