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A<sc>bstract</sc> We explore the possibility that our universe’s current accelerated expansion is explained by a quintessence model with an exponential scalar potential,V=V₀e^{−λ ϕ}, keeping an eye towardsλ≥$$ \sqrt{2} $$ $\sqrt{2}$and an open universe, favorable to a string theory realisation and with no cosmological horizon. We work out the full cosmology of the model, including matter, radiation, and optionally negative spatial curvature, for allλ> 0, performing an extensive analysis of the dynamical system and its phase space. The minimal physical requirements of a past epoch of radiation domination and an accelerated expansion today lead to an upper boundλ≲$$ \sqrt{3} $$ $\sqrt{3}$, which is driven slightly up in the presence of observationally allowed spatial curvature. Cosmological solutions start universally in a kination epoch, go through radiation and matter dominated phases and enter an epoch of acceleration, which is only transient forλ>$$ \sqrt{2} $$ $\sqrt{2}$. Field distances traversed between BBN and today are sub-Planckian. We discuss possible string theory origins and phenomenological challenges, such as time variation of fundamental constants. We provide theoretical predictions for the model parameters to be fitted to data, most notably the varying dark energy equation of state parameter, in light of recent results from DES-Y5 and DESI. 

Abstract Strongly non-geodesic, or rapidly turning trajectories in multifield inflation have attracted much interest recently from both theoretical and phenomenological perspectives. Most models with large turning rates in the literature are formulated as effective field theories. In this paper we investigate rapid-turn inflation in supergravity as a first step towards understanding them in string theory. We find that large turning rates can be generated in a wide class of models, at the cost of high field space curvature. In these models, while the inflationary trajectories are stable, one Hessian eigenvalue is always tachyonic and large, in Hubble units. Thus, these models satisfy the de Sitter swampland conjecture along the inflationary trajectory. However, the high curvatures underscore the difficulty of obtaining rapid-turn inflation in realistic string-theoretical models.In passing, we revisit the η -problem in multifield slow-roll inflation and show that it does not arise, inasmuch as the inflatons, ϕ i , can all be heavier (in absolute value) that the Hubble scale: | m i | /H >1, ∀ i . 

The standard model of cosmology has provided a good phenomenological description of a wide range of observations both at astrophysical and cosmological scales for several decades. This concordance model is constructed by a universal cosmological constant and supported by a matter sector described by the standard model of particle physics and a cold dark matter contribution, as well as very early-time inflationary physics, and underpinned by gravitation through general relativity. There have always been open questions about the soundness of the foundations of the standard model. However, recent years have shown that there may also be questions from the observational sector with the emergence of differences between certain cosmological probes. In this White Paper, we identify the key objectives that need to be addressed over the coming decade together with the core science projects that aim to meet these challenges. These discordances primarily rest on the divergence in the measurement of core cosmological parameters with varying levels of statistical confidence. These possible statistical tensions may be partially accounted for by systematics in various measurements or cosmological probes but there is also a growing indication of potential new physics beyond the standard model. After reviewing the principal probes used in the measurement of cosmological parameters, as well as potential systematics, we discuss the most promising array of potential new physics that may be observable in upcoming surveys. We also discuss the growing set of novel data analysis approaches that go beyond traditional methods to test physical models. These new methods will become increasingly important in the coming years as the volume of survey data continues to increase, and as the degeneracy between predictions of different physical models grows. There are several perspectives on the divergences between the values of cosmological parameters, such as the model-independent probes in the late Universe and model-dependent measurements in the early Universe, which we cover at length. The White Paper closes with a number of recommendations for the community to focus on for the upcoming decade of observational cosmology, statistical data analysis, and fundamental physics developments