Recently, all duality invariant α -corrections to the massless NS-NS sector of string theory on time-dependent backgrounds were classified and the form of their contribution to the action were calculated. In this paper we introduce matter sources in the resulting equations of motion in an O(d, d) covariant way. We show that either starting with the corrected equations and sourcing them with matter or considering corrections to the matter sourced lowest order equations give the same set of equations that defines string cosmology to all orders in α . We also discuss perturbative and non-perturbative de Sitter solutions including matter, and explicitly show that de Sitter solutions are allowed non-perturbatively. *

We provide further evidence to support the fact that a four-dimensional effective field theory description with de Sitter isometries in IIB string theory, overcoming the no-go and the swampland criteria, can only exist if de Sitter space is realized as a Glauber-Sudarshan state. We show here that this result is independent of the choice of de Sitter slicings. The Glauber-Sudarshan state, constructed by shifting the interacting vacuum in the M-theory uplift of the scenario, differs from a standard coherent state in QFT in the sense that the shape and size of the state changes with respect to time, implying changes in the graviton and the flux quanta. Despite this, the expectation values of the graviton and flux operators in such a state reproduce the exact de Sitter background, as long as we are within the temporal bound set by the onset of the strong coupling in the dual type IIA side, and satisfy the corresponding Schwinger-Dyson's equations in the presence of hierarchically controlled perturbative and non-perturbative quantum corrections. Additionally, we provide a detailed study of the fluxes supporting the Glauber-Sudarshan state in the M-theory uplift of the IIB scenario. We show explicitly how the Bianchi identities, anomaly cancellation and flux quantization conditions, along-with the constraints from the Schwinger-Dyson's equations, conspire together to provide the necessary temporal dependences to support such a state in full M-theory. We also discuss how our analysis points towards a surprising connection to the four-dimensional null energy condition, for a Friedman-Lemaitre-Robertson-Walker state in the IIB side, as a consistency condition for the existence of an effective field theory description in M-theory. Lord Carnarvon: Can you see anything? Howard Carter: Yes ..... wonderful things! − Reply that Howard Carter gave to Lord Carnarvon just before entering the main annexe of the tomb of Tut.Ankh.Amen on Sunday, November 26, 1922 around 4:00 pm. Taken from [1].

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We review O(d, d) Covariant String Cosmology to all orders in α in the presence of matter and study its solutions. We show that the perturbative analysis for a constant dilaton in the absence of a dilatonic charge does not lead to a time-independet equation of state. Meanwhile, the non-perturbative equations of motion allow de Sitter solutions in the String frame parametrized by the equation of state and the dilatonic charge. Among this set of solutions, we show that a cosmological constant equation of state implies a de Sitter solution both in String and Einstein frames while a winding equation of state implies a de Sitter solution in the former and a static phase in the latter. We also consider the stability of these solutions under homogeneous linear perturbations and show that they are not unstable, therefore defining viable cosmological scenarios.

In a recent paper we developed a string cosmology background from classical string geometry. Here, we show that this background yields a solution to the size and horizon problems of Standard Big Bang cosmology while remaining compatible with the Transplanckian Censorship Conjecture. We also take a first look at the evolution of cosmological perturbations in this model.