The Generalized Uncertainty Principle (GUP) has emerged in numerous attempts to a theory of quantum gravity and predicts the existence of a minimum length in Nature. In this work, we consider two cosmological models arising from Friedmann equations modified by the GUP (in its linear and quadratic formulations) and compare them with observational data. Our aim is to derive constraints on the GUP parameter and discuss the viability and physical implications of such models. We find for the parameter in the quadratic formulation the constraint $$\alpha ^{2}_{Q}<10^{59}$$ α Q 2 < 10 59 (tighter than most of those obtained in an astrophysical context) while the linear formulation does not appear compatible with present cosmological data. Our analysis highlights the powerful role of high-precision cosmological probes in the realm of quantum gravity phenomenology.

A new thermodynamics of scalar-tensor gravity is applied to spatially homogeneous and isotropic cosmologies in this class of theories and tested on analytical solutions. A forever-expanding universe approaches the Einstein “state of equilibrium” with zero effective temperature at late times and departs from it near spacetime singularities. “Cooling” by expansion and “heating” by singularities compete near the Big Rip, where it is found that the effective temperature diverges in the case of a conformally coupled scalar field.

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We refine and slightly enlarge the recently proposed first-order thermodynamics of scalar-tensor gravity to include gravitational scalar fields with timelike and past-directed gradients. The implications and subtleties arising in this situation are discussed and an exact cosmological solution of scalar-tensor theory in first-order thermodynamics is revisited in light of these results.