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State-of-the-art 19th century spectroscopy led to the discovery of quantum mechanics, and 20th century spectroscopy led to the confirmation of quantum electrodynamics. State-of-the-art 21st century astrophysical spectrographs, especially ANDES at ESO's ELT, have another opportunity to play a key role in the search for, and characterization of, the new physics which is known to be out there, waiting to be discovered. We rely on detailed simulations and forecast techniques to discuss four important examples of this point: big bang nucleosynthesis, the evolution of the cosmic microwave background temperature, tests of the universality of physical laws, and a real-time model-independent mapping of the expansion history of the universe (also known as the redshift drift). The last two are among the flagship science drivers for the ELT. We also highlight what is required for the ESO community to be able to play a meaningful role in 2030s fundamental cosmology and show that, even if ANDES only provides null results, such 'minimum guaranteed science' will be in the form of constraints on key cosmological paradigms: these are independent from, and can be competitive with, those obtained from traditional cosmological probes., Competing Interests: Conflicts of interestThe authors declare that they have no conflict of interest., (© The Author(s) 2024.)

The Standard Cosmological Model has experienced tremendous success at reproducing observational data by assuming a universe dominated by a cosmological constant and dark matter in a flat geometry. However, several studies, based on local measurements, indicate that the universe is expanding too fast, in disagreement with the Cosmic Microwave Background. Taking into account combined data from CMB, Baryon Acoustic Oscillation, and type Ia Supernovae, we show that if the mechanism behind the production of dark matter particles has at least a small non-thermal origin, one can induce larger values of the Hubble rate [Formula: see text], within the [Formula: see text]CDM, to alleviate the trouble with [Formula: see text]. In the presence of non-standard cosmology, however, we can fully reconcile CMB and local measurements and reach [Formula: see text]-74 [Formula: see text]., (© 2022. The Author(s).)

A new cosmological scenario driven by a slow rolling homogeneous scalar field whose exponential potential V(Phi) has a quadratic dependence on the field Phi in addition to the standard linear term is discussed. The derived equation of state for the field predicts a transient accelerating phase, in which the Universe was decelerated in the past, began to accelerate at redshift z approximately 1, is currently accelerated, but, finally, will return to a decelerating phase in the future. This overall dynamic behavior is profoundly different from the standard evolution of the cold dark matter model with a cosmological constant, and may alleviate some conflicts in reconciling the idea of a dark-energy-dominated universe with observables in String or M theory. Some theoretical predictions for the present scalar field plus dark matter dominated stage are confronted with cosmological observations in order to test the viability of the scenario.

We have revisited the fragment-asperity interaction model recently introduced by Sotolongo-Costa and Posadas [Phy. Rev. Lett. 92, 048501 (2004)] by considering a different definition for mean values in the context of Tsallis nonextensive statistics and introducing a scale between the earthquake energy and the size of fragment epsilon proportional to r3. The energy-distribution function (EDF) deduced in our approach is considerably different from the one obtained in the above reference. We have also tested the viability of this EDF with data from two different catalogs (in three different areas), namely, the NEIC and the Bulletin Seismic of the Revista Brasileira de Geofísica. Although both approaches provide very similar values for the nonextensive parameter , other physical quantities, e.g., energy density, differ considerably by several orders of magnitude.