We know we don't know

A few days ago on Nature Astronomy it was published a paper by a team of italian researchers with an unequivocal title: Planck evidence for closed Universe and a possible crisis for cosmology⁽⁶⁾. We can consider it as one of the first scientific articles that seriously takes into consideration a situation that it is becoming increasingly pressing: a crisis in cosmology.
The standard cosmological model, based on cosmic inflation⁽²⁾ and on empirical constants that evaluate unknown physical quantities as dark matter and dark energy, although very well verified, has not yet passed the last step: the detection of gravitational waves in cosmic microwave background (CMB). One of the fundamental points of this model, but also of many of the surviving competing models, is the accelerated expansion of spacetime at speed greater than that of light which explains the flatness of the early universe.
This flatness emerges in particular when studying the cosmic microwave background, the residual energy of the initial expansion of spacetime. This radiation has come down to us from the point where it was produced, a little less than 14 billion years ago, crossing the whole universe. This means that in the signal detected there must also be gravitational lens effects⁽¹⁾ due to the amount of matter, usual and dark, present in the universe. These effects have long been known and calculated⁽⁴⁾ and can already be seen in the image produced by Planck⁽⁵⁾.

JMP 58, 2: quantum abstract

I'm returning with the selections from the Journal of Mathematical Physics. I'm arranging two further post for this series for the next weeks. Stay tuned!

Alhaidari, A., & Taiwo, T. (2017). Wilson-Racah quantum system Journal of Mathematical Physics, 58 (2) DOI: 10.1063/1.4975138 (arXiv)

Using a recent formulation of quantum mechanics without a potential function, we present a four-parameter system associated with the Wilson and Racah polynomials. The continuum scattering states are written in terms of the Wilson polynomials whose asymptotics give the scattering amplitude and phase shift. On the other hand, the finite number of discrete bound states are associated with the Racah polynomials.

Dorsch, F. (2017). Accumulation rate of bound states of dipoles generated by point charges in strained graphene Journal of Mathematical Physics, 58 (2) DOI: 10.1063/1.4976201 (arXiv)

We consider strained graphene, modelled by the two-dimensional massive Dirac operator, with potentials corresponding to charge distributions with vanishing total charge, non-vanishing dipole moment and finitely many point charges of subcritical coupling constants located in the graphene sheet. We show that the bound state energies accumulate exponentially fast at the edges of the spectral gap by determining the leading order of the accumulation rate.