Taking the recently reported non-zero rotation angle of the cosmic microwave background (CMB) linear polarization β = 0.35±0.14 deg as the hint for a pseudo Nambu-Goldstone boson quintessence dark energy (DE), we study the electroweak (EW) axion quintessence DE model where the axion mass is generated by the EW instantons. We find that the observed value of β implies a non-trivial U (1) electromagnetic anomaly coefficient (cγ), once the current constraint on the DE equation of state is also taken into account. With the aid of the hypothetical high energy structure of the model inspired by the experimentally inferred cγ, the model is shown to be able to make prediction for the current equation of state (wDE,0) of the quintessence DE. This is expected to make our scenario distinguishable in comparison with the cosmological constant (w = −1) and testable in future when the error in the future measurement of wDE,0 is reduced to O(1)% level (δw = O(10 −2 )).

The acoustic peaks in the angular power spectrum of cosmic microwave background (CMB) temperature and polarization anisotropies play an important role as a probe of the nature of new relativistic particles contributing to the radiation density in the early universe, parametrized by ∆N ef f . The amplitude and phase of the acoustic oscillations provide information about whether the extra species are free-streaming particles, like neutrinos, or tightly-coupled, like the photons, during eras probed by the CMB. On the other hand, some extensions of the Standard Model produce new relativistic particles that decouple from their own non-gravitational interactions after neutrinos, but prior to photons. We study the signature of new relativistic species that decouple during this intermediate epoch. We argue that the decoupling species will cause a scale-dependent change in the amplitude and phase shift of the acoustic oscillations, different from the usual constant shifts on small scales. For intermediate decoupling times, the phase and amplitude shifts depend not only on ∆N ef f but the redshift z dec,X at which the new species decoupled. For ∆N ef f > 0.334, a Stage IV CMB experiment could determine N ef f at the percent level and z dec,X at the ∼ 10% level. For smaller values, ∆N ef f ∼ 0.1, constraints on z dec,X weaken but remain ∼ 20 − 50% for z dec,X ∼ O(10 3 − 10 4 ). As an application, we study the contributions to ∆N ef f and determine the z dec,X values for simple implementations of the so-called N naturalness model.

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We present a model in which the question about a nature of the dark energy and the recently raised Hubble tension can be addressed at once. We consider the electroweak axion in the minimal supersymmetric standard model where the axion energy density is identified with the observed dark energy. Along with this, imposing a gauged Z10 symmetry makes it possible to have a gravitino dark matter whose mass amounts to ∼ O(1) GeV. We find that the gravitino with mass ∼ O(1) GeV can be a good candidate of a decaying dark matter of which decay after recombination can reconcile discrepancy in local measurements of the Hubble expansion rate H0 and that inferred from the cosmic microwave background observation.

We present two new one-parameter families of scheme transformations and apply these to study the scheme dependence of the infrared zero in the beta function of an asymptotically free non-Abelian gauge theory up to four-loop order. Our results provide a further quantitative measure of this scheme dependence, showing that for moderate values of the gauge coupling and the parameter specifying the scheme transformation, this dependence is relatively mild. We also remark on a generalized multi-parameter family of rational scheme transformations.