Break the primordial-non-Gaussianity–energy-injection degeneracy

Determine the individual constraints on scale-dependent primordial non-Gaussianity, characterized by the parameters f_NL and n_NL, and anomalous early-Universe energy injection, characterized by alpha_inj, using broader multipole coverage to break their degeneracy in ISW–tSZ cross-correlation measurements.

Background

The analysis finds strong posterior correlations among the scale-dependent primordial non-Gaussianity parameters and the early-Universe energy-injection amplitude, particularly between f_NL and n_NL and between n_NL and alpha_inj. These correlations indicate that the current ISW–tSZ data do not independently determine the scale dependence of primordial non-Gaussianity and the amplitude of energy injection.

The authors identify broader multipole coverage from future surveys as the means of resolving this issue. Establishing separate constraints would improve the interpretation of the ISW–tSZ signal and distinguish primordial mode coupling from energy-injection effects.

References

Most notably, the PNG and energy injection parameters exhibit tight couplings: $f_{\rm NL}$ and $n_{\rm NL}$ are positively correlated ($r \simeq +0.92$), as well as $n_{\rm NL}$ and $\alpha_{\rm inj}$ ($r \simeq +0.93$), indicating that current data may not give individual constraints on scale-dependent primordial non-Gaussianity and anomalous energy injection. A broader multipole coverage from future surveys is required to break the parameter degeneracy.

— Constraining primordial non-Gaussianity and energy injection with the thermal Sunyaev-Zeldovich effect and integrated Sachs-Wolfe effect cross-correlation  (2608.25809 - Ibitoye et al., 26 Aug 2026) in Section 3, Results and Discussion