An arXiv preprint reports sharply different estimates for early-Universe energy injection depending on how the model treats that contribution. In an unbounded fit, the energy-injection amplitude αinj was −3.93, with asymmetric 68% confidence uncertainties of +1.34 and −0.99. In a second fit with a physical prior—an assumption restricting the allowed parameter values—the result became a one-sided upper limit, αinj < 1.79 at 95% confidence.
The same fits also returned different estimates of primordial non-Gaussianity, or PNG, a possible departure from Gaussian initial conditions. The fiducial scale-independent fit gave fNL = −358, with 68% uncertainties of +140 and −114, while the physical-prior run gave fNL = 86 ± 73.
Allowing PNG to vary with scale produced an amplitude of −296, with uncertainties of +173 and −157, and a running parameter nNL of 0.62, with uncertainties of +1.02 and −0.64. These scale-dependent results were quoted at 68% confidence and described as consistent with Gaussian initial conditions.
The signal behind the estimates
The study asks whether a cross-correlation between the integrated Sachs–Wolfe (ISW) and thermal Sunyaev–Zeldovich (tSZ) effects can jointly constrain primordial non-Gaussianity and early-Universe energy injection, including the standard contribution from the intergalactic medium, or IGM.
The measured spectra supplied 10 band powers spanning multipoles ℓ = 16 to 190. The theoretical cross-spectrum summed ISW, PNG and energy-injection contributions in a model with eight free parameters.
The posterior estimates came from Markov chain Monte Carlo (MCMC), a method for exploring the model’s parameter space, with Gaussian priors tied to Planck 2018 cosmological inputs.
Why the numbers move
These estimates should be read as outputs of different model choices, not as separate direct measurements. The authors interpret the negative central values in the unbounded fits as consequences of an internal degeneracy between fNL and αinj rather than detections, and regard the physical-prior results as consistent with Gaussian initial conditions and the standard thermal history.
Scale running remained largely out of reach. A change-in-fit test found that every tested nNL value from −3 to 2.5 changed the fit by less than 1, indicating insufficient leverage to constrain running.
Overall, the full MCMC best fit gave a reported statistic of 7.60/3 and a PTE of 0.055. The text says this does not indicate model failure.
Checks on the result
Alternative binning moved fNL and αinj by less than 0.3 standard deviations and changed the fit by less than 0.5. Excluding the lowest CIB-dominated bin shifted parameters by at most 0.4 standard deviations and changed the fit by about 0.7.
Reported correlations between the IGM amplitude and PNG or energy-injection parameters all had an absolute value below 0.2.
With a Planck bispectrum prior, the reported αinj uncertainty was 2.5 times smaller, without significant changes to other parameters.
A sharper test would need better data
The results are model-dependent: they come from the specified ISW–tSZ data vector, cross-spectrum components, priors and covariance assumptions. The energy-injection term is represented by a template and rescaling parameter rather than a uniquely identified physical mechanism.
A future-survey forecast projected uncertainties of σ(fNL) ≃ 5.2 and σ(αinj) ≃ 3.3 × 10−2, with a parameter correlation r ≃ 0.31. Those figures are projections for future data, not measurements made in this analysis.
The manuscript is an arXiv version 1 document dated 26 Aug 2026; journal publication and peer-review status are not reported.
Paper data and sources
Original title: Constraining primordial non-Gaussianity and energy injection with the thermal Sunyaev-Zeldovich effect and integrated Sachs-Wolfe effect cross-correlation
Authors: Ayodeji Ibitoye, Yin-Zhe Ma, Prabhakar Tiwari
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text