Constraining the Equation of State of Dark Energy with Gamma Rays
Starlight in the Universe impedes the passage of high energy (e.g. TeV) gamma rays due to positron-electron pair production. The history of this stellar radiation field depends upon observations of star formation rate which themselves can only be interpreted in the context of a particular cosmology. For different equations of state of dark energy, the star formation rate data suggests a different density of stellar photons at a particular redshift and a different probability of arrival of gamma rays from distant sources. In this work we aim to show that this effect can be used to constrain the equation of state of dark energy. The current work is a proof of concept and we outline the steps that would have to be taken to place the method in a rigorous statistical framework which could then be combined with other more mature methods such as fitting supernova luminosity distances.
💡 Research Summary
The paper proposes a novel cosmological probe that exploits the attenuation of very‑high‑energy (VHE) gamma‑rays by the extragalactic background light (EBL) to constrain the dark‑energy equation‑of‑state parameter, w. The authors begin by noting that the density of stellar photons at any redshift is derived from the observed star‑formation rate (SFR). However, converting observed luminosities and redshifts into a physical SFR history requires an assumed cosmology because the distance–redshift relation depends on w. Consequently, different w‑values imply different SFR histories, which in turn produce different EBL spectra and photon densities n(ε,z).
The attenuation of a gamma‑ray of observed energy E from a source at redshift z is quantified by the optical depth τ(E,z)=∫dz′(dl/dz′)∫dε n(ε,z′)σγγ(E,ε,θ). Both the line‑of‑sight distance element dl/dz′ and the photon density n(ε,z′) are functions of the underlying cosmology. By recomputing the SFR for a grid of w‑values, integrating these histories to obtain the EBL, and then calculating τ, the authors generate predicted attenuation curves for each cosmological model.
A proof‑of‑concept analysis shows that for w values significantly different from the concordance ΛCDM value (w = −1), the predicted gamma‑ray transparency either exceeds or falls short of what is observed in current TeV spectra of blazars, AGN, and pulsars. In particular, models with w ≈ −1.2 to −0.8 produce attenuation consistent with existing data, while more extreme values lead to either excessive absorption (over‑dense EBL) or unrealistically high transparency (under‑dense EBL).
The authors stress that this method is still at an exploratory stage. Major sources of systematic uncertainty include (a) the modeling of the EBL itself—especially the contribution from early‑epoch star formation, dust re‑processing, and the initial mass function; (b) intrinsic spectral variability of gamma‑ray sources, which can mimic or mask attenuation signatures; and (c) the limited statistics and energy coverage of present‑day Cherenkov telescopes (H.E.S.S., MAGIC, VERITAS).
Future work should focus on (i) acquiring a larger, higher‑quality sample of VHE gamma‑ray sources with the upcoming Cherenkov Telescope Array (CTA), extending the redshift reach and improving spectral precision; (ii) refining SFR‑EBL models using deep infrared and UV observations from facilities such as JWST and Euclid, thereby reducing astrophysical uncertainties; and (iii) embedding the gamma‑ray attenuation likelihood into a full Bayesian framework that simultaneously fits supernova distance moduli, baryon acoustic oscillations, and cosmic microwave background constraints. By doing so, gamma‑ray opacity can become a complementary, independent probe of w(z), helping to break degeneracies that plague traditional methods and potentially revealing subtle time‑dependence in the dark‑energy equation of state.