The failure of testing for cosmic opacity via the distance-duality relation

Abstract

<jats:title>Abstract</jats:title> <jats:p>The distance-duality relation (DDR) between the luminosity distance DL and the angular diameter distance DA is viewed as a powerful tool for testing for the opacity of the Universe, being independent of any cosmological model. It was applied by many authors, who mostly confirm its validity and report a negligible opacity of the Universe. Nevertheless, a thorough analysis reveals that applying the DDR in cosmic opacity tests is tricky. Its applicability is strongly limited because of a non-unique interpretation of the DL data in terms of cosmic opacity and a rather low accuracy and deficient extent of currently available DA data. Moreover, authors usually assume that cosmic opacity is frequency independent and parametrize it in their tests by a prescribed phenomenological function. In this way, they only prove that cosmic opacity does not follow their assumptions. As a consequence, no convincing evidence of transparency of the universe using the DDR has so far been presented.</jats:p>

Gravitational-wave constraints on the cosmic opacity at $z\sim 5$: forecast from space gravitational-wave antenna DECIGO

“…Yet, interestingly, the HII region data favors a transition from τ = 0 at low redshift to τ > 0 at higher redshift, a behavior that is consistent with the true optical depth increasing with redshifts. Such tendency, which is different from that obtained in the framework of parameterized form, is supported by the recent works of Ma & Corasaniti (2018); Vavryčuk & Kroupa (2020) stressing the importance of cosmic-opacity test without a prescribed phenomenological function.…”

“…Considering the fact that X-ray photons can destroy dust grains instead of being absorbed, physically different processes could be detected from the observations of X-ray fluxes, instead of simple luminosity dimming due to dust absorption of low-energy photons (Draine & Hao 2002;Morgan et al 2014). Our final results showed that the cosmic opacity could attain different values for different types of D L data covering different wavelengths (optical for HII regions, SNe Ia Pantheon sample, ultraviolet for quasar sample), although such effect is still difficult to be precisely quantified (see Vavryčuk & Kroupa (2020) for a detailed discussion). Thus, the goal of our test is not just to check the resolution power of the GW data, but also to assess the performance of the combination of current and future available data in gravitational wave (GW) and electromagnetic (EM) domain.…”

“…If ǫ = 0, it means that photon number is conserved and the universe is transparent. However, one should also be aware of the disadvantage of the first method, i.e., the opacity test just proves whether the opacity follows a specific phenomenological function, as stressed in (Vavryčuk & Kroupa 2020). Therefore, in the subsequent analysis the optical depth will also be studied in individual redshift bins, in order to perform the opacity test in a more generalized way and show how decisive conclusions about the transparency of the universe can be deduced from such tests.…”

“…It should be pointed out that according to the recent analysis of Vavryčuk (2019); Vavryčuk & Kroupa (2020), the cosmic opacity could vary with frequency since it strongly depends on wavelength according to the extinction law (Mathis 1990;Li & Draine 2001;Draine 2003). The problem was recognized a long time ago (Aguirre 2000;Corasaniti 2006), with a heuristic suggestion that the luminosity distance data sets covering different frequencies might be differently sensitive to the transparency of the universe (Vavryčuk & Kroupa 2020). In our analysis, we combined the predicted future GW observations from DECIGO with three types of EM data (HII regions, SNe Ia Pantheon sample, quasar sample), and furthermore checked whether these EM data can be affected by cosmic opacity in different ways.…”

“…It is obvious that cosmic opacity assessed from the DDR is frequency independent, in contrast to most physically viable mechanisms of opacity affecting D L measurements. We recommend a detailed discussion of Vavryčuk & Kroupa (2020) concerning cosmic opacity tests based on the DDR. We will come back to this issue in the concluding section.…”