A validation of the cosmic distance duality (CDD) relation, h() ( ) () () z zdz dz º+ = 1 A L 1 2 , coupling the
luminosity (dL) and angular-diameter (dA) distances, is crucial because its violation would require exotic new
physics. We present a model-independent test of the CDD, based on strong lensing and a reconstruction of the H II
galaxy Hubble diagram using Gaussian processes, to confirm the validity of the CDD at a very high level
of confidence. Using parameterizations h( )z z = +1 h0 and h( )z zz =+ + 1 h h 1 2
2, our best-fit results are
h = -
+ 0.0147 0 0.066
0.056, and h = -
+ 0.1091 1 0.1568
0.1680 and h = - -
+ 0.0603 2 0.0988
0.0999, respectively. In spite of these strong
constraints, however, we also point out that the analysis of strong lensing using a simplified single isothermal
sphere (SIS) model for the lens produces some irreducible scatter in the inferred CDD data. The use of an extended
SIS approximation, with a power-law density structure, yields very similar results, but does not lessen the scatter
due to its larger number of free parameters, which weakens the best-fit constraints. Future work with these strong
lenses should therefore be based on more detailed ray-tracing calculations to determine the mass distribution more
Quasars at high redshift provide direct information on the mass growth of supermassive black holes (SMBHs) and, in turn, yield important clues about how the universe evolved since the first (Pop III) stars started forming. Yet even basic questions regarding the seeds of these objects and their growth mechanism remain unanswered. The anticipated launch of eROSITA and ATHENA is expected to facilitate observations of high-redshift quasars needed to resolve these issues. In this paper, we compare accretion-based SMBH growth in the concordance Lambda CDM model with that in the alternative Friedmann-Robertson-Walker cosmology known as the R-h = ct universe. Previous work has shown that the timeline predicted by the latter can account for the origin and growth of the greater than or similar to 10(9) M-circle dot highest redshift quasars better than that of the standard model. Here, we significantly advance this comparison by determining the soft X-ray flux that would be observed for Eddington-limited accretion growth as a function of redshift in both cosmologies. Our results indicate that a clear difference emerges between the two in terms of the number of detectable quasars at redshift z greater than or similar to 7, raising the expectation that the next decade will provide the observational data needed to discriminate between these two models based on the number of detected high-redshift quasar progenitors. For example, while the upcoming ATHENA mission is expected to detect similar to 0.16 (i.e., essentially zero) quasars at z similar to 7 in R-h = ct, it should detect similar to 160 in Lambda CDM-a quantitatively compelling difference.
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