The Cosmic Distance Duality Relation with Strong Lensing and Gravitational Waves: An Opacity-free Test

Abstract

The cosmic distance duality relation (CDDR) is a fundamental assumption in cosmological studies. Given the redshift z, it relates luminosity distance D L with angular diameter distance D A through (1 + z) 2 D A /D L ≡ 1. Many efforts have been devoted to test the CDDR with various observational approaches. However, to the best of our knowledge, those methods are always affected by cosmic opacity which could make the CDDR violated due to the non-conservation of photon number. Such mechanism is more related with astropartical physics. In this work, to directly study the nature of space-time, i.e., to disentangle it from astropartical physics, we propose a new strategy to test the CDDR with strong lensing providing D A and gravitational wave providing D L . It is known that the propagation of gravitational wave is unaffected by cosmic opacity. We demonstrate distances from optical lensing observation are also opacity-free. These two kinds of distance measurements make it possible to test any metric theories of gravity where photons travel along null geodesics. Our results show the constraints on deviations of the CDDR will be very competitive to current techniques.

Euclid: Forecast constraints on the cosmic distance duality relation with complementary external probes

“…For such models, the combination of distance and temperature measurements as two independent probes of the same underlying mechanism shrunk the constraints on the deviation of T (z) to 0.8% (Avgoustidis et al 2016). Other possible observables to constrain possible violations of the DDR include galaxy clusters (Holanda et al 2010;Li et al 2011), the Sunyaev-Zeldovich effect (Holanda et al 2012), strong gravitational lensing (Liao et al 2016), and standard sirens from gravitational wave observations (Liao 2019;Hogg et al 2020).…”

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

“…Next, the accuracy of the D A measurements is increased 4 times to simulate uncertainties anticipated in future strong lensing data (Liao 2019). If both D L and D A are determined under no a priori assumption of the cosmological model ( Figs 5 and 7a), the data reveal the true increasing tendency in the retrieved optical depth τ(z) (Fig.…”

“…This points to the essential importance of valid D A data with z 0.6 and to the danger of reducing the analysis to data with z 0.6. If D A data are used at z 0.6 only (Cao et al 2017(Cao et al , 2018Liao 2019), the D A offset must be determined by some calibration and any information provided by the D A data is lost in this way.…”

Considering light-matter interactions in Friedmann equations

“…A modelindependent method proposed by Clarkson et al (2007) is based on reconstructing the comoving distances by Hubble parameter data and comparing with the luminosity distances (Li et al 2016;Wei & Wu 2017) or the angular diameter distances (Yu & Wang 2016). The cosmic curvature can also be constrained using strongly gravitational lensed SNe Ia (Qi et al 2019) and using lensing time delays and gravitational waves (Liao 2019). The authors report the curvature term Ω k ranging between -0.3 to 0 indicating a closed universe, not significantly departing from flat geometry.…”