Large-scale imprint of relativistic effects in the cosmic magnification

Apart from the known weak gravitational lensing effect, the cosmic magnification acquires relativistic corrections owing to Doppler, integrated Sachs-Wolfe, time-delay and other (local) gravitational potential effects, respectively. These corrections grow on very large scales and high redshifts z, which will be the reach of forthcoming surveys. In this work, these relativistic corrections are investigated in the magnification angular power spectrum, using both (standard) noninteracting dark energy (DE), and interacting DE (IDE). It is found that for noninteracting DE, the relativistic corrections can boost the magnification large-scale power by ~ 40% at z = 3, and increases at lower z. It is also found that the IDE effect is sensitive to the relativistic corrections in the magnification power spectrum, particularly at low z---which will be crucial for constraints on IDE. Moreover, the results show that if relativistic corrections are not taken into account, this may lead to an incorrect estimate of the large-scale imprint of IDE in the cosmic magnification; including the relativistic corrections can enhance the true potential of the cosmic magnification as a cosmological probe.