Investigating the imprint of quintessence in cosmic magnification

We study cosmic magnification beyond lensing in a late-time universe dominated by quintessence and cold dark matter. The cosmic magnification angular power spectrum, especially going beyond the well-known lensing effect, provides an independent avenue for investigating the properties of quintessence, and hence, dark energy. By analyzing the magnification power spectrum at different redshifts, it is possible to extract new information about the large-scale imprint of dark energy, including whether we are able to disentangle different models from one another. Using three well-known quintessence models, we analyze the cosmic magnification angular power spectrum while taking relativistic corrections into account. We found that it will be difficult to distinguish between quintessence models, and quintessence from the cosmological constant, in lensing magnification angular power spectrum on large scales, at redshifts <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>z</a:mi><a:mo>≤</a:mo><a:mn>1</a:mn></a:mrow></a:math>; whereas, when relativistic corrections are incorporated, the total magnification angular power spectrum holds the potential to distinguish between the models, at the given <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>z</c:mi></c:math>. At <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>z</e:mi><e:mo>≥</e:mo><e:mn>3</e:mn></e:math>, the lensing magnification angular power spectrum can be a reasonable approximation of the total magnification angular power spectrum. We also found that both the total relativistic and the Doppler magnification signals, respectively, surpass cosmic variance at <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>z</g:mi><g:mo>≤</g:mo><g:mn>0.5</g:mn></g:math>; hence, the effect may be detectable at the given <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>z</i:mi></i:math>. On the other hand, the ISW and the time-delay magnification signals, respectively, are surpassed by cosmic variance on all scales, at epochs up to <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>z</k:mi><k:mo>=</k:mo><k:mn>4.5</k:mn></k:math>, with the gravitational-potential magnification signal being zero.