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Investigating the imprint of quintessence in cosmic magnification

Enas Mohamed, Didam Duniya, Hassan Abdalla, Bishop Mongwane

TL;DR

This work investigates how quintessence models imprint on cosmic magnification beyond lensing by computing the total magnification angular power spectrum $C_\ell(z_S)$ in a $\varphi$CDM universe, incorporating Doppler, ISW, time-delay, and gravitational-potential corrections. It compares RP, SUGRA, and DExp quintessence potentials against $\Lambda$CDM, showing that relativistic corrections enhance sensitivity to dark energy parameters at $z_S \lesssim 1$, while for $z_S \gtrsim 3$ the lensing spectrum closely approximates the total spectrum. The study finds that cosmic variance dominates on large scales and that distinct quintessence models are difficult to distinguish in $C_\ell$ at many redshifts, though total relativistic signals can surpass cosmic variance for $z_S \leq 0.5$. These results highlight the potential and challenges of using cosmic magnification, including the need for multi-tracer analyses to beat cosmic variance and robustly detect relativistic magnification signals.

Abstract

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 analysing 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 analyse 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 $z \,{\leq}\, 1$; whereas, when relativistic corrections are incorporated, the total magnification angular power spectrum holds the potential to distinguish between the models, at the given $z$. At $z \,{\geq}\, 3$, 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 $z \,{\leq}\, 0.5$: hence the effect may be detectable at the given $z$. 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 $z \,{=}\, 4.5$, with the gravitational-potential magnification signal being zero.

Investigating the imprint of quintessence in cosmic magnification

TL;DR

This work investigates how quintessence models imprint on cosmic magnification beyond lensing by computing the total magnification angular power spectrum in a CDM universe, incorporating Doppler, ISW, time-delay, and gravitational-potential corrections. It compares RP, SUGRA, and DExp quintessence potentials against CDM, showing that relativistic corrections enhance sensitivity to dark energy parameters at , while for the lensing spectrum closely approximates the total spectrum. The study finds that cosmic variance dominates on large scales and that distinct quintessence models are difficult to distinguish in at many redshifts, though total relativistic signals can surpass cosmic variance for . These results highlight the potential and challenges of using cosmic magnification, including the need for multi-tracer analyses to beat cosmic variance and robustly detect relativistic magnification signals.

Abstract

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 analysing 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 analyse 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 ; whereas, when relativistic corrections are incorporated, the total magnification angular power spectrum holds the potential to distinguish between the models, at the given . At , 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 : hence the effect may be detectable at the given . 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 , with the gravitational-potential magnification signal being zero.

Paper Structure

This paper contains 13 sections, 60 equations, 7 figures.

Table of Contents

  1. Introduction
  2. The Observed Magnification Overdensity
  3. The Magnification Angular Power Spectrum
  4. The $\varphi$CDM Universe
  5. The Quintessence Models
  6. The Background Evolutions
  7. The Magnification $C_\ell$'s
  8. Conclusion
  9. Gauge Invariance
  10. Gauge-invariant 4-velocity
  11. Gauge-invariance of Phi, Psi, and V
  12. Redshift-space area density contrast
  13. The Cosmological Equations

Figures (7)

  • Figure 1: The plots of the equation of state parameters \ref{['w_RP']}, \ref{['w_SUGRA']}, and \ref{['w_DExp']} for RP, SUGRA, and DExp models, respectively, with respect to scale factor $a$. These govern the background evolution of quintessence in the respective models.
  • Figure 2: The plots of the total magnification angular power spectrum $C_\ell$ (solid lines) and the lensing magnification angular power spectrum $C^{\rm lensing}_\ell$ (dashed lines), where $C^{\rm lensing}_\ell$ is computed with only the first integral in \ref{['f_ell']} being considered: for RP \ref{['w_RP']}, SUGRA \ref{['w_SUGRA']}, and DExp \ref{['w_DExp']} models, respectively, and that of the $\Lambda$CDM, at source redshifts $z_S \,{=}\, 0.5$ (top left), $z_S \,{=}\, 1$ (top right), $z_S \,{=}\, 3$ (bottom left), and $z_S \,{=}\, 4.5$ (bottom right). Shaded regions denote cosmic variance, on $C_\ell$.
  • Figure 3: The plots of fractional difference (in percentage) of the magnification angular power spectra of $\varphi$CDM relative to those of $\Lambda$CDM, at source redshifts: $z_S \,{=}\, 0.5$ (top left), $z_S \,{=}\, 1$ (top right), $z_S \,{=}\, 3$ (bottom left), and $z_S \,{=}\, 4.5$ (bottom right). Solid lines denote fractional difference of $C_\ell$, and dashed lines denote fractional difference of $C^{\rm lensing}_\ell$. Notations are as in FIG. \ref{['fig:totalCls']}.
  • Figure 4: The plots of the combined relativistic signal, $(C_\ell - C^{\rm lensing}_\ell) / C^{\rm lensing}_\ell$, in the total magnification angular power spectrum as a function of multipole $\ell$: at source redshifts $z_S \,{=}\, 0.5$ (top left), $z_S \,{=}\, 1$ (top right), $z_S \,{=}\, 3$ (bottom left), and $z_S \,{=}\, 4.5$ (bottom right). Shaded regions denote cosmic variance.
  • Figure 5: The plots of the Doppler signal, $(C_\ell - C^{(\rm no\, Doppler)}_\ell) / C^{(\rm no\, Doppler)}_\ell$, in the total magnification angular power spectrum as a function of multipole $\ell$: at source redshifts $z_S \,{=}\, 0.5$ (top left), $z_S \,{=}\, 1$ (top right), $z_S \,{=}\, 3$ (bottom left), and $z_S \,{=}\, 4.5$ (bottom right). Shaded regions denote cosmic variance.
  • ...and 2 more figures