Cosmic magnification in beyond-Horndeski gravity

TL;DR

The paper investigates cosmic magnification as a probe of beyond-Horndeski gravity by computing the angular power spectrum $C_ll(z_S)$ of the observed magnification overdensity, including all relativistic corrections, under constant and dynamic Unified Dark Energy phenomenologies. It analyzes both the total relativistic signal and the individual relativistic contributions (Doppler, ISW, time-delay, and gravitational-potential effects), and assesses detectability with SKA2-like sky coverage using cosmic variance as the error model. The main findings are that the total relativistic signal can exceed cosmic variance at low redshift ($z_S\u2264 0.5$), with Doppler magnification dominating there; at high redshift, constant phenomenology can make ISW, time-delay, and potential magnifications more prominent, while dynamic phenomenology suppresses these signals. The results emphasize that multi-tracer analyses will often be required to isolate relativistic signals, and they highlight the importance of allowing time-variation in model parameters to identify the true beyond-Horndeski signatures in cosmic magnification.

Abstract

Cosmic magnification is able to probe the geometry of large-scale structure on cosmological scales, thereby providing another window for probing theories of the late-time cosmic acceleration. It holds the potential to reveal new information on the nature of dark energy and modified gravity. By using the angular power spectrum, we investigated cosmic magnification beyond weak lensing (incorporating all known relativistic corrections) in beyond-Horndeski gravity$-$with both constant phenomenology and dynamic phenomenology, respectively. For both phenomenologies our results show that the total relativistic signal surpasses cosmic variance (considering an SKA2-like sky coverage) in the magnification angular power spectrum at low redshifts ($z\lesssim 0.5$), hence cosmic-variance reduction methods like multi-tracer analysis will not be needed for surveys at the given $z$. For the individual relativistic signals, we found that the Doppler magnification signal also surpasses cosmic variance and remains the dominant signal, at low $z$, for both phenomenologies. However, the integrated-Sachs-Wolfe, the time-delay, and the gravitational (potential) magnification signals, respectively, are subdominant to both the Doppler magnification signal and cosmic variance, at the same $z$; hence multi-tracer analysis will be needed to isolate these signals. At high redshifts ($z\gtrsim 3$), the integrated-Sachs-Wolfe, the time-delay, and the gravitational magnification signals, respectively, appear to surpass cosmic variance and dominate over the Doppler magnification signal for constant phenomenology; whereas for dynamic phenomenology, all these signals diminish significantly and are well below cosmic variance, at all $z$ (consistent with recent quintessence analysis). Suggesting that including time-variation in the parameters will be crucial in identifying the true signature of the beyond-Horndeski gravity.

Figures (11)

• Figure 1: The plots of the total magnification angular power spectrum $C_\ell$ as a function of multipole $\ell$. Left: Plots for constant $\alpha_i$ ($i \,{\neq}\, M$) scenario \ref{['case1']}, where the Horndeski parameter $\alpha_H \,{=}\, e_H \,{=}\, 0.085,\, 0.1,\, 0.15$ and, $\alpha_B \,{=}\, e_B$ and $\alpha_T \,{=}\, e_T$ are given by \ref{['alphaT-alphaB']}. Right: Plots for dynamic $\alpha_i$ scenario \ref{['case2']}, where $\alpha_H \,{\neq}\, e_H \,{=}\, 0.085,\, 0.1,\, 0.15$ and, $\alpha_B \,{\neq}\, e_B$ and $\alpha_T \,{\neq}\, e_T$, with $\alpha_H$, $\alpha_K$, $\alpha_B$, and $\alpha_T$ being given by \ref{['alphas']} and $e_B$ and $e_T$ being given by \ref{['alphaT-alphaB']}. For all numerical computations, $\alpha_M$ is dynamic and given by \ref{['params']} with $\alpha_M \,{\neq}\, e_M \,{=}\, 0.06$, and $\alpha_K \,{=}\, e_K \,{=}\, 0$. The different panels in both Left and Right are at the source redshifts $z_S \,{=}\, 0.5$ ( top), $z_S \,{=}\, 1.0$ ( middle), and $z_S \,{=}\, 3.0$ ( bottom), respectively. Shaded regions show the extent of cosmic variance.
• Figure 2: The plots of the total relativistic signal in the magnification angular power spectrum $C_\ell$ for the same UDE parameters and scenarios as in Fig. \ref{['fig:totalCls']}. Left: Plots for constant $\alpha_i$ ($i \neq M$) scenario \ref{['case1']}. Right: Plots for dynamic $\alpha_i$ scenario \ref{['case2']}. The Left and Right panels show the plots at $z_S \,{=}\, 0.5$ ( top), $z_S \,{=}\, 1.0$ ( middle) and $z_S \,{=}\, 3.0$ ( bottom), where we have $\Delta{C}_\ell \,{=}\, C_\ell - C^{\rm std}_\ell$.
• Figure 3: The plots of Doppler signal in the total magnification angular power spectrum $C_\ell$ for the same UDE parameters and scenarios as in Fig. \ref{['fig:totalCls']}. Left: Plots for constant $\alpha_i$ ($i \neq M$) scenario \ref{['case1']}. Right: Plots for dynamic $\alpha_i$ scenario \ref{['case2']}. Similarly, the Left and Right panels show the plots at $z_S \,{=}\, 0.5$ ( top), $z_S \,{=}\, 1.0$ ( middle), and $z_S \,{=}\, 3.0$ ( bottom), where $\Delta{\hat{C}}_\ell \,{=}\, C_\ell \,{-}\, C^{(\rm no\, Doppler)}_\ell$.
• Figure 4: The plots of ISW signal in the total magnification angular power spectrum $C_\ell$ for the same UDE parameters and scenarios as in Fig. \ref{['fig:totalCls']}. Left: Plots for constant $\alpha_i$ ($i \neq M$) scenario \ref{['case1']}. Right: Plots for dynamic $\alpha_i$, scenario \ref{['case2']}. The plots in the Left and Right panels at $z_S \,{=}\, 0.5$ ( top), $z_S \,{=}\, 1.0$ ( middle), and $z_S \,{=}\, 3.0$ ( bottom), where we have $\Delta{\hat{C}}_\ell \,{=}\, C_\ell \,{-}\, C^{(\rm no\, ISW)}_\ell$.
• Figure 5: The plots of time-delay signal in the total magnification angular power spectrum $C_\ell$ for the same UDE parameters and scenarios as in Fig. \ref{['fig:totalCls']}. Left: Plots for constant $\alpha_i$ ($i \neq M$) scenario \ref{['case1']}. Right: Plots for dynamic $\alpha_i$ scenario \ref{['case2']}. Similarly, the plots in the Left and Right panels at $z_S \,{=}\, 0.5$ ( top), $z_S \,{=}\, 1.0$ ( middle), and $z_S \,{=}\, 3.0$ ( bottom), where $\Delta{\hat{C}}_\ell \,{=}\, C_\ell \,{-}\, C^{(\rm no\, timedelay)}_\ell$.