Fast radio bursts shed light on direct gravity test on cosmological scales

Abstract

A key measure of gravity is the relation between the Weyl potential $Ψ+Φ$ and the matter overdensity $δ_m$, capsulized as an effective gravitational constant $G_{\rm light}$ for light motion. Its value, together with the possible spatial and temporal variation, is essential in probing physics beyond Einstein gravity. However, the lack of an unbiased proxy of $δ_m$ prohibits direct measurement of $G_{\rm light}$. We point out that the equivalence principle ensures the dispersion measure (DM) of localized fast radio bursts (FRBs) as a good proxy of $δ_m$. We further propose a FRB-based method $F_G$ to directly measure $G_{\rm light}$, combining galaxy-DM of localized FRBs and galaxy-weak lensing cross-correlations. The measurement, with a conservative cut $k\leq 0.1h$/Mpc, can achieve a precision of $\lesssim 10\% \sqrt{10^5/N_{\rm FRB}}$ over 10 equal-width redshift bins at $z\lesssim 1$. The major systematic error, arising from the clustering bias of electrons traced by the FRB DM, is subdominant ($\sim 5\%$). It can be further mitigated to the $\lesssim 1\%$ level, based on the gastrophysics-agnostic behavior that the bias of total baryonic matter (ionized diffuse gas, stars, neutral hydrogen, etc) approaches unity at sufficiently large scales. Therefore, FRBs shed light on gravitational physics across spatial and temporal scales spanning over 20 orders of magnitude.

Figures (4)

• Figure 1: Statistical errors of the tomographic $F_G$ measurement. The forecast assumes the fiducial values $F_G=1$, i.e., $G_{\rm light}=G$, and combines all scales at $k\leq 0.1\, {\rm Mpc}^{-1}h$ to estimate uncertainties. The $F_G$ measurement requires three data sets: a galaxy catalog chosen as a DESI-like catalog, a weak lensing catalog chosen as an LSST-like shear catalog, and a DM catalog of localized FRBs. The limiting factor is the number of localized FRBs, which we chose as $N_{\rm FRB}=10^5$. Additionally, we present the reciprocal of electron bias $b_e^{-1}$ measured in simulations TNG300-1 (green dashed) and Illustris-1 (blue dashed). If uncorrected, it induces a systematic shift in $F_G$ at $1\%\sim 5\%$ level, which remains subdominant to statistical errors.
• Figure 2: The residual systematic errors of the $F_G$ measurement after systematics mitigation, where $\widehat{f_eb}_e$ is estimated by Eq. (\ref{['equ:be_from_bb']}) and $f_e b_e$ is the true value. The major systematic bias in $F_G$ arises from the determination of $f_eb_e$, where $b_e\neq 1$ as shown in Fig. \ref{['fig:FG']}. The proposed Eq. (\ref{['equ:be_from_bb']}) addresses this issue by expressing $f_eb_e$ in terms of stellar and neutral gas contributions, based upon the weak equivalence principle. Despite dramatically different strengths of AGN feedback adopted in simulations, both TNG300-1 (green line) and Illustris-1 (blue line) validate Eq. (\ref{['equ:be_from_bb']}) to $1\%$ accuracy, demonstrating its insensitivity to these gastrophysics. Therefore, we can infer $f_eb_e$ using observations of stars and neutral gas, thereby reducing the systematic errors in $F_G$ to the $\sim 1\%$ level.
• Figure 3: Tracer bias $b_i=P_{im}/P_{mm}$ measured in TNG300-1 (solid lines) and Illustris-1 (dashed lines) simulations. The left panel shows the bias measured for stars and black holes (orange lines) and for neutral hydrogen (green lines). Since both stars and black holes form in overdense regions of the cosmic web, their bias values are typically greater than unity. A similar trend holds for neutral hydrogen at early times, but astrophysical processes deplete neutral gas in massive halos, leading to a decline in its bias value at later times. The right panel shows the bias measured for electrons (red lines), total baryons (black lines), and gas components (blue lines). The apparent deviation $b_b\lesssim 1$ at low redshifts arises from the limited box volume of the Illustris-1 simulation. These measurements are consistent with similar results presented in the IllustrisTNG publication Springel_2017.
• Figure 4: Baryon mass fraction $f_i = \Omega_i/\Omega_b$ measured in simulations. The labels of tracers are the same as Fig. \ref{['fig:tracer_bias']}. The electron fraction is given by $f_e= f_{\rm HII} + {1\over 2}f_{\rm HeIII} \simeq (M_{\rm H} + {1\over 2} M_{\rm He})\, f_{\rm HII}/f_{\rm H}$, where $f_{\rm HII}$, $M_{\rm H}$ and $M_{\rm He}$ are directly accessed in simulation products. The large differences in the cold gas fractions between TNG300-1 and Illustris-1 indicate that these two simulation suites adopt highly distinct subgrid physics.