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Register a new userk-cut Cosmic Shear: Tunable Power Spectrum Sensitivity to Test Gravity
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Peter L. Taylor
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If left unchecked modeling uncertainties at small scales, due to poorly understood baryonic physics and non-linear structure formation, will significantly bias Stage IV cosmic shear two-point statistic parameter constraints. While it is perhaps possible to run N-body or hydrodynamical simulations to determine the impact of these effects this approach is computationally expensive; especially to test a large number of theories of gravity. Instead we propose directly removing sensitivity to small-scale structure from the lensing spectrum, creating a statistic that is robust to these uncertainties. We do this by taking a redshift-dependent l-cut after applying the Bernardeau-Nishimichi-Taruya (BNT) nulling scheme. This reorganizes the information in the lensing spectrum to make the relationship between the angular scale, l, and the structure scale, k, much clearer compared to standard cosmic shear power spectra -- for which no direct relationship exists. We quantify the effectiveness of this method at removing sensitivity to small scales and compute the predicted Fisher error on the dark energy equation of state, w0, for different k-cuts in the matter power spectrum.
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The precision of Stage IV cosmic shear surveys will enable us to probe smaller physical scales than ever before, however, model uncertainties from baryonic physics and non-linear structure formation will become a significant concern. The $k$-cut method -- applying a redshift-dependent $ell$-cut after making the Bernardeau-Nishimichi-Taruya transform -- can reduce sensitivity to baryonic physics; allowing Stage IV surveys to include information from increasingly higher $ell$-modes. Here we address the question of whether it can also mitigate the impact of making the reduced shear approximation; which is also important in the high-$kappa$, small-scale regime. The standard procedure for relaxing this approximation requires the repeated evaluation of the convergence bispectrum, and consequently can be prohibitively computationally expensive when included in Monte Carlo analyses. We find that the $k$-cut cosmic shear procedure suppresses the $w_0w_a$CDM cosmological parameter biases expected from the reduced shear approximation for Stage IV experiments, when $ell$-modes up to $5000$ are probed. The maximum cut required for biases from the reduced shear approximation to be below the threshold of significance is at $k = 5.37 , h{rm Mpc}^{-1}$. With this cut, the predicted $1sigma$ constraints increase, relative to the case where the correction is directly computed, by less than $10%$ for all parameters. This represents a significant improvement in constraints compared to the more conservative case where only $ell$-modes up to 1500 are probed, and no $k$-cut is used. We also repeat this analysis for a hypothetical, comparable kinematic weak lensing survey. The key parts of code used for this analysis are made publicly available.
We compute the spherical-sky weak-lensing power spectrum of the shear and convergence. We discuss various approximations, such as flat-sky, and first- and second- order Limber equations for the projection. We find that the impact of adopting these approximations is negligible when constraining cosmological parameters from current weak lensing surveys. This is demonstrated using data from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). We find that the reported tension with Planck Cosmic Microwave Background (CMB) temperature anisotropy results cannot be alleviated. For future large-scale surveys with unprecedented precision, we show that the spherical second-order Limber approximation will provide sufficient accuracy. In this case, the cosmic-shear power spectrum is shown to be in agreement with the full projection at the sub-percent level for l > 3, with the corresponding errors an order of magnitude below cosmic variance for all l. When computing the two-point shear correlation function, we show that the flat-sky fast Hankel transformation results in errors below two percent compared to the full spherical transformation. In the spirit of reproducible research, our numerical implementation of all approximations and the full projection are publicly available within the package nicaea at http://www.cosmostat.org/software/nicaea.
Using Subaru Hyper Suprime-Cam (HSC) year 1 data, we perform the first $k$-cut cosmic shear analysis constraining both $Lambda$CDM and $f(R)$ Hu-Sawicki modified gravity. To generate the $f(R)$ cosmic shear theory vector, we use the matter power spectrum emulator trained on COLA (COmoving Lagrangian Acceleration) simulations. The $k$-cut method is used to significantly down-weight sensitivity to small scale ($k > 1 h {rm Mpc }^{-1}$) modes in the matter power spectrum where the emulator is less accurate, while simultaneously ensuring our results are robust to baryonic feedback model uncertainty. We have also developed a test to ensure that the effects of poorly modeled small scales are nulled as intended. For $Lambda$CDM we find $S_8 = sigma_8 (Omega_m / 0.3) ^ {0.5} = 0.789 ^{+0.039}_{-0.022}$, while the constraints on the $f(R)$ modified gravity parameters are prior dominated. In the future, the $k$-cut method could be used to constrain a large number of theories of gravity where computational limitations make it infeasible to model the matter power spectrum down to extremely small scales.
We present a new method, called $x$-cut cosmic shear, which optimally removes sensitivity to poorly modeled scales from the two-point cosmic shear signal. We show that the $x$-cut cosmic shear covariance matrix can be computed from the correlation function covariance matrix in a few minutes, enabling a likelihood analysis at virtually no additional computational cost. Further we show how to generalize $x$-cut cosmic shear to galaxy-galaxy lensing. Performing an $x$-cut cosmic shear analysis of the Dark Energy Survey Year 1 (DESY1) shear data, we reduce the error on $S_8= sigma_8 (Omega_m / 0.3) ^ {0.5}$ by $32 %$ relative to a correlation function analysis with the same priors and angular scale cut criterion, while showing our constraints are robust to different baryonic feedback models. Largely driven by information at small angular scales, our result, $S_8= 0.734 pm 0.026$, yields a $2.6 sigma$ tension with the Planck Legacy analysis of the cosmic microwave background. As well as alleviating baryonic modelling uncertainties, our method can be used to optimally constrain a large number of theories of modified gravity where computational limitations make it infeasible to model the power spectrum down to extremely small scales. The key parts of our code are made publicly available.
We use the cosmic shear data from the Canada-France-Hawaii Telescope Lensing Survey to place constraints on $f(R)$ and {it Generalized Dilaton} models of modified gravity. This is highly complimentary to other probes since the constraints mainly come from the non-linear scales: maximal deviations with respects to the General-Relativity + $Lambda$CDM scenario occurs at $ksim1 h mbox{Mpc}^{-1}$. At these scales, it becomes necessary to account for known degeneracies with baryon feedback and massive neutrinos, hence we place constraints jointly on these three physical effects. To achieve this, we formulate these modified gravity theories within a common tomographic parameterization, we compute their impact on the clustering properties relative to a GR universe, and propagate the observed modifications into the weak lensing $xi_{pm}$ quantity. Confronted against the cosmic shear data, we reject the $f(R)$ ${ |f_{R_0}|=10^{-4}, n=1}$ model with more than 99.9% confidence interval (CI) when assuming a $Lambda$CDM dark matter only model. In the presence of baryonic feedback processes and massive neutrinos with total mass up to 0.2eV, the model is disfavoured with at least 94% CI in all different combinations studied. Constraints on the ${ |f_{R_0}|=10^{-4}, n=2}$ model are weaker, but nevertheless disfavoured with at least 89% CI. We identify several specific combinations of neutrino mass, baryon feedback and $f(R)$ or Dilaton gravity models that are excluded by the current cosmic shear data. Notably, universes with three massless neutrinos and no baryon feedback are strongly disfavoured in all modified gravity scenarios studied. These results indicate that competitive constraints may be achieved with future cosmic shear data.
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