The matter density PDF for modified gravity and dark energy with Large Deviations Theory

Abstract

We present an analytical description of the probability distribution function (PDF) of the smoothed three-dimensional matter density field for modified gravity and dark energy. Our approach, based on the principles of Large Deviations Theory, is applicable to general extensions of the standard ΛCDM cosmology. We show that late-time changes to the law of gravity and background expansion can be included through Einstein-de Sitter spherical collapse dynamics combined with linear theory calculations and a calibration measurement of the non-linear variance of the smoothed density field from a simple numerical simulation. In a comparison to 𝑁-body simulations for 𝑓 (𝑅), DGP and evolving dark energy theories, we find percent level accuracy around the peak of the distribution for predictions in the mildly non-linear regime. A Fisher forecast of an idealised experiment with a Euclid-like survey volume demonstrates the power of combining measurements of the 3D matter PDF with the 3D matter power spectrum. This combination is shown to halve the uncertainty on parameters for an evolving dark energy model, relative to a power spectrum analysis on its own. The PDF is also found to substantially increase the detection significance for small departures from General Relativity, with improvements of up to six times compared to the power spectrum alone. This analysis is therefore very promising for future studies including non-Gaussian statistics, as it has the potential to alleviate the reliance of these analyses on expensive high resolution simulations and emulators.

One-Point Statistics Matter in Extended Cosmologies

“…In [15] we validated the predicted matter PDFs against a suite of modified gravity and dark energy simulations, and found them to be accurate to 2% over the range of densities used in the final analysis. All PDFs and the analysis presented here are based on the LDT model, calculated using pyLDT 1 , a modularised and user-friendly Python code that takes advantage of the PyJulia interface for computationally intensive tasks.…”

“…where the precise prefactor can be determined by a more detailed analysis (see equations 5a and 5b from [15]). For a standard ΛCDM universe, there are only three quantities needed for this theoretical model of the matter PDF (through the decay-rate function in equation 3):…”

“…The data covariance was measured from the fiducial ΛCDM runs of the Quijote suite of simulations [16] subsequently rescaled to correspond to a Euclid-like survey volume of 20 (Gpc/h) 3 . For the matter PDF we combined three sizes of spheres (10,15,20 Mpc/h), while for the matter power spectrum we included information up to k max = 0.2 h/Mpc.…”

“…For this reason, in the cases of dark energy and DGP gravity, the degeneracy is mainly broken by a difference in the redshift (and scale) dependence. and for w 0 w a CDM about a ΛCDM fiducial (forecasts for DGP gravity can be found in [15]). In both the modified gravity and the dark energy extended cosmologies, the matter PDF alone provides constraints competitive with the matter power spectrum.…”

On the road to percent accuracy: The Reaction Way

“…(iii ) AGN feedback redistributes the gas content of massive halos (M h 10 13.5 M /h) thus changing their overall density profiles. This effect can be readily incorporated into the reaction formalism, which together with multi-wavelength observations of groups and clusters of galaxies will put us in a better position to break degeneracies between astrophysical systematics and cosmology, currently a major limiting factor in cosmic shear analyses; (iv ) the reaction framework enables the simultaneous treatment of various physics beyond the standard gravity-only paradigm, and thanks to the growing library of models implemented in ReACT it will be easier in the future to study the combined effect of exotic dark matter particles, new interactions, gravity beyond GR and astrophysics on the non-linear matter power spectrum; (v ) finally, Cataneo et al (2021) 20 found that for sufficiently large smoothing scales the real and pseudo modified gravity probability distribution functions of the matter density field are remarkably similar. This bodes well for potential applications of the reaction to higherorder statistics, e.g.…”