Measuring neutrino masses with large-scale structure: Euclid forecast with controlled theoretical error

Abstract

We present a Markov-Chain Monte-Carlo (MCMC) forecast for the precision of neutrino mass and cosmological parameter measurements with a Euclidlike galaxy clustering survey. We use a complete perturbation theory model for the galaxy one-loop power spectrum and tree-level bispectrum, which includes bias, redshift space distortions, IR resummation for baryon acoustic oscillations and UV counterterms. The latter encapsulate various effects of short-scale dynamics which cannot be modeled within perturbation theory. Our MCMC procedure consistently computes the non-linear power spectra and bispectra as we scan over different cosmologies. The second ingredient of our approach is the theoretical error covariance which captures uncertainties due to higher-order non-linear corrections omitted in our model. Having specified characteristics of a Euclid-like spectroscopic survey, we generate and fit mock galaxy power spectrum and bispectrum likelihoods. Our results suggest that even under very agnostic assumptions about non-linearities and short-scale physics a future Euclid-like survey will be able to measure the sum of neutrino masses with a standard deviation of 28 meV. When combined with the most recent Planck likelihood, this uncertainty decreases to 19 meV. Reducing the theoretical error on the bispectrum down to the two-loop level marginally tightens the bound to 17 meV. 1 chudy@ms2.inr.ac.ru 2 mi1271@nyu.edu arXiv:1907.06666v1 [astro-ph.CO] 15 Jul 2019 exploit the potential of upcoming surveys will strongly depend on the understanding on these effects, which is not yet complete.Fortunately, the bulk of information about the neutrino free-streaming is encoded in mildly non-linear scales which can be robustly and systematically described within perturbation theory. One of the most popular approaches is Eulerian standard cosmological perturbation theory (SPT) [14]. The basic formulation of SPT, however, does not correctly capture the non-linear evolution of baryon acoustic oscillations (BAO) [15] and short-scale physics beyond the single-stream pressureless perfect fluid hydrodynamics [16][17][18]. These problems have been intensely studied in the recent years.First, it has been shown that the non-linear suppression and distortion of the BAO can be captured by a resummation of contributions describing the tidal effects of large-scale bulk flows. This procedure, called infrared (IR) resummation, is essential for an accurate description of the BAO and has been formulated within various theoretical frameworks [19][20][21][22][23][24][25]. We will adopt a systematic approach of [22,24] streamlined in the context of time-sliced perturbation theory [26].Second, we will use the effective field theory of large-scale structure (EFT) to account for the back-reaction of small scale nonlinearities on larger scales [17,27,28]. This approach removes the unphysical UV sensitivity of perturbation theory loop integrals and parameterizes the ignorance about short scale-dynamics by various effective operators in the equations of motion for ...

Nonlinear perturbation theory extension of the Boltzmann code CLASS

“…[93], which showed that the leading effect of massive neutrinos is always a suppression of the linear power spectrum, and any residual scale dependence of this suppression is insignificant even for volumes as large as 100 ðGpc=hÞ 3 . This observation was also confirmed in various forecasts, e.g., [17,96]. Given these reasons, we expect that using the usual FFTLog formulas in the presence of massive neutrinos will be a good approximation even for future surveys like DESI or Euclid.…”

“…To that end, we interface CLASS-PT with the MCMC sampler MONTEPYTHON v3.0 [6,12]. We will analyze a full-shape likelihood built out of the publicly available BOSS data and products that can be accessed, 17 see Refs. [103,104] for more detail.…”

“…Lower panels: comparison between the nonlinear models for the lensing potential power spectrum and the lensed CMB TT power spectrum. 16 Note that even if the two-loop corrections are not directly included in the model, one can still use the one-loop perturbation theory prediction evaluated by our code at high k max provided that the two-loop corrections are included in the theoretical error covariance [17,38].…”

“…is also adopted in the measurement of rms velocity fluctuation fσ 8 . This method has a number of limitations which can compromise the cosmological analysis of future high-precision data [13,17]. 18 An alternative to the fixed shape approach is to return to the methodology of measuring the cosmological parameters of a given model from the full power spectrum.…”

“…Moreover, in Ref. [17] it was used to assess the accuracy of the neutrino mass and cosmological parameter measurements with a future Euclid-like galaxy survey.…”