Cosmological Simulations Featured Project: Power spectra via perturbation theory

Impact of neutrino mass on matter power spectrum.
Caption: 

Shifts in the baryon wiggles in the matter power spectrum at (z = 0) due to the effects of neutrino mass. Vertical arrows show the locations of local extrema.

(Authors: Amol Upadhye, Rahul Biswas, Adrian Pope, Katrin Heitmann, Salman Habib, Hal Finkel, Nicholas Frontiere)

LSST measurements that will further our understanding of dark energy will probe deep into the nonlinear regime of structure formation. Precision predictions in this regime will be essential and can only be obtained from detailed simulations over a wide range of cosmological models, augmented by observational inputs. These predictions will be important for all analysis teams and their associated tasks. As described in Section 4.1 in the LSST DESC White Paper (arXiv:1211.0310), theoretical predictions can be obtained by building so-called emulators, accurate prediction tools built from a (relatively) limited set of high-quality simulations. The work described here is the very first step to build an emulator for the matter power spectrum, essential for analysing weak lensing measurements. Covering large volumes using simulations directly is a daunting task since many realizations are required to obtain a smooth result. As has been shown in previous work, a superior alternative is to use perturbation theory on large scales, matching at an intermediate length scale -- where perturbation theory is still highly accurate -- to the simulation results. A large body of work exists in this field but is mainly focused on cosmologies very close to LCDM. For LSST we must go significantly further and include a broader range of dark energy models and other effects, such as those due to massive neutrinos, that also affect the power spectrum. In the current project we focus on the treatment of dynamical dark energy, described by the popular parameterization of the dark energy equation of state w(z) via (w0, wa) and massive neutrinos. We have released an extended version of the Copter Code (J. Carlson, M. White and N. Padmanabhan, Phys. Rev. D80, 043531, 2009) and an extended version of the CAMB code (A. Lewis, A. Challinor, and A. Lasenby, Astrophys. J. 538, 473, 2000) to enable precision predictions for the matter power spectrum on quasilinear scales. In addition to building an emulator for the matter power spectrum, our work also has implications for BAO reconstruction as detailed in the paper. 

We implement our approach within the framework of Time Renormalization Group (Time-RG) perturbation theory. Massive neutrinos lead to a scale-dependent growth rate which is incompatible with most perturbative methods. Time-RG perturbation theory accommodates massive neutrinos by directly integrating the evolution equation of the power spectrum. The treatment of (w0, wa) is relatively straightforward. Our extended CAMB version includes the effects of perturbations of the dark energy fluid. In order to validate our implementation in the Copter Code, we also carried out a set of simulations, including neutrinos and dynamical dark energy models. We used the simulations to  establish the accuracy of the Time-RG perturbation theory approach at different length scales and redshifts. 

The codes are available at http://www.hep.anl.gov/cosmology/pert.html .  Submitted to Physical Review D, arxiv:1309.5872