Decomposed Cosmic Velocity
Field in f(R) Gravity
Xiaoqi Yu
Gustavus Adolphus College
xyu@gustavus.edu Midstate Symposia in
Physical Science
The University of Chicago
Nov, 4th, 2017
The Accelerated Cosmic Expansion
LCDM Model
The f(R) Gravity
The Ricci Scalar in the Einstein-Hilbert Action is replaced by a
variable function.
What Cosmological Information do the three
velocity eigen-components contain?
●Vδ: The only components at large scales. By comparing Vδ in
f(R) and GR model at large scale, we can probe the linear
structure formation of these two cosmologies.
●VS: Arisen from nonlinear evolution, VS can tell us the
formation history at the galactic scale, making it a good
candidate for testing gravity.
●VB: Grows only when the nonlinearity is sufficiently large. It is
expected that VBis of less significance in probing modified
gravity.
The Simulation
●The ELEPHANT (Extended LEnsing PHysics with ANalytical ray
Tracing) Simulation using ECOSMOG Code, with F6, F5 and GR
cosmology. F6 deviate less from GR compared to F5.
●10243dark matter particles evolved in various box sizes with side
length 1024 Mpc/h (3 realisations), 900 Mpc/h, and 450 Mpc/h
respectively using the same cosmological parameters. Another set
of simulation using different parameters in box of 250 Mpc/h.
●Velocity assignment: 2563, 5123, and 10243grid points were drawn
to find the best representation of velocity. Each grid point finds its
nearest particle. The velocity of the nearest particle is assigned to
the grid point. (NP Method)
●Density assignment: Nearest Grid Point Interpolation for each
particle into the grid (NGP Method).
The Power Spectra of Velocity Field. First decomposed into divergence and curl
components in (a), and then the divergence component is further decomposed into
density coupling component, and stochasticity component in (b)
(a) First Order Decomposition (b)Second Order Decomposition
The Power Spectra of Decomposed Velocity Field, Convergence Tested against
(a) Different Realization and (b) different box size
(a) (b)
The Power Spectra of Decomposed Velocity Field, Convergence Tested against
different grid size in (a) 1024 Mpc/h box, and (b) 250 Mpc/h box.
(a) (b)
The deviation of the power spectra of velocity components in (a) F5, and (b) F6
from that in GR.
(a) (b)
The deviation of the power spectra of VBcomponents in (a) F5, and (b) F6 from
that in GR.
(a) (b)
Conclusion and Future
Implications
●Vs is the powerful and reliable one to probe gravity at galactic and
cosmological scales among all components.
●The cosmic velocity field will be a powerful tool to study the nature
of gravity when future redshift survey observation collect enough
data.
●Finer interpolation and smoothing methods can be used in further
velocity assignments such that observing data, which is small in
size compared to simulation data, can be also incorporated to
recover the velocity and matter density field.
Acknowledgement
●My supervisors Dr.Jie Wang from Laboratory of Computational
Cosmology at National Astronomical Observatories of China for
the opportunity and guidance, and Dr.Baojiu Li from Institute for
Computational Cosmology at Durham University for the simulation
data and useful feedback.
●This work used the DiRAC Data Centric system at Durham
University, operated by the Institute for Computational Cosmology
on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk).
This equipment was funded by BIS National E-infrastructure
capital grant ST/K00042X/1, STFC capital grant ST/H008519/1,
and STFC DiRAC Operations grant ST/K003267/1 and Durham
University. DiRAC is part of the National E-Infrastructure.
References
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