Reconstructing Gravity with Peculiar VelocitiesRussell Johnston

University of the Western CapeSouth Africa

~collaborators~David Bacon (ICG, Portsmouth)Luis Teodoro (NASA, AMES)Bob Nichol (ICG, Portsmouth)Mike Warren (Los Alamos)Catherine Cress (CHPC, Cape Town)

~in association with~

gravity mapspeculiar velocities weak lensing

( + �)

ds

2 = �(1� 2 )dt2 + a

2(t)(1 + 2�)dx2

Newtonian potentials

�

temporal perturbations

spatial perturbations

THE CONCEPTWe are interested in extending velocity maps to higher redshifts,

concentrating on test.( � �)

vpec

= czobs

�H0d

inferred distance

measured from e.g. Tully-Fisher or Fundamental Plane

typical error on d ~ 20%

THE CONCEPT

V truepec

RECONSTRUCTING THE PECULIAR VELOCITY FIELD

binning in observed redshift

384 Mpc

Creating an observed velocity field

vpec

= czobs

�H0d

propagate errors on inferred distance into the peculiar

velocities.

�d = 0.3

low-z “high”-z

regularising the reconstruction

Pr(Vhyp|Vdata) / Pr(Vdata|Vhyp) Pr(Vhyp|�v,Pk)

Velocity field derived from a redshift galaxy survey

distribution.

The prior

gravitational potential

@ galz = i gal(k)kz

a new velocity field

�v

gal(k) =3⌦mH2

0�z(k)

2a(t)(k2 + �k2z)

Create a velocity field derived from the galaxy distribution:

The prior �v

The field@ z The fieldcompared to V truez

�v =

NpixX

i=1

(V̂ rec � @ z)2

��v

regularisation parameter

The prior Uses a theoretical velocity power spectrum to regularise V̂ rec

Pk

Pk =ktotX

i=1

[P̂v(k)rec � Pv(k)th]2

[�vP (k)]

2

regularisation parameter

Putting it altogether

Pr(Vhyp|Vdata) / Pr(Vdata|Vhyp) Pr(Vhyp|�v,Pk)

The reconstructed field can be V or

The data could be PV+WL and jointly reconstruct

� &

Pr( hyp|Vdata) / Pr(Vdata| hyp) Pr( hyp|� , P k )

0.174 < z < 0.180

True V-field

Reconstructed V-field

observed vs. truereconstructed vs. true

r[Vnoisy

, Vtrue

]

r[Vrec, Vtrue]

�v =

NpixX

i=1

(V̂ rec � @ z)2

��v

final reconstruction.

Vtrue

@

Embed artificial mass in the field

@ Propagate through to field

an sdss type survey...

RECONSTRUCTING GRAVITY

r[ rec, gal]

Pr( hyp|Vdata) / Pr(Vdata| hyp) Pr( hyp|� , P k )