Optimising cosmic shear surveys to measure modifications to gravity on cosmic scales

Abstract

We consider how upcoming photometric large scale structure surveys can be
optimized to measure the properties of dark energy and possible cosmic scale
modifications to General Relativity in light of realistic astrophysical and
instrumental systematic uncertainities. In particular we include flexible
descriptions of intrinsic alignments, galaxy bias and photometric redshift
uncertainties in a Fisher Matrix analysis of shear, position and position-shear
correlations, including complementary cosmological constraints from the CMB. We
study the impact of survey tradeoffs in depth versus breadth, and redshift
quality. We parameterise the results in terms of the Dark Energy Task Force
figure of merit, and deviations from General Relativity through an analagous
Modified Gravity figure of merit. We find that intrinsic alignments weaken the
dependence of figure of merit on area and that, for a fixed observing time, a
fiducial Stage IV survey plateaus above roughly 10,000deg2 for DE and peaks at
about 5,000deg2 as the relative importance of IAs at low redshift penalises
wide, shallow surveys. While reducing photometric redshift scatter improves
constraining power, the dependence is shallow. The variation in constraining
power is stronger once IAs are included and is slightly more pronounced for MG
constraints than for DE. The inclusion of intrinsic alignments and galaxy
position information reduces the required prior on photometric redshift
accuracy by an order of magnitude for both the fiducial Stage III and IV
surveys, equivalent to a factor of 100 reduction in the number of spectroscopic
galaxies required to calibrate the photometric sample.

Full text

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arXiv:1109.4536v2 [astro-ph.CO] 8 Oct 2011
Mon. Not. R. Astron. Soc. 000, 1–13 (2009)Printed 11 October 2011(MN LATEX style file v2.2)
Optimising cosmic shear surveys to measure modifications
to gravity on cosmic scales
Donnacha Kirk1,Istvan Laszlo2, Sarah Bridle1, Rachel Bean2
1Department of Physics & Astronomy, University College London, Gower Street, London, WC1E 6BT, UK
2Department of Astronomy, Cornell University, Ithaca, NY 14853, USA
11 October 2011
ABSTRACT
We consider how upcoming photometric large scale structure surveys can be opti-
mized to measure the properties of dark energy and possible cosmic scale modifications
to General Relativity in light of realistic astrophysical and instrumental systematic
uncertainities. In particular we include flexible descriptions of intrinsic alignments,
galaxy bias and photometric redshift uncertainties in a Fisher Matrix analysis of
shear, position and position-shear correlations, including complementary cosmolog-
ical constraints from the CMB. We study the impact of survey tradeoffs in depth
versus breadth, and redshift quality. We parameterise the results in terms of the Dark
Energy Task Force figure of merit, and deviations from General Relativity through an
analagous Modified Gravity figure of merit. We find that intrinsic alignments weaken
the dependence of figure of merit on area and that, for a fixed observing time, halving
the area of a Stage IV reduces the figure of merit by 20% when IAs are not included
and by only 10% when IAs are included. While reducing photometric redshift scatter
improves constraining power, the dependence is shallow. The variation in constrain-
ing power is stronger once IAs are included and is slightly more pronounced for MG
constraints than for DE. The inclusion of intrinsic alignments and galaxy position
information reduces the required prior on photometric redshift accuracy by an order
of magnitude for both the fiducial Stage III and IV surveys, equivalent to a factor
of 100 reduction in the number of spectroscopic galaxies required to calibrate the
photometric sample.
Key words: cosmology: gravitational lensing: weak – dark energy – equation of state
– cosmological parameters – large-scale structure of Universe
1INTRODUCTION
The dawn of “precision cosmology” was heralded by the re-
sults of surveys which, for the first time, produced data of
sufficient quantity and quality that our cosmological probes
could begin to accurately measure some of the fundamen-
tal properties of the Universe. The outcome has been the
ΛCDM concordance cosmology, a description of the Universe
compatible with the joint constraints from many sources of
cosmological information. The next decades will see a step-
change in our ability to measure cosmological parameters as
new surveys produce orders of magnitude more data than
has previously been available. This will allow us to test the
standard cosmological model as never before.
The standard ΛCDM model describes a Universe made
up of ∼75% Dark Energy, a smooth, negative pressure fluid,
∼20% Dark Matter, collisionless massive particles which in-
teract solely via gravity, and just ∼5% baryons making up
the potentially visible mass of the Universe (Dunkley et al.
2009). The standard model also assumes gravity to be de-
scribed by Einstein’s General Relativity (GR).
A Universe governed by GR and populated by standard
gravitating matter cannot explain the observed acceleration.
The dark energy fluid was proposed to solve this paradox,
reviving the idea of a cosmological constant which Einstein
had originally included in his GR field equations and sub-
sequently discarded. Much effort has been devoted to char-
acterising the nature of dark energy- particularly attempts
to discriminate between a pure cosmological constant and
a dynamic scalar potential with time-varying equation of
state w(a) (Albrecht et al. 2006). In all its forms, dark en-
ergy poses problems of fine-tuning for which we have, as yet,
no physical motivation.
Rather than invoke dark energy, an alternative expla-
nation for cosmic acceleration has been proposed – that our
standard theory of gravity is incomplete and that a cor-
rect theory of gravity would explain cosmic acceleration
at late times and large scales in a universe populated by
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2Donnacha Kirk, Istvan Laszlo, Sarah Bridle, Rachel Bean
matter with positive pressure. There are a large number
of theoretically motivated modified theories of gravity, see
Jain & Khoury (2010) for a review. Testing the theory of
gravity on cosmic scales will be one of the most interesting
opportunities afforded by upcoming survey data.
Weak gravitational lensing (WL) is a particularly use-
ful probe of gravity because it is sensitive to φ+ψ, the sum
of the metric potentials. Through the modified growth of
structure and geometry via the lensing integral cosmic shear
can constrain both the ratio of metric potentials and mod-
ifications to the Poisson equation. In contrast probes such
as galaxy redshift surveys and galaxy peculiar velocities de-
pend only on the Newtonian potential, ψ. WL constraints
also have the benefit that they probe the dark matter distri-
bution directly, avoiding the impact of galaxy biasing. Joint
constraints from combining multiple probes can help break
degeneracies between free parameters, producing the tight-
est constraints.
Cosmic shear is the name given to weak gravitational
lensing in random patches of the sky and was first de-
tected a decade ago (Kaiser et al. 2000; Wittman et al.
2000; van Waerbeke et al. 2000; Bacon et al. 2000). The
latest constraints on cosmology come from the Hubble
Space TelescopeCOSMOS
2009; Massey et al. 2007), and the Canada-France-Hawaii
Telescope Legacy Survey (CFHTLS) (Fu et al. 2008). In ad-
dition the 100 square degree survey (Benjamin et al. 2007)
combines data from several smaller surveys (Hoekstra et al.
2002;Hetterscheidt et al.2007;
Hoekstra et al. 2002).
Cosmic shear has been identified as the method with
the most potential to uncover the nature of dark energy
(Albrecht et al. 2006; Peacock et al. 2006) and therefore a
number of surveys are planned with a major cosmic shear
component. Upcoming “Stage III” projects include Kilo-
degree Survey (KIDS) on the Very Large Telescope (VLT)
Survey Telescope (VST), the Panoramic Survey Telescope
and Rapid Response System (Pan-STARRS) project, the
Subaru Meaurement of Images and Redshifts (HSC) sur-
vey using HyperSUPRIMECam, the Dark Energy Survey
(DES) on the Blanco Telescope. More ambitious “Stage IV”
imaging projects are the Large Synoptic Survey Telescope
(LSST) ground-based project and in space the proposed Eu-
ropean Space Agency mission Euclid and the NASA pro-
posed Wide-Field Infrared Survey Telescope (WFIRST).
Greater accuracy demands better treatment of system-
atic effects. One of the main systematics in cosmic shear
studies is the contamination by the intrinsic alignment (IA)
of galaxy shapes. This systematic manifests in two main
ways, in the first physically close galaxies have preferen-
tially aligned ellipticities, this is known as the Intrinsic-
Intrinsic (II) correlation. In the second galaxies close on
the sky by separated radially are anti-correlated as the
foreground gravitational potential shapes the closer galaxy
while also gravitationally lensing the background galaxy,
this is called the Gravitational-Intrinsic (GI) correlation.
The former adds to the cosmic shear signal we wish to
measure, the latter subtracts from it. In an earlier pa-
per (I. Laszlo, R. Bean, D. Kirk and S. Bridle 2011), herein
“LBKB”, we established how, for a fixed survey specifica-
tion, the inclusion of a realistic IA model and the inher-
ent uncertainties in the model significantly degrade the con-
survey (Schrabback et al.
Le F` evre et al.2004;
straining power of a cosmic shear survey for dark energy
and modified gravity cosmological models. This work deep-
ened the conclusions of Bernstein (2009); Joachimi & Bridle
(2009) and expanded them into the MG domain.
What is encouraging, however, is that the use of
position-position correlations, nn, and particularly position-
shear, nǫ, cross-correlations can go some way towards mit-
igating the impact of IAs. This data is already collected
by a standard WL survey. In the presence of IAs, con-
straints from ǫǫ + nǫ + nn are roughly twice as strong as
those from ǫǫ alone. Until now, the discussion of optimal
survey parameters has generally assumed that ǫǫ correla-
tions alone will be included, without IAs. In this paper we
investigate the impact of survey strategy and design on dif-
ferent combinations of probes, with and without IAs. This
is a continuation of the cosmic shear survey optimisation
work begun by, among others, Amara & Refregier (2006);
Bridle & King (2007); Joachimi & Bridle (2009); Ma et al.
(2006); Huterer et al. (2006); Huterer et al. (2006)
In this paper we expand on the work on LBKB to fully
understand how the observing strategy of a given survey is
central to the type of data and the quality of results that sur-
vey will produce. Different survey geometries with the same
instrument will produce different statistical errors due to a
different balance between survey characteristics, the most
important for cosmic shear being survey area galaxy num-
ber density on the sky and median redshift of the galaxy
distribution. Other properties such as required redshift ac-
curacy are important guidelines for instrument designers
and those preparing analysis pipelines and follow-up or cali-
bration studies (Amara & Refregier 2006). While more area
and increased number density will always be desirable, it
is important to keep firm goals in mind when producing
desiderata for future surveys which will always be limited by
technology and finite observing time. In particular learning
about dark energy and modified gravity may benefit from
different survey strategies and call for the prioritisation of
different properties.
The paper is organised as follows: in section 2, we sum-
marise our standard cosmology, fiducial surveys and models
for deviations from GR, Intrinsic Alignments and bias pa-
rameterisation, as well as our figures of merit for DE and
MG. In section 3 we investigate the sensitivity of dark en-
ergy and modified gravity constraints to changes in survey
specification. In section 3.1 we present the effect of varying
survey area and the impact of finite survey time on overall
strategy and the ability to constrain MG. The importance
of photometric redshift accuracy is addressed in sections 3.2
and 3.3. Conclusions are made in section 4.
2COSMOLOGICAL SET-UP
The paper deals with the impact of various aspects of sur-
vey strategy and redshift quality on the power of cosmic
shear and galaxy position information to constrain dark en-
ergy and deviations from General Relativity. In 2.1 we sum-
marise our cosmic shear formalism, 2.2 extends it to include
intrinsic alignments and 2.3 adds galaxy position auto- and
cross-correlations and introduces a coherent biasing formal-
ism for IAs and galaxy bias. 2.4 reviews the MG parameter-
isation we use and how it enters our angular power spectrum
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Optimising cosmic shear surveys to measure modifications to gravity3
integrals. In 2.5 we summarise some basic cosmology we use
throughout the paper and 2.6 describes the fiducial survey
parameters we use in the following sections.
2.1 Cosmic Shear
Cosmic shear is the shape-distortion induced in the image
of a distant galaxy due to the bending of its light by gravity
as it passes massive structure in the Universe. If we assume
General Relativity holds then we can define the cosmic shear
angular power spectrum under the Limber approximation as
CGG
ij (l) =
?
dχ
χ2Wi(χ)Wj(χ)Pδδ(k,z) (1)
where Pδδ(k,z) is the three dimensional matter power spec-
trum, χ is the comoving distance in units of h−1Mpc and
W(χ) is the lensing efficiency function
Wi(χ) =4πG
c2ρ(z)a2(z)χ
?
dχ′ni(χ′)χ′− χ
χ′
(2)
2.2 Intrinsic Alignments
The intrinsic alignment (IA) of galaxy ellipticities is a prime
contaminant to the measured cosmic shear signal. A naive
approach to cosmic shear assumes that galaxy’s intrinsic el-
lipticities are randomly distributed on the sky so, when we
average over observed ellipticity in a small patch, intrinsic
ellipticity cancels and we are left with the induced shear.
Unfortunately, this assumption is invalid because
galaxy ellipticities are aligned due to two effects arising from
the same physical intrinsic alignment origin. Physically close
galaxies tend to align with the local gravitational tidal field
and so are positively correlated with each other, this is the
Intrinsic-Intrinsic (II) alignment. Background galaxies can
have their light lensed by foreground gravitational fields
which align the intrinsic ellipticity of foreground galaxies.
This induces an anti-correlation and is the gravitational-
intrinsic (GI) alignment.
We follow the procedure of LBKB and implement IAs
using an updated version of the corrected LA model of
Hirata & Seljak (2004), incorporating their correction of er-
ratum 2010 and assuming that all IA physics occurs at a
high-z epoch of galaxy formation hence the IA signal de-
pends only on the linear matter power spectrum rather
than the subsequent nonlinear evolution. The rest of the
LA model enters as a factor of
bI = −C1ρm(z = 0)(3)
where ρm(z = 0) is the matter density today and C1 =
5×10−14(h2M⊙Mpc−3)−1is the amplitude of the IA term,
normalised to redshift zero (Bridle & King 2007). This fac-
tor appears in the IA projected angular power spectra,
linearly in the Gravitational-Intrinsic (GI) correlation and
squared for the Intrinsic-Intrinsic (II). The window function
associated with IAs is the galaxy redshift distribution, n(z),
see table 1 for the full angular power spectra equations.
In section 2.3 we expand our notation to allow nuisance
parameters to parameterise our knowledge of IAs, galaxy
bias and their cross-correlations. In this more general case
bI given in eqn. 3 becomes the fiducial value of a variable IA
term which appears quadratically in the II power spectrum
and linearly in the GI and gI power spectra.
The total observed lensing signal is then the sum of the
cosmic shear and the IA terms
Cǫǫ
l = CGG
l
+ CII
l
+ CGI
l
.(4)
2.3Galaxy Position Data
A cosmic shear survey contains galaxy position information
(angular position on the sky and redshift) as well as mea-
surements of galaxy shear. Joachimi & Bridle (2009) provide
a formalism for including this additional information in cos-
mological parameter constraints and show how this extra
information can serve to partially mitigate the impact of
IAs. This approach follows from the work of Zhang (2008);
Hu & Jain (2004)
The extra observables we use are galaxy position-
position power spectra and the position-shear cross-spectra,
defined analogously to the shear-shear power spectrum:
Cnn
l
Cnǫ
l
= Cgg
l
(5)
= CgI
l
+ CgG
l
. (6)
We now assign nuisance parameters to each component Cl
in a self-consistent way as explained in LBKB. The four
bias function are bg, bI, rg and rI. bg and bI model bias
from galaxy position and IAs amplitudes, and their cross-
correlations are modelled by rg and rI. This unified ap-
proach was first introduced by Bernstein (2009). Table 1
summarises the full power spectra equations, consistent with
the definitions in LBKB eqns. 37, 38, 43 and 44.
We let each bias parameter vary in amplitude and as a
function of scale and redshift using a Nk×Nz grid of free pa-
rameters interpolated over k-,z-space, i.e. each nuisance fac-
tor, bX = AxQX(k,z) is the product of a variable constant
amplitude parameter, AX, and a variable grid, QX(k,z) in
k and z. Throughout this paper the grid size is set to the
fiducial value of Nk= Nz = 5, which means marginalisation
over 104 nuisance parameters when the full ǫǫ+nǫ+nn probe
combination is considered in the presence of IAs. The nui-
sance parameters multiply linearly into the angular power
spectra integrands and each power spectrum depends on a
subset of the bias parameters as follows:
CGG
l
CII
l
CGI
l
:− ,
bIbI,
bIrI,
CgG
l
CgI
l
Cgg
l
:
:
:
bgrg
:
:
bgbIrgrI
bgbg
(7)
As mentioned in the previous section, the fiducial value of
bI is given by eqn. 3. bg has fiducial value 1 while rg and rI
vary around the fiducial value 0.9 to avoid more than perfect
cross-correlation.
We have ignored the effect of lensing magnification and
followed LBKB and Joachimi & Bridle (2009) in applying a
cut on multipole l to any redshift bin combination ij which
includes galaxy position information (i.e. nn or nǫ) accord-
ing to ℓmax(i) = kmax
for uncertainties in the galaxy bias model at small scales.
For nǫ bin pairs, the cut is made on the galaxy, i.e. n, bin.
For position-position, nn, pairs there is a choice of bin on
which to apply the cut. We follow Joachimi & Bridle (2009)
in making the optimistic choice and cutting on the higher
redshift bin. Shear-shear, ǫǫ, pairs do not depend on galaxy
bias and are therefore used up to the full range in l.
lin (z(i)
med)χ(z(i)
med). This aims to account
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4Donnacha Kirk, Istvan Laszlo, Sarah Bridle, Rachel Bean
Table 1. Summary of the projected angular power spectra considered in this work.
Correlation2D PS
ShearCGG
ij
(l) =?dχ
ij(l) =?dχ
CII
Cgg
CgG
χ2Wi(χ)Wj(χ)
χ2Wi(χ)nj(χ)Q(z)Q(zf)R(zf)(1 +R(z)
ij(l) =?dχ
ij(l) =?dχ
ij(l) =?dχ
CgI
χ2ni(χ)nj(χ)Q(zf)R(zf)bg(k,z)bI(k,z)rg(k,z)rI(k,z)
Cǫǫ
ij
+ CII
ij
Cnn
ijij
Cnǫ
ij
?
Q(z)1+R(z)
2
?2Pδδ(k,z)
Intrinsic-shearCGI
2
)bI(k,z)rI(k,z)
√Pδδ(k,zf)Pδδ(k,z)
D(zf)
Intrinsic
χ2ni(χ)nj(χ)b2
χ2ni(χ)nj(χ)b2
χ2ni(χ)Wj(χ)Q(z)1+R(z)
ij(l) =?dχ
ij= CGG
= Cgg
ij= CgI
I(k,z)Q2(zf)R2(zf)Pδδ(k,z)
g(k,z)Pδδ(k,z)
bg(k,z)rg(k,z)Pδδ(k,z)
Galaxy clustering
Clustering-shear
2
Clustering-intrinsic
√Pδδ(k,zf)Pδδ(k,z)
D(zf)
Galaxy ellipticity (observable)
Galaxy number density (observable)
Number density-ellipticity (observable)
ij+ CGI
ij+ CgG
2.4Modified Gravity
There are a large number of modifications or extensions
of Einstein’s general theory of relativity on cosmic scales
which come under the general heading of Modified Grav-
ity theories. These can be motivated by the presence of
extra dimensions, as in DGP, or extra degrees of freedom
compared to the GR action equation, as in f(R), TeVeS
etc. (Dvali et al. 2000; Carroll et al. 2006; Skordis 2009;
Jain & Khoury 2010). As in LBKB, we do not assume a
particular modified theory of gravity but rather concentrate
on “trigger parameters” whose deviation from their GR val-
ues would indicate the presence of some physics beyond that
in the standard GR picture.
In the conformal newtonian gauge the metric for a flat
FRW spacetime is written
ds2= −a(τ)2[1 + 2ψ(x,t)]dτ2+ a(τ)2[1 − 2φ(x,t)]dx2
(8)
where ψ and φ are the scalar potentials which describe per-
turbations to the time- and space-parts of the metric respec-
tively. We parameterise deviations from GR through two
parameters, Q and R. One alters the way the Newtonian
potential responds to mass via the Poisson equation,
k2ψ(x,t) = −4πGQρa2δ (9)
and the other modifies the ratio of the metric potentials
ψ(x,t) = Rφ(x,t)(10)
Q and R are assumed to be scale-independent and vary with
redshift as
Q = (Q0− 1)as
R = (R0− 1)as
(11)
(12)
where a is the scale-factor and Q0,R0 are the free parame-
ters we vary for MG, and s = 3. We are interested in MG
theories which explain the acceleratin expansion of the Uni-
verse observed at late times. s = 3 allows any modification
to “turn-on” and late times and avoids violating early Uni-
verse constraints from the Cosmic Microwave Background
(CMB) and Big Bang Nucleosynthesis (BBN).
The modified gravity parameters enter the projected
angular power spectra in different combinations, as shown
in Table 1, due to their different dependencies on the mater
density field. As well as modifying the angular power spec-
tra, Q and R enter the angular power spectrum integrals
via their response to the metric potentials through the
Fiducial Survey Paramters
ParameterStage IIIStage IV
Area
ng
σγ
Nz
δz
fcat
∆z
z0
α
β
5,000deg2
10
0.23
5
0.07
0
1
0.8/1.412
2
1.5
20,000deg2
35
0.35
10
0.05
0
1
0.9/1.412
2
1.5
Table 2. Fiducial survey parameter values for the DES-like (stage
III) and Euclid-like (stage IV) surveys.
linear growth function. The potential for weak lensing to
constrain deviations from GR has previously been noted
in Bean & Tangmatitham (2010); Laszlo & Bean (2008);
Beynon et al. (2009).
The full projected angular power spectra, including IAs,
MG and bias parameters, is summarised in Table 1. Note
also that deviations from GR will also manifest in the growth
function which produces the matter power spectra in Ta-
ble 1. We include modifications to growth via a ratio of
MG/GR power spectra calculated using the modified ver-
sion of CAMB used for LBKB. For ease, LBKB also provide
a fitting function to compute this ratio over a range of Q0,
R0 and s values.
2.5General Cosmology
Throughout this paper we assume a flat ΛCDM cosmological
model with fiducial parameter values equal to the WMAP7
best-fit values: Ωm = 0.262, Ωb= 0.0445, w0 = −1, wa = 0,
σ8 = 0.802, h = 0.714, ns = 0.969, Ων = 0. Where Ωm,Ωb
and Ων are the dimensionless matter, baryon and neutrino
densities respectively, w0 and wa are the dark energy equa-
tion of state parameters (Albrecht et al. 2006),σ8 is the nor-
malisation of the linear matter power spectrum, h is the di-
mensionless Hubble parameter today and nsis the power law
of the primordial power spectrum. The linear matter power
spectrum is given by the fitting formula of Eisenstein & Hu
(1998), with nonlinear corrections from Smith et al. (2003).
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Optimising cosmic shear surveys to measure modifications to gravity5
When we treat MG we assume that the background
expansion of the Universe is consistent with our fiducial dark
energy model and deviations due to non-GR physics enter
through the growth of structure from initial perturbations.
Unless otherwise specified all plots include CMB priors from
a Planck-type survey as described in LBKB. We divide our
survey galaxy redshift distributions into redshift slices with
equal galaxy number density to allow redshift tomography
where auto- and cross-correlations of these redshift bins are
considered, allowing us to measure redshift evolution of the
observables.
We calculate constraints on cosmological parameters us-
ing the Fisher Matrix formalism
Fµν =
Nd
?
m,n
Nmax
l?
l
∂Dm(l)
∂pµ
Cov−1
mn(l)∂Dn(l)
∂pν
(13)
where m, n label tomographic redshift bins, Dm(l) is the
data vector, in our case some combination of the angular
power spectra Cǫǫ
l
and Cnn
ance matrix, defined as in Joachimi & Bridle (2009), pµ are
the parameters varied and Nd is the number of indepen-
dent combinations of tomographic bins. Unless otherwise
stated the Fisher matrix varies the cosmological parameters:
p = {Ωm,w0,wa,h,σ8,Ωb,ns}.
Using the Fisher matrix formalism the lower limit on
the minimum variance bound on the error of a parameter pµ
marginalised over all other parameters of interest, is given
by σ(pµ) =
?(F−1)µµ. We quote results in terms of the
l, Cnǫ
l
. Covmn(l) is the covari-
DETF FoM for Dark Energy
FoMDE =
1
?
det?(F−1
GR)w0,wa
?. (14)
Here (F−1
matrix for cosmological and nuisance parameters excluding
the MG parameters are excluded (these are fixed at their
GR values). The FoM is proportional to the inverse of the
area of the constraint contour in w0− wa space.
By analogy we define a MG FoM as
GR)w0,wais the 2×2 submatrix of the inverted Fisher
FoMMG =
1
?
det?(F−1)Q0,Q0(1+R0/2)
?. (15)
where we have inverted the full fisher matrix including the
modified gravity parameters and dark energy parameters.
2.6 General Survey Parameters
LBKB investigated the degeneracy between IAs and MG pa-
rameters for a fixed survey specification. It was found that
the inclusion of a realistic IA model reduced the FoM (dark
energy or MG) for a typical stage-IV cosmic shear survey
by ∼70%. The effect could be substantially mitigated by
the inclusion of galaxy position data and galaxy-shear cross-
correlations. The constraining power of ǫǫ+nǫ+nn, includ-
ing IAs, is roughly double that of ǫǫ, including IAs, alone.
We showed that our results were robust to different num-
bers of free nuisance parameters, accounting for flexibility
in the galaxy clustering and IA bias models. The results
were broadly similar for attempts to constrain dark energy
equation of state parameters and deviations from GR.
In this paper we vary certain survey parameters around
a fiducial cosmic shear survey set-up, corresponding to Stage
IV project. This survey has an area = 20000deg2, number
density of galaxies projected onto the sky, ng = 35 arcmin−2,
and galaxy intrinsic ellipticity dispersion, σγ = 0.35, a Gaus-
sian photometric redshift scatter of width δz = 0.05 which
is related to the (redshift dependent) rms photometric dis-
persion via σz(z) = (1+z)δz, with a fraction of catastrophic
outliers, fcat = 0. We analyse the results using cosmic shear
tomography with 10 tomographic redshift bins of equal num-
ber density.
The redshift distribution of galaxes, n(z) is assumed to
be given by a Smail-type distribution (Smail et al. 1994)
n(z) ∝ zαexp
?
−z
z0
?β
(16)
with α = 2, β = 1.5 and z0 = zm/1.412, where the median
redshift, zm = 0.9.
For comparison purposes, some results are also pre-
sented for the stage-III Dark Energy Survey (DES), due to
see first light in early 2012. Table 2 summarises the specifi-
cations for both surveys.
3SURVEY SPECIFICATIONS AND
FORECAST CONSTRAINTS
In this section we analyse the sensitivity of the prospective
dark energy and modified gravity figures of merit on vari-
ations in survey specification, principally focusing on their
relationship to the survey area and depth, and the precision
of the photometric redshift measurements when uncertain-
ties in how intrinsic alignments are included in the modeling.
Throughout, we quantify constraints using the dark en-
ergy (DE) and modified gravity (MG) figures of merit in
(14) and (15) normalised relative to a ‘baseline’ figure of
merit for the shear-only auto-correlations ‘GG’, with IAs
excluded, using the fiducial survey described in Table 2.
3.1Survey area
Figs. 1 and 2 present the key results showing how the con-
straining power of a survey, for dark energy equation of state
and modified gravity parameters, varies with the survey
area. We consider two alternative approaches, firstly a sim-
ple option where the increased area derives from an increase
in survey time, and secondly a more realistic option when
survey time is fixed, and increased survey area is achieved
by a reduction in survey depth/ limiting flux.
Let us first consider the case where all survey parame-
ters are kept fixed except for the survey area. We focus on
the quantitative implications for the Stage IV survey, the
results for a Stage III survey, presented in figure 2 are qual-
itatively similar.
When IAs are excluded from the analysis the improve-
ment in FoM with increasing area can be roughly described
by a power law dependence FoM∝Areaxwith x = 0.4 and
0.7 for CMB+shear correlations alone for the DE and MG
FoMs. The MG FoM is slightly more sensitive to changes in
area than the DE FoM. The DE index is lower than that
reported in Amara & Refregier (2006) only because of the
inclusion of, survey area independent, CMB priors.
c ? 2009 RAS, MNRAS 000, 1–13