Sistemas procesales en relación con el proceso penal

In addition to the baseline Euclid surveys, a possibility may exist for an auxiliary Euclid survey, for example focused on Type Ia supernovae. Type Ia supernovae used as standardized candles (luminosity distance indicators) led to the discovery of cosmic acceleration and they retain signif- icant leverage for revealing the nature of dark energy. Their observed flux over the months after explosion (the light curve) is calibrated by an empirical brightness–light curve width relation into a luminosity distance multiplied by a factor involving the unknown absolute brightness and Hubble constant. This nuisance factor cancels when supernovae at different redshifts are used as a relative distance measure. The relative distance is highly sensitive to cosmic acceleration and provides strong complementarity with other cosmological probes of dark energy, at the same or different redshifts.

Another advantageous property of supernovae is their immunity to systematics from cosmology theory – they are purely geometric measures and do not care about the matter power spectrum, coupling to dark matter, cosmologically modified gravity, dark energy clustering, etc. Their astro- physical systematics are independent of other probes, giving important crosschecks. The cosmolog- ical parameter likelihood function arising from supernovae constraints can to a good approximation simply be multiplied with the likelihood from other probes. Current supernovae likelihoods are in user friendly form from the joint lightcurve analysis (JLA) of the Supernova Legacy Survey (SNLS) and Sloan Digital Sky Survey (SDSS) of [175] or the Union2.1 compilation of [1136]. In the near future the Union3 compilation should merge these sets and all other current supernova data, within an improved Bayesian framework.

The Euclid Supernovae Science Working Group proposed a six month auxiliary survey with Euclid, the Dark Energy Supernova InfraRed Experiment (DESIRE) [85]. This delivers substantial improvements on dark energy equation of state constraints relative to ground-based supernova surveys, with a 50% higher figure of merit, as shown in Table 15.

Table 15: Cosmological performance of the simulated surveys. The FoMs assume a 1-D geometrical

Planckprior and flatness. zp is the redshift at which the equation of state uncertainty reaches its

minimumσ(wp). The FoM is defined as [Det(Cov(w0, wa))]−1/2 = [σ(wa)σ(wp)]−1 and accounts

for a suite of systematic uncertainties (see [85]).

σ(wa) zp σ(wp) FoM low-z + LSST-DDF 0.22 0.25 0.022 203.2 + DESIRE low-z + LSST-DDF 0.28 0.22 0.026 137.1 LSST-DDF + DESIRE 0.40 0.35 0.031 81.4

Other dark-energy projects will enable the cross-check of the dark-energy constraints from Euclid. These include Planck, BOSS, WiggleZ, HETDEX, DES, Panstarrs, LSST, BigBOSS and SKA.

Planck will provide exquisite constraints on cosmological parameters, but not tight constraints on dark energy by itself, as CMB data are not sensitive to the nature of dark energy (which has to be probed atz <2, where dark energy becomes increasingly important in the cosmic expansion history and the growth history of cosmic large scale structure). Planck data in combination with Euclid data provide powerful constraints on dark energy and tests of gravity. In the next Section 1.8.9.1, we will discuss how to create a Gaussian approximation to the Planck parameter constraints that can be combined with Euclid forecasts in order to model the expected sensitivity.

The galaxy redshift surveys BOSS, WiggleZ, HETDEX, and BigBOSS are complementary to Euclid, since the overlap in redshift ranges of different galaxy redshift surveys, both space and ground-based, is critical for understanding systematic effects such as bias through the use of multiple tracers of cosmic large scale structure. Euclid will survey Hα emission line galaxies at 0.5< z <2.0 over 15,000 square degrees. The use of multiple tracers of cosmic large scale structure can reduce systematic effects and ultimately increase the precision of dark-energy measurements from galaxy redshift surveys [see, e.g., 1067].

Currently on-going or recently completed surveys which cover a sufficiently large volume to measure BAO at several redshifts and thus have science goals common to Euclid, are the Sloan Digital Sky Survey III Baryon Oscillations Spectroscopic Survey (BOSS for short) and the WiggleZ survey.

BOSS13 _{maps the redshifts of 1.5 million Luminous Red Galaxies (LRGs) out toz∼0.7 over}

10,000 square degrees, measuring the BAO signal, the large-scale galaxy correlations and extracting information of the growth from redshift space distortions. A simultaneous survey of 2.2< z <3.5 quasars measures the acoustic oscillations in the correlations of the Lyman-αforest. LRGs were chosen for their high bias, their approximately constant number density and, of course, the fact that they are bright. Their spectra and redshift can be measured with relatively short exposures in a 2.4 m ground-based telescope. The data-taking of BOSS will end in 2014.

The WiggleZ14_{survey is now completed, it measured redshifts for almost 240,000 galaxies over}

1000 square degrees at 0.2 < z < 1. The target are luminous blue star-forming galaxies with spectra dominated by patterns of strong atomic emission lines. This choice is motivated by the fact that these emission lines can be used to measure a galaxy redshift in relatively short exposures of a 4 m class ground-based telescope.

Red quiescent galaxies inhabit dense clusters environments, while blue star-forming galaxies trace better lower density regions such as sheets and filaments. It is believed that on large cosmo-

13

http://www.sdss3.org/surveys/boss.php

logical scales these details are unimportant and that galaxies are simply tracers of the underlying dark matter: different galaxy type will only have a different ‘bias factor’. The fact that so far results from BOSS and WiggleZ agree well confirms this assumption.

Between now and the availability of Euclid data other wide-field spectroscopic galaxy redshift surveys will take place. Among them, eBOSS will extend BOSS operations focusing on 3100 square degrees using a variety of tracers. Emission line galaxies will be targeted in the redshift window 0.6< z <1. This will extend to higher redshift and extend the sky coverage of the WiggleZ survey. Quasars in the redshift range 1 < z <2.2 will be used as tracers of the BAO feature instead of galaxies. The BAO LRG measurement will be extended toz∼0.8, and the quasar number density atz >2.2 of BOSS will be tripled, thus improving the BAO Lyman-αforest measure.

HETDEX aims at surveying 1 million Lyman-α emitting galaxies at 1.9 < z < 3.5 over 420 square degrees. The main science goal is to map the BAO feature over this redshift range.

Further in the future, we highlight here the proposed BigBOSS survey and SuMIRe survey with HyperSupremeCam on the Subaru telescope. The BigBOSS survey will target [OII] emission line galaxies at 0.6 < z < 1.5 (and LRGs at z <0.6) over 14,000 square degrees. The SuMIRe wide survey proposes to survey∼2000 square degrees in the redshift range 0.6< z <1.6 targeting LRGs and [OII] emission-line galaxies. Both these surveys will likely reach full science operations roughly at the same time as the Euclid launch.

Wide field photometric surveys are also being carried out and planned. The on-going Dark Energy Survey (DES)15_{will cover 5000 square degrees out toz∼1.3 and is expected to complete}

observations in 2017; the Panoramic Survey Telescope & Rapid Response System (Pan-STARRS), on-going at the single-mirror stage, The PanSTARSS survey, which first phase is already on-going, will cover 30,000 square degrees with 5 photometry bands for redshifts up toz∼1.5. The second pause of the survey is expected to be competed by the time Euclid launches. More in the future the Large Synoptic Survey Telescope (LSST) will cover redshifts 0.3< z <3.6 over 15,000 square degrees, but is expected to begin operations in 2021, after Euclid’s planned launch date. The galaxy imaging surveys DES, Panstarrs, and LSST will complement Euclid imaging survey in both the choice of band passes, and the sky coverage.

SKA (which is expected to begin operations in 2020 and reach full operational capability in 2024) will survey neutral atomic hydrogen (HI) through the radio 21 cm line, over a very wide area of the sky. It is expected to detect HI emitting galaxies out to z ∼ 1.5 making it nicely complementary to Euclid. Such galaxy redshift survey will of course offer the opportunity to measure the galaxy power spectrum (and therefore the BAO feature) out to z ∼1.5. The well behaved point spread function of a synthesis array like the SKA should ensure superb image quality enabling cosmic shear to be accurately measured and tomographic weak lensing used to constrain cosmology and in particular dark energy. This weak lensing capability also makes SKA and Euclid very complementary. For more information see, e.g., [1000, 188].

Figure 35 puts Euclid into context. Euclid will survey Hαemission line galaxies at 0.5< z <2.0 over 15,000 square degrees. Clearly, Euclid with both spectroscopic and photometric capabilities and wide field coverage surpasses all surveys that will be carried out by the time it is launched. The large volume surveyed is crucial as the number of modes to sample for example the power spectrum and the BAO feature scales with the volume. The redshift coverage is also important especially at z <2 where the dark-energy contribution to the density of the universe is non-negligible (atz >2 for most cosmologies the universe is effectively Einstein–de Sitter, therefore, high redshifts do not contribute much to constraints on dark energy). Having a single instrument, a uniform target selection and calibration is also crucial to perform precision tests of cosmology without having to build a ‘ladder’ from different surveys selecting different targets. On the other hand it is also easy to see the synergy between these ground-based surveys and Euclid: by mapping different targets (over the same sky area and ofter the same redshift range) one can gain better control over issues

Figure 35: Redshift coverage and volume for the surveys mentioned in the text. Spectroscopic surveys only are shown. Recall that while future and forthcoming photometric surveys focus on weak gravitational lensing, spectroscopic surveys can extract the three dimensional galaxy clustering information and therefore measure radial and tangential BAO signal, the power spectrum shape and the growth of structure via redshift space distortions. The three-dimensional clustering information is crucial for BAO. For example to obtain the same figure of merit for dark-energy properties a photometric survey must cover a volume roughly ten times bigger than a spectroscopic one.

such as bias. The use of multiple tracers of cosmic large scale structure can reduce systematic effects and ultimately increase the precision of dark-energy measurements from galaxy redshift surveys [see, e.g., 1067].

Moreover, having both spectroscopic and imaging capabilities Euclid is uniquely poised to ex- plore the clustering with both the three dimensional distribution of galaxies and weak gravitational lensing.

1.8.9.1 The Planck prior

Planck will provide highly accurate constraints on many cosmological parameters, which makes the construction of a Planck Fisher matrix somewhat non-trivial as it is very sensitive to the detailed assumptions. A relatively robust approach was used by [892] to construct a Gaussian approximation to the WMAP data by introducing two extra parameters,

R≡

q

ΩmH02r(zCMB), la≡πr(zCMB)/rs(zCMB), (1.8.38)

wherer(z) is the comoving distance from the observer to redshiftz, andrs(zCMB) is the comoving

size of the sound-horizon at decoupling.

In this scheme, la describes the peak location through the angular diameter distance to de-

coupling and the size of the sound horizon at that time. If the geometry changes, either due to non-zero curvature or due to a different equation of state of dark energy,lachanges in the same way

as the peak structure. Rencodes similar information, but in addition contains the matter density which is connected with the peak height. In a given class of models (for example, quintessence dark energy), these parameters are “observables” related to the shape of the observed CMB spectrum, and constraints on them remain the same independent of (the prescription for) the equation of state of the dark energy.

As a caveat we note that if some assumptions regarding the evolution of perturbations are changed, then the corresponding R and la constraints and covariance matrix will need to be

recalculated under each such hypothesis, for instance, if massive neutrinos were to be included, or even if tensors were included in the analysis [342]. Further, R as defined in Eq. (1.8.38) can be badly constrained and is quite useless if the dark energy clusters as well, e.g., if it has a low sound speed, as in the model discussed in [714].

In order to derive a Planck fisher matrix, [892] simulated Planck data as described in [924] and derived constraints on our base parameter set {R, la,Ωbh2, ns} with a MCMC based likelihood

analysis. In addition to Rand la they used the baryon density Ωbh2, and optionally the spectral

index of the scalar perturbationsns, as these are strongly correlated withR andla, which means

that we will lose information if we do not include these correlations. As shown in [892], the resulting Fisher matrix loses some information relative to the full likelihood when only considering Planck data, but it is very close to the full analysis as soon as extra data is used. Since this is the intended application here, it is perfectly sufficient for our purposes.

The following tables, from [892], give the covariance matrix for quintessence-like dark energy (high sound speed, no anisotropic stress) on the base parameters and the Fisher matrix derived from it. Please consult the appendix of that paper for the precise method used to computeR and la as the results are sensitive to small variations.