Dark Energy

Baryon Acoustic Oscillations :: Type Ia Supernovae (SNe) :: Weak Lensing (WL)

Baryon Acoustic Oscillations (BAO)

Cartoon of BAO spherical shell with H(z) and DA(z) measurements.

All of the structure in the Universe observed today was initially seeded by primordial matter density fluctuations in the early Universe. Initial regions of over-density were also regions of greater than average pressure which drove the expansion of spherical sound waves. In particular, photons, electrons, and the baryon gas behaved as a single fluid until the expansion and cooling of the Universe reached the epoch of decoupling, leaving an extra abundance of baryons in spherical shells around the initially over-dense regions. The cosmic microwave background (CMB) photons free streamed away. The sky is filled with these spherical shells of baryons with fixed radii at decoupling of 153 Mpc, corresponding to the size of the horizon at the drag epoch (which occurred shortly after decoupling, when baryons overcame the pressure of photons to undergo gravitational collapse). The power spectrum of the galaxy distribution map shows the series of oscillatory peaks and troughs from these baryon acoustic oscillations.

WMAP provided the BAO calibration (Bennett et al. 2003; Komatsu et al. 2009), and future calibration improvements will come from the Planck mission. This established a "standard ruler" against which the Universe can be measured (Eisenstein & Bennett 2008). The shells of gas around the initial over-dense locations enhance the probability that galaxies formed with separations on the BAO scale. In 2005, the expected ~ 1% excess galaxy correlation was observed at the expected scale (Eisenstein et al. 2005).

Because galaxy correlations are enhanced by only 0.01 at the BAO scale, the use of BAO to probe dark energy requires that accurate redshifts and positions of large numbers of galaxies be observed over large regions of the sky. Observations of the spherical sound waves are possible both along the line-of-sight and transverse to the line of sight. The transverse measurement requires the two-dimensional positions of galaxies. This is especially useful if there is information about the redshifts of the same galaxies.

Taking the tangential co-moving size as the sound horizon at the drag epoch, measured by the CMB, the tangential BAO measurements result in a measure of the angular diameter distance. The angular diameter distance is robustly based on the geometry between the observer and the horizon. This provides a distance similar to that of Type Ia supernovae but based on different physical processes. It has fewer known systematics and good statistics at z>1. At low redshifts, where there is insufficient cosmic volume for the BAO to achieve strong constraints and nonlinear effects become significant, the supernovae are singularly invaluable. The power of BAO dark energy measurements increases with redshift

Taking the co-moving size as the sound horizon at the drag epoch, the radial BAO gives the most precise direct measurement of the expansion rate H(z). Also, the BAO measurements require only spectroscopic galaxy redshifts and positions, two of the least demanding and best established measurements in astrophysics.

WFIRST will dwarf previous galaxy redshift surveys by measuring millions of galaxy redshifts. The wide-field spectrometer will simultaneously disperse the light from all of the galaxies in the field of view, providing redshifts from the bright H-α spectral line. Three dimensional galaxy positions (α, δ, z) will also be accurately determined.

WFIRST enables a large advance over ground-based BAO surveys in two key ways:

Space NIR measurements have ~1000 times less background than those from the ground which must contend with the bright atmosphere. Broad-band, sensitive NIR coverage, which is uniquely available from space, enables a galaxy survey using the H-α spectral line at z<2. This provides a greatly expanded cosmic volume for BAO observations compared to that available from the ground.
A space mission gives nearly uniform coverage over a large part of the sky with tight systematics control. WFIRST can perform a redshift survey of millions of galaxies and harvest the full available BAO information to near the cosmic variance limit.

Redshift Space Distortions

Peculiar velocities of galaxies lead to systematic differences between redshift-space and real-space measurements, and the effects are a combination of large-scale coherent flows induced by the gravity of large-scale structure, and a small-scale random peculiar velocity of each galaxy. The large-scale flows compress the contours of the galaxy redshift-space two-point correlation function along the line of sight, with the degree of compression determined by the growth rate of cosmic large scale structure and the bias factor between galaxy and matter distributions. The small-scale random motion of galaxies leads to a smearing in the radial direction, known as the "Finger of God" effect. Thus the measured 3D galaxy distribution on large scales from the sky positions and redshifts of galaxies provides a direct measurement of the cosmic large structure growth rate, which enables us to test general relativity, and differentiate between an unknown energy component and a modification of gravity as the true nature of dark energy. The angular diameter measurement and the expansion rate measurement form a built-in check of systematic errors. The Alcock-Paczynski (1979) test provides an additional cross-check. Comparison with weak lensing measurements is another cross-check.

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Type Ia Supernovae (SNe)

The Hubble diagram for SN Ia observations from the ground and space (HST). Plotted is the distance modulus, μ = apparent magnitude - absolute magnitude as a function of redshift.

Type Ia supernovae are believed to be the explosive disintegrations of a white dwarf star in a binary system that accretes material in excess of its Chandrasekhar stability limit of 1.38 solar masses. Because the progenitor masses of such supernovae are nearly all the same, the total energy released is expected to be the same (around 10⁴⁴ Joules), and thus they offer the potential of providing excellent standard candles. For a known supernova luminosity L_SN, and measured flux F, the relation F = L_SN/4πD_L² can be used to calculate the luminosity distance D_L directly. Certain spectral features in the supernova light may be used to identify the redshift, thereby providing a primary observable of the effect of dark energy: the distance-redshift relation D(z).

The acceleration of the Universe was initially discovered using Type Ia supernova observations at redshifts of z ≤ 0.9. More recently, SNe beyond z = 1 observed from the Hubble Space Telescope (HST) have been employed to observe the transition from an initially matter-dominated Universe to the present dark energy dominance (see figure at right from Kowalski et al. 2008). The SN technique currently shows a dark-energy signal with strong statistical significance and has advanced several generations beyond the original detection. It is thus a mature method with well developed study of systematics. This allows a WFIRST mission to be designed that specifically targets the systematics to bring them below the statistical uncertainties. These include the effects of reddening, a variation of the luminosity with the rest-frame duration of the event (referred to as the light curve width correction), and the variations in luminosity that depends on other properties of the SN or its host galaxy. It is believed that the variations in luminosity can be correlated with other, distance-independent, features of the supernova light curve, spectrum, or host galaxy. Thus Type Ia SNe are standardizable, to a high, systematics-limited degree of precision. This standardization process is empirical, and for WFIRST will rely on having well-sampled light curves and spectra, and with sufficient numbers of events that subsampling for comparison and the estimation of systematic errors from various effects can be examined.

WFIRST will measure the properties of more than a thousand supernovae. A regular cadence of ≤5 days will sample the light curve of all supernovae to provide for correction, while spectroscopy provides simultaneous typing, redshift determination, and other spectral information. Observations covering the visible through near-infrared permit a significant overlap of the entire rest-frame visible light in both photometry and spectroscopy for all events, regardless of redshift.

WFIRST enables a large advance over ground-based SN surveys in five ways:

The low background and high efficiency of a wide-field imaging space telescope permit rapid monitoring of a large number of z~1 galaxies to find and follow many more supernovae than can readily be discovered from the ground. As redshifts increase past z ~0.8, discovery of SNe becomes increasingly difficult form the ground.
The low NIR background, compact PSF, plus weather-free space environment offers high signal-to-noise observations with superior photometric accuracy.
The light curves of SNe can be acquired in a homogeneous, gap-free manner since the space environment has no cloudy or moonlit periods.
Spectroscopy in the near-infrared can process spectra in the rest-frame visible at redshifts higher than would be possible from the ground, permitting accurate typing, redshift derivation, and tracking of spectral features around the time of peak light. Such spectral features can yield intrinsically lower dispersion in the final Hubble diagram and SN Ia subset comparisons to test evolution systematics.
Photometry in the rest-frame infrared, available to WFIRST, has been found to yield intrinsically lower dispersion in the final Hubble diagram as compared to photometry in the rest-frame visible.

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Weak Lensing (WL)

Illustration of the Weak Lensing technique.

Traditional astronomy exploits the fact that photons arrive at Earth bearing information about the conditions of their origin in distant objects. As photons travel to Earth along the null geodesics of spacetime, WL exploits the fact that photons arrive carrying information about the geometry of spacetime between the source and Earth. Fluctuations in the gravitational potential(s) of space cause subtle distortions and magnification of the images of distant sources. In WL, these distortions are measured to infer the mass-density fluctuations that cause them, and the laws of gravity that relate the mass to the metric. WL determines the three dimensional total matter distribution in the Universe to infer the distance-vs-redshift relation, and hence the effect of dark energy on the expansion.

A crucial aspect of the WL method is its ability to provide a robust and precise measure of the growth of gravitational fluctuations over the history of the Universe. This enables a critical test of whether the cosmic acceleration is due to an unseen "dark energy" field, or, if instead it might be some failure of general relativity. The combination of WL data with the galaxy maps produced by a BAO experiment enables tests of several aspects of general relativity.

WFIRST will detect WL by measuring the coherent distortion ("shear") of the images of distant galaxies. Because galaxies come in a variety of intrinsic shapes, it is not possible to tell whether a single galaxy is gravitationally distorted. But lensing causes galaxies on similar lines of sight to align, so averaging large samples of galaxies can effectively map the lensing distortions. The signal is quite subtle: a 1-2% stretch of galaxy images along a typical line of sight. A reliable detection of "cosmic shear" requires >10⁵ galaxy images. Such samples were not available until the advent of CCD mosaic cameras in the late 1990's; a flurry of cosmic-shear detections was published in 2000-2001. Current WL surveys image a few ×10⁶ galaxies over <200 deg² and measure key cosmological parameters to ~ 5% accuracy.

WFIRST enables advances over ground-based WL surveys in four ways:

The low sky background, high efficiency, and high angular resolution of a wide-field imaging space telescope speed up the measurement of galaxy shapes, so that WFIRST can measure more than a billion galaxy shapes, reducing statistical errors substantially.
Ground-based attempts to measure the subtle WL shape distortions to high accuracy are hindered by the image distortions induced by atmospheric fluctuations, plus thermal and gravitational distortions of the telescope optics. Ground-based experiments are limited by systematic errors in trying to distinguish these instrumental effects from true cosmic lensing. The exceptionally sharp and stable optical performance of a space telescope permits this systematic to be reduced and accurately removed.
The lensing survey requires accurate galaxy redshifts. This is essential to map the cosmic evolution of gravity, and to distinguish true cosmic lensing shear from any tidal alignment of neighboring galaxies. It is infeasible to obtain spectroscopic redshifts for 10⁹ galaxies, so all WL surveys rely on photometric redshifts. The photo-z reliabilities needed for WFIRST-quality WL experiments require deep, wide-field, NIR photometric surveys, which are feasible only from space.

The photometric redshift scale must be calibrated using very complete spectroscopic redshift survey of 30,000 - 100,000 galaxies. The unique wide-field spectroscopic capabilities on WFIRST will make this possible by measuring galaxy emission lines in redshift ranges that are inaccessible from the ground.

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