SPHEREx is a NASA Small Explorer mission designed to 1) constrain the physics of inflation by studying its imprints on the three-dimensional large-scale distribution of matter, 2) trace the history of galactic light production through a deep multi-band measurement of large-scale clustering, and 3) investigate the abundance and composition of water and biogenic ices in the early phases of star and planetary disk formation. SPHEREx will measure near-infrared spectra from 0.75-5.0 microns over the entire sky. It implements a simple instrument design with a single observing mode to map the entire sky four times during its nominal 25-month mission. The resulting rich legacy archive of spectra will bear on numerous scientific investigations.


One way to test the theory of inflation is to measure the imprint of inflationary ripples on the large-scale structure (LSS) of galaxies. SPHEREx will probe the statistical distribution of inflationary ripples by measuring the large-scale 3D distribution of galaxies. It will achieve this by measuring galaxy redshifts over a large cosmological volume at low redshifts.

Fig 1.-- SPHEREx establishes powerful constraints on fNL and as compared to other investigations. Ellipses correspond to observational constraints while the shaded regions identify families of models. SPHEREX will discriminate between classes of inflation theories. Euclid bispectrum fNL forecasts do not exist, but our own estimates indicate that they are significantly worse than SPHEREx’s constraints. Note that the extent of a 2-D 68% confidence contour in the direction of a parameter axis corresponds to ~1.5σ, where σ is the uncertainty on the parameter. SPHEREx and Euclid forecasts are centered arbitrarily.

The fNLparameter

The fNL parameter characterizes non-Gaussianity in the distribution of inflationary fluctuations. In particular, multi-field inflationary models generally predict a high level of non-Gaussianity (|fNL| > 1) while single field models generally predict low levels of non-Gaussianity (|fNL| < 1). SPHEREx will achieve a sensitivity of at least fNL=1 (2 σ), allowing it to distinguish between these two classes of models (see Fig 1).


SPHEREx will reduce uncertainty in fNL by a factor of more than 10 over current values. SPHEREx can put better constraints on fNL than can a CMB measurement since the large-volume 3D survey accesses many more modes than a 2D CMB measurement (see Fig 2).

Fig 2.-- SPHEREx probes a much larger effective volume than other cosmological surveys. The effective volume is the physical volume mapped by a given survey, corrected for the sampling noise of a finite number of galaxies. For a well-sampled survey, the effective volume equals the physical volume. The cosmological information content of a given survey is directly proportional to the number of independent spatial modes, and directly proportional to the effective volume. The SPHEREx fNL power spectrum (PoS) sample (red curve) extracts all the cosmological information up to z~1.5 (black dashed curve). The SPHEREx bispectrum (BiS) and cosmological parameters sample (pink curve), based on a smaller sample of high redshift accuracy galaxies, is uniquely powerful at z < 0.8 compared with other planned surveys.

SPHEREx will determine redshifts for hundreds of millions of galaxies by fitting measured spectra to a library of galaxy templates (see Fig 3). SPHEREx's infared range allows it to exploit the nearly universal 1.6um rest frame bump in these fits. The distribution of galaxies extending to moderate redshift (in SPHEREx's spectral range) covers an enormous effective volume (see Fig 2).

Fig 3.-- We determine the redshifts of WISE (diamonds) and Pan- STARSS/DES (circles) galaxies by fitting their measured spectra. Each redshift is assigned an error, a process we have extensively simulated from the COSMOS galaxy catalog. The determination is strongly driven by the 1.6 μm bump, so the target redshift range is well-matched to the 0 .75 - 4.18 µm wavelength coverage. We require a redshift error Δz(1+z)=0.5% to access the finest useful physical scales, which require a spectral resolution of 35.

Cosmological Legacy

SPHEREx utilizes the power spectrum and bispectrum, the Fourier transforms of the 2- and 3-point correlation functions respectively.

SPHEREx will classify galaxies according to redshift accuracy, categorizing ~450 million galaxies at < 10% accuracy and ~10 million galaxies at 0.3% accuracy. The low accuracy sample drives the power spectrum fNL sensitivity, and the high accuracy sample drives the bispectrum as well as key inflationary parameters, i.e. index of spectrum (ns) for departure from scale invariance, its running ( αs), and its departure from geometric flatness ( Ωk). SPHEREx's projected constraints on these parameters are summarized in Fig 1.

SPHEREx will complement planned Euclid and WFIRST spectroscopic surveys, which focus on higher redshifts to probe the equation of state of dark energy. SPHEREx's lower redshift survey will allow its measurement of inflationary parameters to be largely independent. This full suite of inflationary observables, combined with CMB polarization measurements, will give a complete picture of inflation.

Galaxy Formation

The SPHEREx observing strategy naturally generates a wide+deep map at each ecliptic pole (the southern map will be shifted to avoid the LMC). Both maps will enable unique measurements of spatial fluctuations in the extragalactic background light (EBL) which will lead to new insights into the origin and history of galaxy formation. Specifically, SPHEREx will probe signals from the intra-halo light (IHL) and from the epoch of reionization (EOR) to minimum levels in the EBL.

Fig 4.-- Amplitude of large-scale EBL fluctuations measured by CIBER, Spitzer, and AKARI, after removing the contribution from known galaxy populations. The purple solid line shows the expected IHL and the red envelope the EOR signal with modeling uncertainties the bottom of the EOR range is the minimum signal that must be present given the existing z>7 Lyman-break galaxy luminosity functions (Bouwens et al. 2013). The top of the EOR range allows for fainter galaxies below the detection thresholds of deep HST surveys. We show the MEV and CBE instrumental performance as the variance between multipoles l=500 and 2000 in 9 bins between 0.75 and 5.0 µm by the blue and red lines respectively. Note Dl=l(l+1)Cl/(2π).


Surveys which focus only on detection of individual galaxies discard important information available in the diffuse light from faint emission sources, such as intra-halo light (IHL) and dwarf galaxies. Fluctuations in EBL trace these faint sources. The amplitude of the linear clustering signal, proportional to the total photon emission, exceeds that expected from large-scale clustering of known galaxy populations, suggesting EBL is a fruitful signal for probing yet-undiscovered features of the origin and history of galaxy formation.

Fig. 5-- A large-scale mapping measurement like SPHEREx traces the total emission from diffuse components as well as the emission from individual galaxies. The left panel shows a numerical simulation of galaxies superposed with a diffuse emission component, such as IHL and early dwarf galaxies, that follows the structure of dark matter. A galaxy survey (middle) recovers the galaxies but misses the diffuse light component. A large-scale mapping measurement (right), traces the total emission from the diffuse component as well as the individual galaxies due to their clustering.


Diffuse IHL emissions at redshifts of z < 1 arise from stars disassociated from their parent galaxies. During a collision of galaxies, some stars are stripped from their parent galaxies by dynamical friction and form extended stellar halos, some extending out to 300 kpc (Tal & van Dokkum 2011). The substantial IR fluctuations from the IHL are thought to be responsible for the corresponding IR fluctations in the EBL. SPHEREx's sensitive multi-band fluctuations will probe the history of starts producing the IHL.


The Epoch of Reionization (EOR) marks the end of the Universe's dark ages, in which the first collapsed objects produced energetic UV photons that reionized the surrounding hydrogen gas. Estimates of the UV luminosity function at z > 6 suggest the majority of UV intensity driving reionization was due to dwarf galaxies.

EOR fluctions in the EBL trace exactly these dwarf galaxies. By extrapolating the HST-observed luminosity funciton of z > 7 faint galaxies, one can put a lower bound on the EOR component of the EBL. SPHEREx has the sensitivity in multiple spectral bands to probe for the EOR component's distinctive spectral features using information in auto- and cross-correlations.

Water Ice and Biogenic Molecules

SPHEREx will be a game changer in resolving long-standing questions about the amount and evolution of key biogenic molecules (H2O, CO, CO2, and CH3OH) throughout all phases of star and planetary formation.

Molecular Clouds to Protoplanetary Disks

Molecular clouds contain the gas and compounds that give rise to protoplanetary disks and, ultimately, to planets. While ices within these molecular clouds are a repository for important elements, they are also sites of active chemistry. For example, hydrogenation and oxygenation reactions occur within these ices, as does the production of complex organic molecules resulting from the interaction of the ices with radiation.

However, the evolution of molecular clouds to protoplanetary disks is largely unknown, hampered primarily by the lack of spectra data available surveing Galactic molecular clouds and protoplanetary disks. SPHEREx will remedy this by increasing 100-fold the number of ice spectra available of molecular clouds, young stellar objects, and protoplanetary disks. Armed with the SPHEREx data, it will be possible to understand, in a statistically significant way, how ice content correlates with, among other factors, cloud density, internal temperature, presence or absence of embedded sources, external UV and X-ray radiation, elemental abundances (e.g., C/O ratio), gas-phase composition, and cosmic-ray ionization rate.

Fig 6.-- SPHEREx simulations accurately reproduce the input ice spectra. Left panel: A synthetic SPHEREx spectrum used in our simulations. The dashed-orange spectrum is a densely sampled model K5 stellar spectrum seen through high extinction (Av=14). The simulated ice absoprtion features include those in SPHEREx Bands 3 and 4. The red symbols show the 96-element Nyquist-sampled SPHEREx spectrum generated by the simulator. We fitted ice absorption features to determine optical depths and column densities, creating the recovered spectrum (green), which agrees with the input spectrum to better than 10%. Middle and Right panels: Results from numerous simulations comparing recovered to input column densities for H2O and CO2 ice with a range of input optical depths. The simulations were performed for two limiting cases: (1) sources having a continuum brightness of 12 AB mag, sufficient for 20,000 high-quality ice spectra, and (2) fainter sources for which SPHEREx obtains a signal to noise ratio of ~100. The bottom plot in each panel shows the fractional residuals. The dashed red lines indicate residuals of 10%.

Resolving Spectra

SPHEREx has resolving power R=41.4 from λ= 0.75μm - 4.2μm and R=135 from λ= 4.2μm - 5.0μm. This range was designed to match the necessary resolving power of key biogenic molecules. R=20 suffices to resolve the broad H2O feature at 3.3 μm, while a higher resolving power of R=120 is required to separate the narrower features of CO, CO2 and XCN ices (see Fig 6).