SPHEREx is a proposed NASA Medium Explorer mission designed to 1) constrain the physics of inflation by measuring 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 obtain near-infrared 0.75-5.0 um spectra every 6" 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. SPHEREx will also have strong scientific synergies with other missions and observatories, resulting in a rich legacy archive of spectra that 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. 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| < 10-2). 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 (green stars) and Pan-STARSS/DES (black solid 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 - 5.0 µm wavelength coverage. We require a redshift error Δz(1+z)=0.3% to access the finest useful physical scales, which require a spectral resolving power R>30.

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 490 million galaxies at < 10% accuracy and 16 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 8 bins between 0.75 and 4.0 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 available for Galactic molecular clouds and protoplanetary disks. SPHEREx will remedy this by increasing by 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.-- Simulated SPHEREx observations accurately reproduce synthetic input ice spectra. Left panel: A synthetic SPHEREx spectrum (dashed-orange line) of a K5 star seen through high extinction (Av=14) including simulated ice absorption features. Red bars indicate the corresponding end-of-ission Nyquist-sampled SPHEREx spectra generated by the simulator, including noise (measurement residuals in middle-left panel). We fitted the simulated SPHEREx ice features to estimate optical depths and column densities, creating the recovered spectrum (green), which agrees with the input spectrum to within 10%. Middle and Right panels: each input column density for both H2O and CO2 ice was simulated 100 times accounting for variation due to noise. The recovered column densities (purple, with 1-sigma uncertainties) are compared to the input column densities for sources seen by SPHEREx with SNRs of 100 on the continua. Fractional differences between the recovered and input column densities are shown in the bottom panels.

Synergy with other missions

SPHEREx will launch in early 2023, and carry out its survey observations for about two years, ending normal flight operations in early 2025. SPHEREx is therefore well-timed to follow up on the results from missions such as JWST, TESS, and eROSITA, to identify targets for more detailed study by JWST, SOFIA, or ALMA, and to set the stage for later missions such as WFIRST and PLATO. This figure illustrates how SPHEREx will overlap with numerous other missions. Most of those shown are either unbiased or targeted surveys. The synergies of SPHEREx with these many other observatories, which were first discussed at the 2016 SPHEREx community workshop in Pasadena, were developed in detail during the 2nd SPHEREx community workshop in Cambridge in 2018. For details, see Doré et al., 2018.

The chart at left shows the capabilities of different missions (including SPHEREx) in terms of wavelength coverage and spectral resolving power. SPHEREx provides almost unique access with significant spectral resolution to the wavelength range between 2.5 and 5 µm, while also extending to shorter wavelengths to overlap with numerous ground-based and space-based imaging and spectroscopic surveys. The synergy between SPHEREx and JWST is particularly strong, because JWST is the only space-based mission with comparable wavelength grasp and spectral resolution: SPHEREx goes wide while JWST goes deep. Not shown here are the 10-30-meter class telescopes currently operating on the ground and planned for the future. Their overlap with SPHEREx will be similar to that of JWST, with the additional consideration that they will not have full access even to the 2.5-to-5 µm wavelength region because of atmospheric absorption. Nevertheless, we anticipate that these telescopes, with their much higher spectral and spatial resolution, will be effectively used in following up targets and scientific questions identified by SPHEREx.