The Origin of the Universe


Moments after our Universe was born in a hot Big Bang, space-time ‘inflated’ in a rapid, exponential expansion. Inflation is a corner-stone of modern cosmology, explaining the extreme smoothness of the cosmic microwave background and the geometric flatness of the Universe. While the basic predictions of inflation have been verified in increasingly precise measurements, the physical process driving inflation remains elusive. The answer surely lies in the unknown and fundamental physics of space, time and matter. Understanding inflation is arguably the most important goal in cosmology today. One way to test the theory of inflation is to measure the imprint of inflationary ripples on the large-scale matter distribution. 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.

Primordial non-Gaussianity and the f_NL Parameter

SPHEREx MIDEX Inflation Constraints

Fig 1. SPHEREx establishes powerful constraints on fNL. Ellipses correspond to observational constraints while the shaded regions identify families of models.

Primordial "non- Gaussianity", quantified by the fNL parameter, describes the departure in the statistical distribution of inflationary fluctuations from a Gaussian bell curve. The fNL parameter characterizes non-Gaussianity in the distribution of inflationary fluctuations. Measuring fNL provides a unique test between two broad classes of inflation scenarios, "multi-field" and "single-field" models. Inflation models driven by multiple fields often predict |fNL| > 1 while simpler models with a single field generally predict |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 current CMB measurement since the large-volume 3D survey accesses many more modes than a 2D CMB measurement. SPHEREx will determine redshifts for hundreds of millions of galaxies by fitting measured spectra to a library of galaxy templates (see Fig 2). SPHEREx's infared range allows it to exploit the nearly universal 1.6 µm rest frame bump in these fits. The distribution of galaxies extending to moderate redshift (in SPHEREx's spectral range) covers an enormous effective volume. We determine the redshifts using SPHEREx (blue or orange dots) and Pan-STARSS/DES (black solid circles) galaxies by fitting their measured spectra (see Fig. 2).


Fig. 2: Simulated Spectra as Obserbed by SPHEREx.

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 Roman 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.