Euclid will constrain Dark Energy, General Relativity, Dark Matter, and the initial conditions of the Universe with unprecedented accuracy. The Euclid mission has been optimized for the measurement of two probes sensitive to dark energy:

(1) Weak Lensing (WL) - Observing the apparent distortion of the images of galaxies caused by gravitational light deflection from invisible foreground mass concentrations (dark matter) and modified by the expansion of the Universe. From the shape correlation between galaxies as a function of angular scales and redshift, it is possible to determine the properties of dark energy. By measuring the dark matter distribution at many redshifts, weak lensing directly measures the growth of structure in the Universe.

(2) Galaxy Clustering - Observing the imprint of sound waves from the epoch of recombination. These waves imprint a standard preferential distance among galaxies that increases as the Universe ages and expands. As a standard ruler, these baryon acoustic oscillations (BAO) provide Euclid with accurate measurementsof the Hubble parameter and the angular diameter distance, thereby putting constraints on the properties of dark energy. From the same data set, Euclid will perform a measurement of redshift space distortions (RSD), the signature of the anisotropic distribution of galaxies in redshift space due to galaxy peculiar velocities. The RSD technique provides an additional, independent measurement of the growth of structure in the Universe.

The two probes provide a crucial cross-check of systematic effects, which become dominant at Euclid's level of statistical precision.

As described in the its Definition Study Report, Euclid incorporates four main science objectives:

(1) Weak Lensing (WL) - Observing the apparent distortion of the images of galaxies caused by gravitational light deflection from invisible foreground mass concentrations (dark matter) and modified by the expansion of the Universe. From the shape correlation between galaxies as a function of angular scales and redshift, it is possible to determine the properties of dark energy. By measuring the dark matter distribution at many redshifts, weak lensing directly measures the growth of structure in the Universe.

(2) Galaxy Clustering - Observing the imprint of sound waves from the epoch of recombination. These waves imprint a standard preferential distance among galaxies that increases as the Universe ages and expands. As a standard ruler, these baryon acoustic oscillations (BAO) provide Euclid with accurate measurementsof the Hubble parameter and the angular diameter distance, thereby putting constraints on the properties of dark energy. From the same data set, Euclid will perform a measurement of redshift space distortions (RSD), the signature of the anisotropic distribution of galaxies in redshift space due to galaxy peculiar velocities. The RSD technique provides an additional, independent measurement of the growth of structure in the Universe.

The two probes provide a crucial cross-check of systematic effects, which become dominant at Euclid's level of statistical precision.

As described in the its Definition Study Report, Euclid incorporates four main science objectives:

- Dark Energy Properties. Measure the dark energy equation of state parameters, w
_{p}and w_{a}, to a precision of 2% and 10%, respectively, using Euclid's expansion history and structure growth constraints alone. When combined with additional probes and results from Planck, the constraints on w_{p}and w_{a}improve to 0.7% and 3.5% precision, respectively. The combined figure-of-merit represents more than a 300-fold improvement on our best current constraints. - Beyond Einstein's Gravity. Distinguish General Relativity from modified-gravity theories by measuring the galaxy clustering growth factor exponent, γ, with a precision of 2%.
- The nature of dark matter. Test the cold dark matter paradigm for structure formation, and measure the sum of the neutrino masses to a precision better than 0.02 eV when combined with results from the Planck mission.
- The seeds of cosmic structure. Improve by a factor of 20 the determination of the initial condition parameters compared to Planck alone. These parameters include the index of primordial power spectrum fluctuations, n, the power spectrum amplitude, σ
_{8}, and the non-gaussianity parameter, f_{NL}