Euclid: Forecasting constraints on f(R) cosmologies from the spectroscopic and photometric probes

Santiago Casas

TTK, RWTH University Aachen

Santiago Casas, Euclid Consortium Meeting, Oslo 2022

\newcommand{\sg}{\ensuremath{\sigma_{8}}} \newcommand{\de}{\mathrm{d}} S = \frac{c^4}{16\pi G} \int{\de^4 x \sqrt{-g} \left[R+f(R)\right]}

-k^2\Psi =\frac{4\pi\,G}{c^4} \,a^2\mu\bar\rho\Delta\,

Modification of the Einstein-Hilbert action

-k^2\left(\Phi+\Psi\right) = \frac{8\pi\,G}{c^4}\,a^2 \Sigma \bar\rho\Delta

Induces changes in the gravitational potentials *

\mu(a,k) = \frac{1}{1+f_R(a)}\frac {1+4k^2a^{-2}m_{f_R}^{-2}(a) }{1+3k^2a^{-2}m_{f_R}^{-2}(a)}

Scale-dependent growth of matter perturbations

Small changes in lensing potential

\Sigma(a)=\frac{1}{1+f_{R}(a)}\,

*for negligible matter anisotropic stress

Free parameter: \(f_{R0}\)

f(R) = - 6 \Omega_{\rm DE} H_0^2 + |f_{R0}| \frac{\bar R_0^2}{R}\,

\(\lambda_C =32 \rm{Mpc}\sqrt{|f_{R0}|/10^{-4}}\)

"Fifth-force" scale for cosmological densities

Hu, Sawicki (2007)

Santiago Casas, Euclid Consortium Meeting, Oslo 2022

Codes used: for background and scale-dependent linear perturbations: MGCAMB and EFTCAMB

For non-linear power spectrum:

Winther et al (2019) fitting formula

Spectroscopic Galaxy clustering: Take into account non-linear effects and scale-dependent growth
3x2pt photometric probe (WL+GCph+XCph), deeply non-linear regime
Optimistic and Pessimistic Euclid IST:F settings. 3 Fiducial models.
Forecast code validation:
SOAPFish (Sapone), Fishermathica (Casas), STAFF (Cardone), CCCP (Camera), CosmicFish (Casas, Martinelli)

Santiago Casas, Euclid Consortium Meeting, Oslo 2022