arXiv subjects
Publications and source records attributed to Bilal Tüdes.
We derive the one-loop perturbation kernels for a minimal modified gravity model in which dark energy is coupled to dark matter via a constant coupling. We derive the time-dependent kernels via analytical and numerical solutions and provide accurate fitting functions. These kernels can be directly employed to test for modified gravity in forthcoming large-scale surveys.
We forecast constraints on the parameters of the coupled dark energy model using DESI and Euclid data with the one-loop galaxy power spectrum. We investigate the distinguishability of our model from the zero-coupling scenario at the $1σ$ level and explore how the parameter constraints depend on the fiducial coupling $β_{\rm fid}$, the fixed potential slope parameter $ν$, the maximum wavenumber $k_{\max}$, and different prior choices. We find that the inclusion of mildly non-linear scales improves the constraints on the coupling by roughly a factor of five. Then, we address the question of which is the minimum value of $β$ that can be distinguished from zero at $1σ$. We find that for our reference case $k_{\rm max}=0.2 h/$Mpc, $β=0.15$ lies roughly $1σ$ above zero. In the most optimistic case with $k_{\rm max}=0.3 h/$Mpc and including a Planck prior on $Ω_{m0}$, this value can be reduced to $0.05$. These values are substantially larger than the current constraints on $β$, but the latter have been obtained assuming $β$ to be constant from at least the decoupling epoch to today, while we only employ late-time data. We conclude therefore that only models that allow for time-varying couplings can be detected with late-time datasets.
We investigate the nonlinear evolution of cosmological perturbations in theories with scale-dependent perturbation growth, first in general and then focusing on Horndeski gravity. Within the framework of standard perturbation theory, we derive the second- and third-order kernels and show that they are fully determined by two effective functions, \( h_1 \) and \( h_c \), which parametrize deviations from general relativity. Using the Wronskian method, we obtain solutions for the nonlinear growth functions and present explicit expressions for the resulting kernels, including bias and redshift space distortions, valid in the limit in which the $k$-dependent part is subdominant. We show that the kernels are entirely dependent on the linear growing mode: once this is calculated, the kernels are analytic up to a time integral. We also include redshift-space distortions (RSD) and scale-dependent bias. Our approach provides a physically motivated framework for evaluating the one-loop galaxy power spectrum in scale-dependent theories, suitable for the forecasts and actual data analysis.