# LANCELOT¶

LANCELOT is the library for the Large Scale Structure of the Universe, that implements various modified theories of gravitation, such as $$f(Q)$$, $$f(T)$$ and $$f(T,B)$$ gravities in the presence of massive neutrinos. Our library consists of 24 separate simulations:

• $$f(Q)$$ gravity with regular fluid, Dynamical Dark Energy (DDE) and massive neutrinos $$(1+1)\times2$$ simulations

• $$f(T)$$ gravity with regular fluid, Dynamical Dark Energy (DDE) and massive neutrinos $$(1+1)\times2$$ simulations

• $$f(T,B)$$ gravity with regular fluid, Dynamical Dark Energy (DDE) and massive neutrinos $$(1+1)\times2$$ simulations

All aforementioned simulations are carried out with the box size $$L_{\mathrm{box}}=500\mathrm{\;Mpc}/h$$. However, it is planned to also investigate aforementioned theories of gravitation on the smaller scales with bigger resolution of separate galaxies and galaxy clusters (12 simulations in total). For that case, we assume $$L_{\mathrm{box}}=100\mathrm{\;Mpc}/h$$. Softening scales are redefined accordingly and resolution for each simulation is $$(N_{\mathrm{p}})^{1/3}=768$$. The main goals of our project is to:

• Differentiate different novel modified theories of gravity, based on the teleparallelism or symmetric teleparallelism, define whether those theories are viable or not.

• Investigate and comparate the behaviour of previously mentioned MOG theories with both $$\Lambda\mathrm{CDM}$$ and $$\nu\mathrm{CDM}$$ theories. Constrain the parameter space for all three theories using MCMC (Markov Chain Monte Carlo) approach, study Hubble and $$\sigma_8$$ tensions, matter power spectrum $$P(k)$$ and bispectrum $$B(k)$$, 2PCF/3PCF and halo mass functions.