We introduce k-evolution, a relativistic N -body code based on gevolution, which includes clustering dark energy among its cosmological components. To describe dark energy, we use the effective field theory approach. In particular, we focus on k-essence with a speed of sound much smaller than unity but we lay down the basis to extend the code to other dark energy and modified gravity models. We develop the formalism including dark energy non-linearities but, as a first step, we implement the equations in the code after dropping nonlinear self-coupling in the k-essence field. In this simplified setup, we compare k-evolution simulations with those of CLASS and gevolution 1.2, showing the effect of dark matter and gravitational non-linearities on the power spectrum of dark matter, of dark energy and of the gravitational potential. Moreover, we compare k-evolution to Newtonian N -body simulations with back-scaled initial conditions and study how dark energy clustering affects massive halos.

We present MG-evolution, an N-body code simulating the cosmological structure formation for parametrised modifications of gravity. It is built from the combination of parametrised linear theory with a parametrisation of the deeply nonlinear cosmological regime extrapolated from modified spherical collapse computations that cover the range of known screening mechanisms. We test MG-evolution, which runs at the speed of conventional ΛCDM simulations, against a suit of existing exact model-specific codes, encompassing linearised and chameleon f(R) gravity as well as the normal branch of the Dvali-Gabadadz-Porrati braneworld model, hence covering both large-field value and large-derivative screening effects. We compare the nonlinear power spectra produced by the parametrised and model-specific approaches over the full range of scales set by the box size and resolution of our simulations, k = (0.05 − 2.5) h/Mpc, and for two redshift slices, z = 0 and z = 1. We find sub-percent to one-percent level recovery of all the power spectra generated with the model-specific codes for the full range of scales. MG-evolution can be used for generalised and accurate tests of gravity and dark energy with the increasing wealth of high-precision cosmological survey data becoming available over the next decade.

In this Letter, we introduce the nonlinear partial differential equationshowing a new type of instability. Such equations appear in the effective field theory (EFT) of dark energy for the k-essence model as well as in many other theories based on the EFT formalism. We demonstrate the occurrence of instability in the cosmological context using a relativistic N-body code, and we study it mathematically in 3 þ 1 dimensions within spherical symmetry. We show that this term dominates for the low speed of sound limit where some important linear terms are suppressed.

The Cosmic Microwave Background (CMB) radiation lensing is a promising tool to study the physics of early universe. In this work we probe the imprints of deviations from isotropy and scale invariance of primordial curvature perturbation power spectrum on CMB lensing potential and convergence. Specifically, we consider a scale-dependent hemispherical asymmetry in primordial power spectrum. We show that the CMB lensing potential and convergence and also the crosscorrelation of the CMB lensing and late time galaxy convergence can probe the amplitude and the scale dependence of the dipole modulation. As another example, we consider a primordial power spectrum with local feature. We show that the CMB lensing and the cross-correlation of the CMB lensing and galaxy lensing can probe the amplitude and the shape of the local feature. We show that the cross correlation of CMB lensing convergence and galaxy lensing is capable to probe the effects of local features in power spectrum on smaller scales than the CMB lensing. Finally we showed that the current data can constrain the amplitude and moment dependence of dipole asymmetry.