Abstract. We present a general parallelized and easy-to-use code to perform numerical simulations of structure formation using the COLA (COmoving Lagrangian Acceleration) method for cosmological models that exhibit scale-dependent growth at the level of first and second order Lagrangian perturbation theory. For modified gravity theories we also include screening using a fast approximate method that covers all the main examples of screening mechanisms in the literature. We test the code by comparing it to full simulations of two popular modified gravity models, namely f (R) gravity and nDGP, and find good agreement in the modified gravity boost-factors relative to ΛCDM even when using a fairly small number of COLA time steps.

Type Ia supernovae (SNe Ia) are generally accepted to act as standardisable candles, and their use in cosmology led to the first confirmation of the as yet unexplained accelerated cosmic expansion. Many of the theoretical models to explain the cosmic acceleration assume modifications to Einsteinian General Relativity which accelerate the expansion, but the question of whether such modifications also affect the ability of SNe Ia to be standardisable candles has rarely been addressed. This paper is an attempt to answer this question. For this we adopt a semi-analytical model to calculate SNe Ia light curves in non-standard gravity. We use this model to show that the average rescaled intrinsic peak luminosity -a quantity that is assumed to be constant with redshift in standard analyses of Type Ia supernova (SN Ia) cosmology data -depends on the strength of gravity in the supernova's local environment because the latter determines the Chandrasekhar mass -the mass of the SN Ia's white dwarf progenitor right before the explosion. This means that SNe Ia are no longer standardisable candles in scenarios where the strength of gravity evolves over time, and therefore the cosmology implied by the existing SN Ia data will be different when analysed in the context of such models. As an example, we show that the observational SN Ia cosmology data can be fitted with both a model where (ΩM, ΩΛ) = (0.62, 0.38) and Newton's constant G varies as G(z) = G0(1 + z) −1/4 and the standard model where (ΩM, ΩΛ) = (0.3, 0.7) and G is constant, when the Universe is assumed to be flat. I. INTRODUCTIONCosmology observations from Type Ia supernovae (SNe Ia) gave the first evidence for a late-time acceleration in the expansion of the Universe [1,2]. A Type Ia supernova (SN Ia) is the cataclysmic explosion of a white dwarf star that occurs when the white dwarf accretes enough mass from a binary partner for the material in its core to undergo runaway thermonuclear fusion. SNe Ia are thought to act as standardisable candles because of an observed relationship between a SN Ia's peak brightness and how rapidly this peak brightness is achieved and subsequently left behind [3] (the so-called width-luminosity relation, or WLR). After standardisation procedures, which are often at least partially based on the WLR, are applied, any remaining difference in the peak brightnesses of the two SNe Ia should be due to a difference in distance to the observer. Thus the relative distances between SNe Ia can be measured, and along with measurements of their redshifts can be used to infer the details of the expansion of the Universe through the construction of the distance-redshift relation.After the late-time acceleration of the expansion of the Universe was discovered, Einstein's idea of a small, positive cosmological constant Λ was revived and established as the leading candidate for the acceleration's origin. However, the idea of Λ as the cause of cosmic acceleration is not without theoretical difficulties, such as the cosmological constant fine-tuning and coin...

Abstract. The effect of massive neutrinos on the growth of cold dark matter perturbations acts as a scale-dependent Newton's constant and leads to scale-dependent growth factors just as we often find in models of gravity beyond General Relativity. We show how to compute growth factors for ΛCDM and general modified gravity cosmologies combined with massive neutrinos in Lagrangian perturbation theory for use in COLA and extensions thereof. We implement this together with the grid-based massive neutrino method of Brandbyge and Hannestad in MG-PICOLA and compare COLA simulations to full N-body simulations of ΛCDM and f (R) gravity with massive neutrinos. Our implementation is computationally cheap if the underlying cosmology already has scale-dependent growth factors and it is shown to be able to produce results that match N-body to percent level accuracy for both the total and CDM matter power-spectra up to k 1h/Mpc.

The intrinsic peak luminosity of Type Ia supernovae (SNIa) depends on the value of Newton's gravitational constant G, through the Chandrasekhar mass M Ch ∝ G −3/2 . If the luminosity distance can be independently determined, the SNIa can be treated as a tracker to constrain the possible time variation of G in different redshift ranges. The gravitational-wave (GW) standard sirens, caused by the coalescence of binary neutron stars, provide a model-independent way to measure the distance of GW events, which can be used to determine the luminosity distances of SNIa by interpolation, provided the GW and SNIa samples have similar redshift ranges. We demonstrate that combining the GW observations of third-generation detectors with SNIa data provides a powerful and model-independent way to measure G in a wide redshift range, which can constrain the ratio G/G0, where G and G0 are respectively the values in the redshift ranges z > 0.1 and z < 0.1, at the level of 1.5%.