The linear point (LP), defined as the mid-point between the dip and the peak of the two-point clustering correlation function (TPCF), has been shown to be an excellent standard ruler for cosmology. In fact, it is nearly redshift-independent, being weakly sensitive to non-linearities, scale-dependent halo bias and redshift-space distortions. So far, these findings were tested assuming that neutrinos are massless; in this paper we extend the analysis to massive-neutrino cosmologies. In particular, we examine if the scale-dependent growth induced by neutrinos affects the LP position and if it is possible to detect the neutrino masses using the shift of the LP compared to the massless-neutrino case. For our purposes, we employ two sets of state-of-the-art $N$-body simulations with massive neutrinos. For each of them we measure the TPCF of cold dark matter (CDM) and halos and, to estimate the LP, fit the TPCF with a model-independent parametric fit in the range of scales of the Baryon Acoustic Oscillations (BAO). Overall, we find that the LP retains its features as a standard ruler even when neutrinos are massive. The cosmic distances measured with the LP can therefore be employed to constrain the neutrino mass.
We present a halo mass function accurate over the full relevant Hu-Sawicki $f(R)$ parameter space based on spherical collapse calculations and calibrated to a suite of modified gravity $N$-body simulations that include massive neutrinos. We investigate the ability of current and forthcoming galaxy cluster observations to detect deviations from general relativity while constraining the total neutrino mass and including systematic uncertainties. Our results indicate that the degeneracy between massive neutrino and modify gravity effects is a limiting factor for the current searches for new gravi…
We investigate the impact of massive neutrinos on the distribution of matter in the semi-non-linear regime (0.1<k<0.6 h/Mpc). We present a suite of large-scale N-body simulations quantifying the scale dependent suppression of the total matter power spectrum, resulting from the free-streaming of massive neutrinos out of high-density regions. Our simulations show a power suppression of 3.5-90 per cent at k~0.6 h/Mpc for total neutrino mass, m_nu=0.05-1.9 eV respectively. We also discuss the precision levels that future cosmological datasets would have to achieve in order to distinguish the norma…
The paper by Sato and Kobayashi in 1977 studied the cosmological effects of a massive neutrino and obtained constraints on its properties. This paper initiated many studies to use cosmology as a laboratory of particle physics or to use particle physics to explore the very early universe.
We show how Newtonian cosmological simulations can be employed to investigate the non-linear evolution of two particle species in a relativistic context. We discuss the application for massive neutrinos and other multi-species systems such as Cold Dark Matter (CDM) plus baryons or Warm Dark Matter (WDM). We propose a method that allows us to perform simulations including massive neutrinos and general relativistic effects at almost the same computational cost as ordinary CDM only N-body simulations, employing tailor-made initial conditions and a dictionary for the interpretation of the simulati…
We present a new method for simulating cosmologies that contain massive particles with thermal free streaming motion, such as massive neutrinos or warm/hot dark matter. This method combines particle and fluid descriptions of the thermal species to eliminate the shot noise known to plague conventional N-body simulations. We describe this method in detail, along with results for a number of test cases to validate our method, and check its range of applicability. Using this method, we demonstrate that massive neutrinos can produce a significant scale-dependence in the large-scale biasing of deep …
We study the impact of baryonic processes and massive neutrinos on weak lensing peak statistics that can be used to constrain cosmological parameters. We use the BAHAMAS suite of cosmological simulations, which self-consistently include baryonic processes and the effect of massive neutrino free-streaming on the evolution of structure formation. We construct synthetic weak lensing catalogues by ray-tracing through light-cones, and use the aperture mass statistic for the analysis. The peaks detected on the maps reflect the cumulative signal from massive bound objects and general large-scale stru…
Primordial magnetic fields and massive neutrinos can leave an interesting signal in the CMB temperature and polarization. We perform a systematic analysis of general perturbations in the radiation-dominated universe, accounting for any primordial magnetic field and including leading- order effects of the neutrino mass. We show that massive neutrinos qualitatively change the large- scale perturbations sourced by magnetic fields, but that the effect is much smaller than previously claimed. We calculate the CMB power spectra sourced by inhomogeneous primordial magnetic fields, from before and aft…
We investigate impacts of massive neutrinos on the cosmic velocity fields, employing high-resolution cosmological $N$-body simulations provided by the information-optimized CUBE code, where cosmic neutrinos are evolved using collisionless hydrodynamics and their perturbations can be accurately resolved. In this study we focus, for the first time, on the analysis of massive-neutrino induced suppression effects in various cosmic velocity field components of velocity magnitude, divergence, vorticity and dispersion. By varying the neutrino mass sum $M_ν$ from 0 -- 0.4 eV, the simulations show that…
Initial conditions for cosmological N-body simulations are usually calculated by rescaling the present day linear power spectrum obtained from an Einstein-Boltzmann solver to the initial time employing the scale-independent matter growth function. For the baseline Lambda-CDM model, this has been shown to be consistent with General Relativity (GR) even in the presence of relativistic species such as photons. We show that this approach is not feasible in cosmologies with massive neutrinos and present an alternative method employing the Newtonian motion gauge framework.
The main effect of massive neutrinos on the large-scale structure consists in a few percent suppression of matter perturbations on all scales below their free-streaming scale. Such effect is of particular importance as it allows to constraint the value of the sum of neutrino masses from measurements of the galaxy power spectrum. In this work, we present the first measurements of the next higher-order correlation function, the bispectrum, from N-body simulations that include massive neutrinos as particles. This is the simplest statistics characterising the non-Gaussian properties of the matter …
Massive neutrinos make up a fraction of the dark matter, but due to their large thermal velocities, cluster significantly less than cold dark matter (CDM) on small scales. An accurate theoretical modelling of their effect during the non-linear regime of structure formation is required in order to properly analyse current and upcoming high-precision large-scale structure data, and constrain the neutrino mass. Taking advantage of the fact that massive neutrinos remain linearly clustered up to late times, this paper treats the linear growth of neutrino overdensities in a non-linear CDM background…
The effect of massive neutrinos on the evolution of the early type galaxies (ETGs) in size ($R_{e}$) and stellar mass ($M_{\star}$) is explored by tracing the merging history of galaxy progenitors with the help of the robust semi-analytic prescriptions. We show that as the presence of massive neutrinos plays a role of enhancing the mean merger rate per halo, the high-$z$ progenitors of a descendant galaxy with fixed mass evolves much more rapidly in size for a $Λ$MDM ($Λ$CDM + massive neutrinos) model than for the $Λ$CDM case. The mass-normalized size evolution of the progenitor galaxies, $R_{…
The presence of massive neutrinos affects the growth of large-scale structure in the universe, leaving a potentially observable imprint on the abundance and properties of massive dark matter-dominated halos. Cosmological surveys detect large numbers of these halos in the form of rich groups and clusters, using the information as an input to constraining the properties of dark energy. We use a suite of N-body simulations that include the effects of massive neutrinos as well as of dynamical dark energy to study the properties of the mass function. As in our previous work, we follow an approach v…
Do void statistics contain information beyond the tracer 2-point correlation function? Yes! As we vary the sum of the neutrino masses, we find void statistics contain information absent when using just tracer 2-point statistics. Massive neutrinos uniquely affect cosmic voids. We explore their impact on void clustering using both the DEMNUni and MassiveNuS simulations. For voids, neutrino effects depend on the observed void tracers. As the neutrino mass increases, the number of small voids traced by cold dark matter particles increases and the number of large voids decreases. Surprisingly, when…
Using cosmological $N$-body simulation which coevolves cold dark matter (CDM) and neutrino particles, we discover the local effect of massive neutrinos on the spatial distribution of CDM halos, reflected on properties of the Delaunay Triangulation (DT) voids. Smaller voids are generally in regions with higher neutrino abundance and so their surrounding halos are impacted by a stronger neutrino free streaming. This makes the voids larger (surrounding halos being washed outward the void center). On the contrary, larger voids are generally in regions with lower neutrino abundance and so their sur…
Using the publicly available Quijote simulations, we present the first measurements of the assembly bias of dark matter halos in N-body simulations which include massive neutrinos. We focus on the dependence of the linear bias $b_1$ on three halo properties: 1) concentration $c$, 2) spin $λ$, and 3) ellipticity $s$. Although these simulations cover a large volume, superior to any future surveys, we do not detect any effect of neutrinos on the relations $b_1(c)$, $b_1(λ)$ and $b_1(s)$ at fixed halo mass. We further study the dependence of halo properties and environment on neutrinos, finding th…
Jeans mass calculated with different combination of parameters involved has shown interesting variation with remarkable shifting of position of peak value from x = m/T = 0.5 to 5.5. The standard deviation is 2.217. In particular, using the harmonic mean square velocity, shifts the peak Jeans mass to x = m/T ~ 2, which is remarkably less than previously reported value of 4.2. Different scales of neutrino structures including virialized moments have also been compared.
We present a major upgrade of MGCAMB, a patch for the Einstein-Boltzmann solver CAMB used for phenomenological tests of general relativity against cosmological datasets. This new version is compatible with the latest CosmoMC code and includes a consistent implementation of massive neutrinos and dynamical dark energy. The code has been restructured to make it easier to modify to fit the custom needs of specific users. To illustrate the capabilities of the code, we present joint constraints on the modified growth, massive neutrinos and the dark energy equation of state from the latest cosmologic…
A new analytical approach allowing to account for massive neutrinos in the non-linear description of the growth of the large-scale structure of the universe is proposed. Unlike the standard approach in which neutrinos are described as a unique hot fluid, it is shown that the overall neutrino fluid can be equivalently decomposed into a collection of independent flows. Starting either from elementary conservation equations or from the evolution equation of the phase-space distribution function, we derive the two non-linear motion equations that each of these flows satisfies. Those fluid equation…
Modified gravity and massive neutrino cosmologies are two of the most interesting scenarios that have been recently explored to account for possible observational deviations from the concordance $Λ$-cold dark matter ($Λ$CDM) model. In this context, we investigated the large-scale structure of the Universe by exploiting the \dustp simulations that implement, simultaneously, the effects of $f(R)$ gravity and massive neutrinos. To study the possibility of breaking the degeneracy between these two effects, we analysed the redshift-space distortions in the clustering of dark matter haloes at differ…
Over the next decade, cosmological measurements of the large-scale structure of the Universe will be sensitive to the combined effects of dynamical dark energy and massive neutrinos. The matter power spectrum is a key repository of this information. We extend higher-order perturbative methods for computing the power spectrum to investigate these effects over quasi-linear scales. Through comparison with N-body simulations we establish the regime of validity of a Time-Renormalization Group (Time-RG) perturbative treatment that includes dynamical dark energy and massive neutrinos. We also quantif…
We compute the tree-level bispectrum of dark matter in the presence of massive neutrinos in the mildly non-linear regime in the context of the effective field theory of large-scale structure (EFTofLSS). For neutrinos, whose typical free streaming wavenumber ($k_{\rm fs}$) is longer than the non-linear scale ($k_{\mathrm{NL}}$), we solve a Boltzmann equation coupled to the effective fluid equation for dark matter. We solve perturbatively the coupled system by expanding in powers of the neutrino density fraction ($f_ν$) and the ratio of the wavenumber of interest over the non-linear scale ($k/k_…
Boltzmann solvers are an important tool for the computation of cosmological observables in the linear regime. In the presence of massive neutrinos, they involve solving the Boltzmann equation followed by an integration in momentum space to arrive at the desired fluid properties, a procedure which is known to be computationally slow. In this work we introduce the so-called generalized Boltzmann hierarchy (GBH) for massive neutrinos in cosmology, an alternative to the usual Boltzmann hierarchy, where the momentum dependence is integrated out leaving us with a two-parameter infinite set of ordina…
Clusters of galaxies are important probes for the large-scale structure that allow us to test cosmological models. With the REFLEX II galaxy cluster survey we previously derived tight constraints on the cosmological parameters for the matter density, Omega_m, and the amplitude parameter of the matter density fluctuations, sigma_8. Whereas in these previous studies no effect of massive neutrinos was taken into account, we explore these effects in the present publication. We derive cosmological constraints for the sum of the neutrino masses of the conventional three neutrino families in the rang…
We present, for the first time in the literature, a full reconstruction of the total (linear and non-linear) ISW/Rees-Sciama effect in the presence of massive neutrinos, together with its cross-correlations with CMB-lensing and weak-lensing signals. The present analyses make use of all-sky maps extracted via ray-tracing across the gravitational potential distribution provided by the "Dark Energy and Massive Neutrino Universe" (DEMNUni) project, a set of large-volume, high-resolution cosmological N-body simulations, where neutrinos are treated as separate collisionless particles. We correctly r…
Cosmic voids are a promising environment to characterize neutrino-induced effects on the large-scale distribution of matter in the universe. We perform a comprehensive numerical study of the statistical properties of voids, identified both in the matter and galaxy distributions, in massive and massless neutrino cosmologies. The matter density field is obtained by running several independent $N$-body simulations with cold dark matter and neutrino particles, while the galaxy catalogs are modeled by populating the dark matter halos in simulations via a halo occupation distribution (HOD) model to …
We estimate the velocity field in a large set of $N$-body simulations including massive neutrino particles, and measure the auto-power spectrum of the velocity divergence field as well as the cross-power spectrum between the cold dark matter density and the velocity divergence. We perform these measurements at four different redshifts and within four different cosmological scenarios, covering a wide range in neutrino masses. We find that the nonlinear correction to the velocity power spectra largely depend on the degree of nonlinear evolution with no specific dependence on the value of neutrin…
Cosmological neutrinos strongly affect the evolution of the largest structures in the Universe, i.e. galaxies and galaxy clusters. We use large box-size full hydrodynamic simulations to investigate the non-linear effects that massive neutrinos have on the spatial properties of cold dark matter (CDM) haloes. We quantify the difference with respect to the concordance LambdaCDM model of the halo mass function and of the halo two-point correlation function. We model the redshift-space distortions and compute the errors on the linear distortion parameter beta introduced if cosmological neutrinos ar…
We present the results of cosmological simulations of large-scale structure formation with massive neutrinos. The phase-space distribution of the cosmic relic neutrinos is followed, for the first time, by directly integrating the six-dimensional Vlasov-Poisson equations. Our novel approach allows us to represent free streaming and clustering of neutrinos, and their gravitational interaction with cold dark matter accurately. We thus obtain solutions for the collisionless dynamics independent of conventional N-body methods. We perform a suite of hybrid N-body/Vlasov simulations with varying the …
It has been claimed recently that massive sterile neutrinos could bring about a new concordance between observations of the cosmic microwave background (CMB), the large-scale structure (LSS) of the Universe, and local measurements of the Hubble constant, $H_0$. We demonstrate that this apparent concordance results from combining datasets which are in significant tension, even within this extended model, possibly indicating remaining systematic biases in the measurements. We further show that this tension remains when the cosmological model is further extended to include significant tensor mode…
Using a suite of hydrodynamical simulations with cold dark matter, baryons, and neutrinos, we present a detailed study of the effect of massive neutrinos on the 1-D and 3-D flux power spectra of the Lyman-$α$ (Ly$α$) forest. The presence of massive neutrinos in cosmology induces a scale- and time-dependent suppression of structure formation that is strongest on small scales. Measuring this suppression is a key method for inferring neutrino masses from cosmological data, and is one of the main goals of ongoing and future surveys like eBOSS, DES, LSST, Euclid or DESI. The clustering in the Ly$α$…
Using $N$-body simulations with massive neutrino density perturbations, we detect the scale-dependent linear halo bias with high significance. This is the first time that this effect is detected in simulations containing neutrino density perturbations on all scales, confirming the same finding from separate universe simulations. The scale dependence is the result of the additional scale in the system, i.e. the massive neutrino free-streaming length, and it persists even if the bias is defined with respect to the cold dark matter plus baryon (instead of total matter) power spectrum. The separat…
Weak lensing higher-order statistics to disentangle modified gravity and massive neutrinos
INAF - Osservatorio Astronomico di Roma（意大利国家天体物理研究所罗马天文台）；INFN - Sezione di Roma（意大利国家核物理研究所罗马分部）；Tor Vergata University（托尔维加塔大学）；Sapienza Università di Roma（罗马第一大学）；Aix-Marseille Université（艾克斯-马赛大学）；Scuola Superiore Meridionale（南方高等学院）；INFN - Sezione di Napoli（意大利国家核物理研究所那不勒斯分部）；Dipartimento di Fisica e Astronomia, Università di Bologna（博洛尼亚大学物理与天文系）；INAF - Osservatorio di Astrofisica e Scienza dello Spazio di Bologna（意大利国家天体物理研究所博洛尼亚天文与空间科学观测站）
We study the clustering properties of dark matter halos in real- and redshift-space in cosmologies with massless and massive neutrinos through a large set of state-of-the-art N-body simulations. We provide quick and easy-to-use prescriptions for the halo bias on linear and mildly non-linear scales, both in real and redshift space, which are valid also for massive neutrinos cosmologies. Finally we present a halo bias emulator,$\textbf{BE-HaPPY}$, calibrated on the N-body simulations, which is fast enough to be used in the standard Markov Chain Monte Carlo approach to cosmological inference. For…
We study the spherical, top-hat collapse model for a mixed dark matter model including cold dark matter (CDM) and massive neutrinos of mass scales ranging from m_nu= 0.05 to a few 0.1eV, the range of lower- and upper-bounds implied from the neutrino oscillation experiments and the cosmological constraints. To develop this model, we properly take into account relative differences between the density perturbation amplitudes of different components (radiation, baryon, CDM and neutrinos) around the top-hat CDM overdensity region assuming the adiabatic initial conditions. Furthermore, we solve the …
Sterile massive neutrinos are a natural extension of the Standard Model of elementary particles. The energy density of the extra sterile massive states affects cosmological measurements in an analogous way to that of active neutrino species. We perform here an analysis of current cosmological data and derive bounds on the masses of the active and the sterile neutrino states as well as on the number of sterile states. The so-called (3+2) models with three sub-eV active massive neutrinos plus two sub-eV massive sterile species is well within the 95% CL allowed regions when considering cosmologic…
The cosmic neutrino background anisotropy is calculated for massive neutrino states by solving the full Boltzmann equation. The effect of weak gravitational lensing, including the Limber approximation, is also derived for massive particles, and subsequently applied to the case of massive neutrinos.
The non-zero mass of neutrinos suppresses the growth of cosmic structure on small scales. Since the level of suppression depends on the sum of the masses of the three active neutrino species, the evolution of large-scale structure is a promising tool to constrain the total mass of neutrinos and possibly shed light on the mass hierarchy. In this work, we investigate these effects via a large suite of N-body simulations that include massive neutrinos using an analytic linear-response approximation: the Cosmological Massive Neutrino Simulations (MassiveNuS). The simulations include the effects of…
We provide a quantitative analysis of the halo model in the context of massive neutrino cosmologies. We discuss all the ingredients necessary to model the non-linear matter and cold dark matter power spectra and compare with the results of N-body simulations that incorporate massive neutrinos. Our neutrino halo model is able to capture the non-linear behavior of matter clustering with a $\sim 20\%$ accuracy up to very non-linear scales of $k=10~h/$Mpc (which would be affected by baryon physics). The largest discrepancies arise in the range $k=0.5-1~h/$Mpc where the 1-halo and 2-halo terms are …
We consider the possibility of an interaction in the dark sector in the presence of massive neutrinos, and study the observational constraints on three different scenarios of massive neutrinos using the most recent CMB anisotropy data in combination with type Ia supernovae, baryon acoustic oscillations, and Hubble parameter measurements. When a sterile neutrino is introduced in the interacting dark sector scenario in addition to the standard model prediction of neutrinos, we find that the coupling parameter, characterizing the interaction between dark matter and dark energy, is non-zero at 2$σ…
We provide exact analytic expressions for the density, pressure, average number density and pseudo-pressure for massive neutrinos and generic dark matter particles, both fermions and bosons. We then focus on massive neutrinos and we compare our analytic expressions with the numerical implementation in the CLASS Boltzmann code. We find that our modifications including the exact analytic expressions are in agreement to better than $10^{-4}\%$ with the default CLASS implementation in the estimation of the CMB power spectrum; our modifications do not have an impact on the performance of the code. …
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 $Λ$CDM 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 $\texttt{MG-PICOLA}$ and compare COLA simulations to full $\it N$…
Some of the dark matter in the Universe is made up of massive neutrinos. Their impact on the formation of large scale structure can be used to determine their absolute mass scale from cosmology, but to this end accurate numerical simulations have to be developed. Due to their relativistic nature, neutrinos pose additional challenges when one tries to include them in N-body simulations that are traditionally based on Newtonian physics. Here we present the first numerical study of massive neutrinos that uses a fully relativistic approach. Our N-body code, gevolution, is based on a weak-field for…
We review the impact of massive neutrinos on cosmological observables at the linear order. By means of N-body simulations we investigate the signatures left by neutrinos on the fully non-linear regime. We present the effects induced by massive neutrinos on the matter power spectrum, the halo mass function and on the halo-matter bias in massive neutrino cosmologies. We also investigate the clustering of cosmic neutrinos within galaxy clusters.
Accurate cosmological simulations that include the effect of non-linear matter clustering as well as of massive neutrinos are essential for measuring the neutrino mass scale from upcoming galaxy surveys. Typically, Newtonian simulations are employed and the neutrino distribution is sampled with a large number of particles in order to beat down the shot noise. Here we perform very efficient simulations with light massive neutrinos which require virtually no extra cost over matter-only simulations, and furthermore do not require tracer particles for the neutrinos. Instead, we use a weak-field di…
We present a novel method for detecting the relic neutrino background that takes advantage of structured quantum degeneracy to amplify the drag force from neutrinos scattering off a detector. Developing this idea, we present a characterization of the present day relic neutrino distribution in an arbitrary frame, including the influence of neutrino mass and neutrino reheating by $e^+e^-$ annihilation. We present explicitly the neutrino velocity and de Broglie wavelength distributions for the case of an Earthbound observer. Considering that relic neutrinos could exhibit quantum liquid features a…
Cosmological measurements are affected by the energy density of both active and sterile massive neutrinos. We extend here a recent analysis of current cosmological data to non minimal cosmologies. Several possible scenarios are examined: a constant w \neq -1 dark energy equation of state, a non flat universe, a time varying dark energy component and coupled dark matter dark energy universes or modified gravity scenarios. When considering cosmological data only, (3+2) massive neutrino models with ~0.5 eV sterile species are allowed at 95% CL. This scenario has been shown to reconcile reactor, L…
A consistent formulation to incorporate massive neutrinos in the perturbation theory of the effective CDM+baryons fluid is introduced. In this formulation all linear k dependence in the growth functions of CDM+baryons perturbations, as well as all consequent additional mode coupling at higher orders, are taken into account to any desirable accuracy. Our formulation regards the neutrino fraction, which is constant in time after the non-relativistic transition of neutrinos, and much smaller than unity, as the coupling constant of the theory. Then the "bare" perturbations are those in the massles…
Tensions between several cosmic observations were found recently, such as the inconsistent values of $H_{0}$ (or $σ_{8}$) were indicated by the different cosmic observations. Introducing the massive neutrinos in $Λ$CDM could potentially solve the tensions. Viable $f(R)$ gravity producing $Λ$CDM background expansion with massive neutrinos is investigated in this paper. We fit the current observational data: Planck-2015 CMB, RSD, BAO and SNIa to constrain the mass of neutrinos in viable $f(R)$ theory. The constraint results at 95\% confidence level are: $Σm_ν<0.202$ eV for the active neutrino ca…
Halo abundance and clustering in cosmologies with massive and asymmetric neutrinos
Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University（北京师范大学前沿天文与天体物理研究所）；School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院）；Institut d’Astrophysique de Paris, UMR 7095, CNRS, Sorbonne Université（巴黎天体物理研究所）；Department of Physics, the Chinese University of Hong Kong（香港大学物理系）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；School of Physics and Laboratory of Zhongyuan Light, Zhengzhou University（郑州大学物理学院与中原之光实验室）
In this paper, we consider rolling tachyon, with steep run-away type of potentials non-minimally coupled to massive neutrino matter. The coupling dynamically builds up at late times as neutrino matter turns non-relativistic. In case of scaling and string inspired potentials, we have shown that non-minimal coupling leads to minimum in the field potential. Given a suitable choice of model parameters, it is shown to give rise to late-time acceleration with the desired equation of state.
We use a suite of N-body simulations that incorporate massive neutrinos as an extra-set of particles to investigate their effect on the halo mass function. We show that for cosmologies with massive neutrinos the mass function of dark matter haloes selected using the spherical overdensity (SO) criterion is well reproduced by the fitting formula of Tinker et al. (2008) once the cold dark matter power spectrum is considered instead of the total matter power, as it is usually done. The differences between the two implementations, i.e. using $P_{\rm cdm}(k)$ instead of $P_{\rm m}(k)$, are more pron…
We revise the cosmological bounds on Hořava gravity taking into accounts the stringent constraint on the speed of propagation of gravitational waves from GW170817 and GRB170817A. In light of this we also investigate the degeneracy between massive neutrinos and Hořava gravity. We show that a luminal propagation of gravitational waves suppresses the large-scale Cosmic Microwave Background (CMB) radiation temperature anisotropies and the presence of massive neutrinos increases this effect. On the contrary large neutrinos mass can compensate the modifications induced by Hořava gravity in the lensi…
