We compute the Bayesian Evidence for models considered in the main analysis of Planck cosmic microwave background data. By utilising carefully-defined nearest-neighbour distances in parameter space, we reuse the Monte Carlo Markov Chains already produced for parameter inference to compute Bayes factors $B$ for many different model-dataset combinations. Standard 6-parameter flat $Λ$CDM model is favoured over all other models considered, with curvature being mildly favoured only when CMB lensing is not included. Many alternative models are strongly disfavoured by the data, including primordial correlated isocurvature models ($\ln B=-7.8$), non-zero scalar-to-tensor ratio ($\ln B=-4.3$), running of the spectral index ($\ln B = -4.7$), curvature ($\ln B=-3.6$), non-standard numbers of neutrinos ($\ln B=-3.1$), non-standard neutrino masses ($\ln B=-3.2$), non-standard lensing potential ($\ln B=-4.6$), evolving dark energy ($\ln B=-3.2$), sterile neutrinos ($\ln B=-6.9$), and extra sterile neutrinos with a non-zero scalar-to-tensor ratio ($\ln B=-10.8$). Other models are less strongly disfavoured with respect to flat $Λ$CDM. As with all analyses based on Bayesian Evidence, the final numbers depend on the widths of the parameter priors. We adopt the priors used in the Planck analysis, while performing a prior sensitivity analysis. Our quantitative conclusion is that extensions beyond the standard cosmological model are disfavoured by Planck data. Only when newer Hubble constant measurements are included does $Λ$CDM become disfavoured, and only mildly, compared with a dynamical dark energy model ($\ln B\sim +2$).
We study linear cosmological perturbations in the ``healthy extension'' of Horava-Lifshitz gravity which has recently been analyzed \cite{BPS2}. We find that there are two degrees of freedom for scalar metric fluctuations, but that one of them decouples in the infrared limit. Also, for appropriate choices of the parameters defining the Lagrangian, the extra mode can be made well-behaved even in the ultraviolet.
It has been claimed that the standard model of cosmology (LCDM) cannot easily account for a number of observations on relatively small scales, motivating extensions to the standard model. Here we introduce a new suite of cosmological simulations that systematically explores three plausible extensions: warm dark matter, self-interacting dark matter, and a running of the scalar spectral index of density fluctuations. Current observational constraints are used to specify the additional parameters that come with these extensions. We examine a large range of observable metrics on small scales, incl…
We propose a method based on the process of extracting gravitational wave (GW) parameters from GW signals to simulate the binary neutron-star (BNS) merging events. We simulate 1000 GW standard sirens based on the observation of the Einstein Telescope (ET). Almost all the simulated GW data are in the redshift range of $[0,3]$. The role of the GW standard siren in the inference of the cosmological parameters is investigated. We find that the GW data can help improve the accuracy of cosmological parameters. Moreover, the degeneracy of cosmological parameters is broken by the GW data. The GW stand…
In this work we show that the general singlet extension of the MSSM can naturally provide a self-interacting singlino dark matter to solve the small cosmological scale anomalies (a large Sommerfeld enhancement factor can also be obtained). However, we find that the NMSSM (the singlet extension of the MSSM with Z3 symmetry) cannot achieve this due to the restricted parameter space. In our analysis we introduce the concept of symmetric and antisymmetric viscosity cross sections to deal with the non-relativistic Majorana-fermion dark matter scattering.
We provide a new extension of general relativity (GR) which has the remarkable property of being more constrained than GR plus a cosmological constant, having one less free parameter. This is implemented by allowing the cosmological constant to have a consistent space-time variation, through coding its dynamics in the torsion tensor. We demonstrate this mechanism by adding a `quasi-topological' term to the Einstein action, which naturally realizes a dynamical torsion with an automatic satisfaction of the Bianchi identities. Moreover, variation of the action with respect to this dynamical $Λ$ f…
Reports of "cosmology in crisis" are in vogue, but as Mark Twain said, "the report of my death was an exaggeration". We explore what we might actually mean by the standard cosmological model, how tensions - or their apparent resolutions - might arise from too narrow a view, and why looking at the big picture is so essential. This is based on the seminar "All Cosmology, All the Time".
In this paper, we used standard rulers and standard candles (separately and jointly) to explore five popular dark energy models under assumption of spatial flatness of the Universe. As standard rulers, we used a data set comprising 118 galactic-scale strong lensing systems (individual standard rulers if properly calibrated for the mass density profile) combined with BAO diagnostics (statistical standard ruler). Supernovae Ia served asstandard candles. Unlike in the most of previous statistical studies involving strong lensing systems, we relaxed the assumption of singular isothermal sphere (SI…
In the minimal supersymmetric standard model (MSSM) extended by a singlet superfield, when the coupling between the singlet sector and the MSSM sector is tiny, the singlet sector can be a quasi dark sector with supersymmetry (SUSY). We investigate the cosmological phenomena in this scenario and obtain the following observations: (i) In the parameter space solving the small cosmological scale anomalies via self-interacting singlino dark matter (SIDM), a first-order phase transition (FOPT) can readily happen but requires rather light dark matter below MeV; (ii) The corresponding parameter space …
Gravitational waves (GWs) from compact binary stars at cosmological distances are promising and powerful cosmological probes, referred to as the GW standard sirens. With future GW detectors, we will be able to precisely measure source luminosity distances out to a redshift $z\sim5$. To extract cosmological information, previously proposed cosmological studies using the GW standard sirens rely on source redshift information obtained through an extensive electromagnetic follow-up campaign. However, the redshift identification is typically time consuming and rather challenging. Here, we propose a…
Recently, an extension of the geodesic equations of motion using the Dark Energy length scale was proposed. Here, we apply this extension to the analyzing the motion of test particles at the galactic scale and longer. A cosmological check of the extension is made using the observed rotational velocity curves and core sizes of 1393 spiral galaxies. We derive the density profile of a model galaxy using this extension, and with it, we calculate $σ_8$ to be $0.73_{\pm 0.12}$; this is within experimental error of the WMAP value of $0.761_{-0.048}^{+0.049}$. We then calculate $R_{200}$ to be $206_{\…
The accurate understanding of the ionization history of the Universe plays a fundamental role in modern cosmology. It includes a phase of cosmological reionization after the standard recombination epoch, possibly associated to the early stages of structure and star formation. While the simple "τ-parametrization" of the reionization process and, in particular, of its imprints on the CMB anisotropy likely represents a sufficiently accurate modelling for the interpretation of current CMB data, a great attention has been recently posed on the accurate computation of the reionization signatures in …
The presence of complex hierarchical gravitational structures is one of the main features of the observed universe. Here, structure formation is studied both for the standard ($Λ\rm CDM$) cosmological model and for the Dirac-Milne universe, a matter-antimatter symmetric universe that was {\gm recently} proposed as an alternative "coasting" cosmological scenario. One-dimensional numerical simulations reveal the analogies and differences between the two models. Although structure formation is faster in the Dirac-Milne universe, both models predict that it ends shortly before the present epoch, a…
In Horava's theory of gravity, Lorentz symmetry is broken in exchange for renormalizability, but the original theory has been argued to be plagued with problems associated with a new scalar mode stemming from the very breaking of Lorentz symmetry. Recently, Blas, Pujolas, and Sibiryakov have proposed a healthy extension of Horava gravity, in which the behavior of the scalar mode is improved. In this paper, we study scalar modes of cosmological perturbations in extended Horava gravity. The evolution of metric and density perturbations is addressed analytically and numerically. It is shown that …
We test extensions to the standard cosmological model with weak gravitational lensing tomography using 450 deg$^2$ of imaging data from the Kilo Degree Survey (KiDS). In these extended cosmologies, which include massive neutrinos, nonzero curvature, evolving dark energy, modified gravity, and running of the scalar spectral index, we also examine the discordance between KiDS and cosmic microwave background measurements from Planck. The discordance between the two datasets is largely unaffected by a more conservative treatment of the lensing systematics and the removal of angular scales most sen…
The purpose of this work is to investigate the prospects of using the future standard siren data without redshift measurements to constrain cosmological parameters. With successful detections of gravitational wave (GW) signals an era of GW astronomy has begun. Unlike the electromagnetic domain, GW signals allow direct measurements of luminosity distances to the sources, while their redshifts remain to be measured by identifying electromagnetic counterparts. This leads to significant technical problems for almost all possible BH-BH systems. It is the major obstacle to cosmological applications …
Before cosmic reionization, hydrogen atoms acquire a spin polarization quadrupole through interaction with the anisotropic 21-cm radiation field. The interaction of this quadrupole with anisotropies in the cosmic microwave background (CMB) radiation field gives a net spin orientation to the hydrogen atoms. The 21-cm radiation emitted by these spin-oriented hydrogen atoms is circularly polarized. Here, we reformulate succinctly the derivation of the expression for this circular polarization in terms of Cartesian (rather than spherical) tensors. We then compute the angular power spectrum of the …
We propose a relativistic model of dark matter reproducing at once the concordance cosmological model $Λ$-Cold-Dark-Matter ($Λ$-CDM) at cosmological scales, and the phenomenology of the modified Newtonian dynamics (MOND) at galactic scales. To achieve this we postulate a non-standard form of dark matter, consisting of two different species of particles coupled to gravity via a bimetric extension of general relativity, and linked together through an internal vector field (a "graviphoton") generated by the mass of these particles. We prove that this dark matter behaves like ordinary cold dark ma…
This is a review article for The Review of Particle Physics 2010 (aka the Particle Data Book). It forms a compact review of knowledge of the cosmological parameters at the beginning of 2010. Topics included are Parametrizing the Universe; Extensions to the standard model; Probes; Bringing observations together; Outlook for the future.
This is a review article for The Review of Particle Physics 2014 (aka the Particle Data Book). It forms a compact review of knowledge of the cosmological parameters at the beginning of 2014. Topics included are Parametrizing the Universe; Extensions to the standard model; Probes; Bringing observations together; Outlook for the future.
We derive several, detailed relationships in terms of the Friedmann, Robertson, Walker (FRW) generalization which describe the Universe during both the radiation and matter dominated epochs. We explicitly provide for the influence of radiation, rather than burying this term within the matter term. Several models allow the cosmological constant (CC) to vary with universe expansion in differing manners. We evaluate these and other popular models including the $Λ$CDM({standard model}), quintessence as presented by Vishwakarma, Equation of State (EoS) and the Carmeli model with data from the 580 U…
We present an improved Minimal Variance (MV) method for using a radial peculiar velocity sample to estimate the average of the three-dimensional velocity field over a spherical volume, which leads to an easily interpretable bulk flow measurement. The only assumption required is that the velocity field is irrotational. The resulting bulk flow estimate is particularly insensitive to smaller scale flows. We also introduce a new constraint into the MV method that ensures that bulk flow estimates are independent of the value of the Hubble constant $H_o$; this is important given the tension between …
Teleparallel gravity offers a new avenue in which to construct gravitational models beyond general relativity. While teleparallel gravity can be framed in a way to be dynamically equivalent to general relativity, its modifications are mostly not equivalent to the traditional route to modified gravity. $f(T,B)$ gravity is one such gravitational theory where the second and fourth order contributions to the field equations are decoupled. In this work, we explore the all important cosmological perturbations of this new framework of gravity. We derive the gravitational propagation equation, its vec…
Cosmological perturbations are generally described by quantum fields on (curved but) classical space-times. While this strategy has a large domain of validity, it can not be justified in the quantum gravity era where curvature and matter densities are of Planck scale. Using techniques from loop quantum gravity, the standard theory of cosmological perturbations is extended to overcome this limitation. The new framework sharpens conceptual issues by distinguishing between the true and apparent trans-Planckian difficulties and provides sufficient conditions under which the true difficulties can b…
We study cosmological perturbations around self-accelerating solutions to two extensions of nonlinear massive gravity: the quasi-dilaton theory and the mass-varying theory. We examine stability of the cosmological solutions, and the extent to which the vanishing of the kinetic terms for scalar and vector perturbations of self-accelerating solutions in massive gravity is generic when the theory is extended. We find that these kinetic terms are in general non-vanishing in both extensions, though there are constraints on the parameters and background evolution from demanding that they have the co…
We investigate the cosmological behavior in a universe governed by time asymmetric extensions of general relativity, which is a novel modified gravity based on the addition of new, time-asymmetric, terms on the Hamiltonian framework, in a way that the algebra of constraints and local physics remain unchanged. Nevertheless, at cosmological scales these new terms can have significant effects that can alter the universe evolution, both at early and late times, and the freedom in the choice of the involved modification function makes the scenario able to produce a huge class of cosmological behavi…
Accepting the fine tuned cosmological constant hypothesis, we have recently proposed that this hypothesis can be tested if the dark matter freeze out occurs at the electroweak scale and if one were to measure an anomalous shift in the dark matter relic abundance. In this paper, we numerically compute this relic abundance shift in the context of explicit singlet extensions of the Standard Model and explore the properties of the phase transition which would lead to the observationally most favorable scenario. Through the numerical exploration, we explicitly identify a parameter space in a single…
Correlation functions of two long-wavelength modes with several short-wavelength modes are shown to be related to lower order correlation functions, using the background wave method, and independently, by exploiting symmetries of the wavefunction of the Universe. These soft identities follow from the non-linear extension of the adiabatic modes of Weinberg, and their generalization by Hinterbichler et. al. The extension is shown to be unique. A few checks of the identities are presented.
Quantum scale invariance in the UV has been recently advocated as an attractive way of solving the gauge hierarchy problem arising in the Standard Model. We explore the cosmological signatures at the electroweak scale when the breaking of scale invariance originates from a hidden sector and is mediated to the Standard Model by gauge interactions (Gauge Mediation). These scenarios, while being hard to distinguish from the Standard Model at LHC, can give rise to a strong electroweak phase transition leading to the generation of a large stochastic gravitational wave background in possible reach o…
The inflationary universe can be viewed as a "Cosmological Collider" with energy of Hubble scale, producing very massive particles and recording their characteristic signals in primordial non-Gaussianities. To utilize this collider to explore any new physics at very high scales, it is a prerequisite to understand the background signals from the particle physics Standard Model. In this paper we describe the Standard Model background of the Cosmological Collider.
Gravitational wave standard sirens can be used to arbitrate the $H_0$ tension within the following several years. In the future, the observation of gravitational wave standard sirens would be developed into a powerful new cosmological probe because they can play an important role in breaking parameter degeneracies formed by other observations. Therefore, gravitational wave standard sirens are of great importance for the future accurate measurement of cosmological parameters.
At the present work, it is studied the extension of F (R) gravities to the new recently proposed theory of gravity, the so-called Horava-Lifshitz gravity, which provides a way to make the theory power counting renormalizable by breaking Lorentz invariance. It is showed that dark energy can be well explained in the frame of this extension, just in terms of gravity. It is also explored the possibility to unify inflation and late-time acceleration under the same mechanism, providing a natural explanation the accelerated expansion.
Exploring $Λ$CDM extensions with SPT-3G and Planck data: 4$σ$ evidence for neutrino masses and implications of extended dark energy models for cosmological tensions
We discuss an extension of the massively parallel cosmological simulation code GADGET-2, which now enables investigation of multiple and distinct gravitational force laws, provided they are dominated by a constant scaling of the Newtonian force. In addition to simplifying investigations of a universally modified force law, the ngravs extension provides a foundation for state-of-the-art collisionless cosmological simulations of exotic gravitational scenarios. We briefly review the algorithms used by GADGET-2, and present our extension to multiple gravities, highlighting additional features that…
Taiji, a space-based gravitational-wave observatory, consists of three satellites forming an equilateral triangle with arm length of $3\times 10^6$ km, orbiting around the Sun. Taiji is able to observe the gravitational-wave standard siren events of massive black hole binary (MBHB) merger, which is helpful in probing the expansion of the universe. In this paper, we preliminarily forecast the capability of Taiji for improving cosmological parameter estimation with the gravitational-wave standard siren data. We simulate five-year standard siren data based on three fiducial cosmological models an…
Reducing cosmological degeneracies by combining multiple classes of LISA gravitational-wave standard sirens
Université de Toulouse（图卢兹大学）；Università di Milano - Bicocca（米兰比可卡大学）；INFN, Sezione di Milano-Bicocca（意大利国家核物理研究所米兰-比可卡分部）；Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut（马克斯·普朗克引力物理研究所爱因斯坦研究所）；SISSA（的里雅斯特高等研究学院）；INFN Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；IFPU - Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）；CERN（欧洲核子研究中心）；Université de Genève（日内瓦大学）；Università di Pisa（比萨大学）；INFN, Sezione di Pisa（意大利国家核物理研究所比萨分部）
We investigate how the properties of dark energy affect the cosmological measurements of neutrino mass and extra relativistic degrees of freedom. We limit ourselves to the most basic extensions of $Λ$ cold dark matter (CDM) model, i.e. the $w$CDM model with one additional parameter $w$, and the $w_{0}w_{a}$CDM model with two additional parameters, $w_{0}$ and $w_{a}$. In the cosmological fits, we employ the 2015 cosmic microwave background temperature and polarization data from the Planck mission, in combination with low-redshift measurements such as the baryon acoustic oscillations, Type Ia s…
We use 38 C IV quasar (QSO) reverberation-mapped (RM) observations, which span eight orders of magnitude in luminosity and the redshift range $0.001064 \leq z \leq 3.368$, to simultaneously constrain cosmological-model and QSO radius-luminosity ($R-L$) relation parameters in six cosmological models, using an improved technique that more correctly accounts for the asymmetric errors bars of the time-lag measurements. We find that $R-L$ relation parameters are independent of the cosmological models used in the analysis and so the $R-L$ relation can be used to standardize the C IV QSOs. The C IV Q…
In the standard model of cosmology, the Universe is static in comoving coordinates; expansion occurs homogeneously and is represented by a global scale factor. The baryon acoustic oscillation (BAO) peak location is a statistical tracer that represents, in the standard model, a fixed comoving-length standard ruler. Recent gravitational collapse should modify the metric, rendering the effective scale factor, and thus the BAO standard ruler, spatially inhomogeneous. Using the Sloan Digital Sky Survey, we show to high significance (P < 0.001) that the spatial compression of the BAO peak location i…
We show that each of the three Dainotti-correlated gamma-ray burst (GRB) data sets recently compiled by Wang et al. and Hu et al., that together probe the redshift range $0.35 \leq z \leq 5.91$, obey cosmological-model-independent Dainotti correlation relations and so are standardizable. We use these GRB data in conjunction with the best currently-available Amati-correlated GRB data, that probe $0.3399 \leq z \leq 8.2$, to constrain cosmological model parameters. The resulting cosmological constraints are weak, providing lower limits on the non-relativistic matter density parameter, mildly fav…
In this work, we use the simulated gravitational wave (GW) standard siren data from the future observation of the Einstein Telescope (ET) to constrain various dark energy cosmological models, including the $Λ$CDM, $w$CDM, CPL, $α$DE, GCG, and NGCG models. We also use the current mainstream cosmological electromagnetic observations, i.e., the cosmic microwave background anisotropies data, the baryon acoustic oscillations data, and the type Ia supernovae data, to constrain these models. We find that the GW standard siren data could tremendously improve the constraints on the cosmological paramet…
Cosmological constraints on the sum of neutrino masses and on the effective number of neutrino species in standard and non-standard scenarios are computed using the most recent available cosmological data. Our cosmological data sets include the measurement of the Baryonic Acoustic Oscillation (BAO) feature in the Data Release 9 CMASS sample of the Baryon Oscillation Spectroscopic Survey (BOSS). We study in detail the different degeneracies among the parameters, as well as the impact of the different data sets used in the analyses. When considering bounds on the sum of the three active neutrino…
The third-generation ground-based gravitational-wave (GW) detector, Cosmic Explorer (CE), is scheduled to start its observation in the 2030s. In this paper, we make a forecast for cosmological parameter estimation with gravitational-wave standard siren observation from the CE. We use the simulated GW standard siren data of CE to constrain the $Λ$CDM, $w$CDM and CPL models. We combine the simulated GW data with the current cosmological electromagnetic observations including the latest cosmic microwave background anisotropies data from Planck, the optical baryon acoustic oscillation measurements…
This paper is a pedagogical introduction to models of gravity and how to constrain them through cosmological observations. We focus on the Horndeski scalar-tensor theory and on the quantities that can be measured with a minimum of assumptions. Alternatives or extensions of General Relativity have been proposed ever since its early years. Because of Lovelock theorem, modifying gravity in four dimensions typically means adding new degrees of freedom. The simplest way is to include a scalar field coupled to the curvature tensor terms. The most general way of doing so without incurring in the Ostr…
We show that the Platinum gamma-ray burst (GRB) data compilation, probing the redshift range $0.553 \leq z \leq 5.0$, obeys a cosmological-model-independent three-parameter fundamental plane (Dainotti) correlation and so is standardizable. While they probe the largely unexplored $z \sim 2.3-5$ part of cosmological redshift space, the GRB cosmological parameter constraints are consistent with, but less precise than, those from a combination of baryon acoustic oscillation (BAO) and Hubble parameter [$H(z)$] data. In order to increase the precision of GRB-only cosmological constraints, we exclude…
TianQin is a space-based gravitational-wave observatory scheduled to be launched in the 2030s. In this work, we make a preliminary forecast for the cosmological parameter estimation with the gravitational-wave standard siren observation from TianQin. We simulate the standard siren data of TianQin based on its 5-year observation after the completion of construction. In the simulation, three models for the population of massive black hole binary (MBHB), i.e., pop III, Q3nod, and Q3d, are considered to predict the event numbers of MBHB mergers. We find that: (i) among the three MBHB models, the Q…
Recently, we have proposed a definition for the vacuum and suggest a mechanism for symmetry breaking. In this mechanism extra massless fields, vacuum fields, arise. We apply our method to the standard model of particle physics and obtain vacuum sector of this model. Vacuum field of the standard model is a four-vector with electromagnetic nature. This field is invariant under $ U(1)_{em} $ gauge transformation. We speculate that it could be responsible for many cosmological phenomena like inflation, dark energy and cosmic magnetic fields.
The standard model of particle physics is extended by adding a purely neutrinophilic dark sector. It is shown that theories which accommodate standard model neutrinos as dark radiation are resurrected. Sterile neutrinos bridge the visible and the dark sector and can keep their mutual interactions effective even after the epoch of big bang nucleosythesis. This prolonged contact between dark matter and standard model neutrinos solves the well-known small-scale structure problems of the cosmological standard model. The dark sector presented in this work satisfies all experimental and observationa…
The multi-messenger observation of GW170817 enabled the first historic measurement of the Hubble constant via a standard siren, so-called in analogy to standard candles that enabled the measurement of the luminosity distance versus redshift relationship at small redshift. In the next decades, third-generation observatories are expected to detect hundreds to thousand of gravitational wave events from compact binary coalescences with potentially a joint electromagnetic counterpart. In the present work, we show how future standard siren detections can be used within the framework of Bayesian mode…
Non-standard interactions (NSI) between neutrinos and electrons can significantly modify the decoupling of neutrinos from the plasma. These interactions have two effects on the overall picture: (i) they alter neutrino oscillations though matter effects and (ii) they modify the scattering and annihilation processes involving neutrinos and electrons and positrons. We study the role of non-universal and flavour-changing NSI in the decoupling and how they impact the determination of the effective number of neutrinos, $N_{eff}$. We examine the degeneracies between NSI parameters and we compare the …
The search for the physical mechanism underlying the observational evidence for the acceleration of the recent universe is a compelling goal of modern fundamental cosmology. Here we quantitatively study a class of homogeneous and isotropic cosmological models in which the matter side of Einstein's equations includes, in addition to the canonical term, a term proportional to the trace of the energy-momentum tensor, $T=ρ-3p$, and constrain these models using low redshift background cosmology data. One may think of these models as extensions of general relativity with a nonlinear matter Lagrangia…
The modern cosmology is based on inflationary models with baryosynthesis and dark matter/energy.It implies extension of particle symmetry beyond the Standard model. Studies of physical basis of the modern cosmology combine direct searches for new physics at accelerators with its indirect non-accelerator probes, in which cosmological consequences of particle models play important role. The cosmological consequences of particle models inevitably go beyond the 'standard' cosmological $Λ$CDM model and some possible feature of such 'nonstandard'cosmological scenarios is the subject of the present b…
In this master's thesis we study the production of axion dark matter through the so-called misalignment mechanism by considering that during that time, the universe was dominated by a new kind of fluid, different than radiation. We perform a very detailed analysis of the oscillation temperature and the relic density today, both analytically and numerically. Our findings show that on the one hand, the oscillation temperature is strongly influenced by the non-standard cosmology, affecting the relic density, and on the other hand, the energy density of the axion gets diluted, because the new flui…
Neutrino non-standard interactions (NSI) with electrons are known to alter the picture of neutrino decoupling from the cosmic plasma. NSI modify both flavour oscillations through matter effects, and the annihilation and scattering between neutrinos and electrons and positrons in the thermal plasma. In view of the forthcoming cosmological observations, we perform a precision study of the impact of non-universal and flavour-changing NSI on the effective number of neutrinos, $N_{eff}$. We present the variation of $N_{eff}$ arising from the different NSI parameters and discuss the existing degener…
