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Register a new userThe Acceleration Scale, Modified Newtonian Dynamics, and Sterile Neutrinos
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General Relativity is able to describe the dynamics of galaxies and larger cosmic structures only if most of the matter in the Universe is dark, namely it does not emit any electromagnetic radiation. Intriguingly, on the scale of galaxies, there is strong observational evidence that the presence of dark matter appears to be necessary only when the gravitational field inferred from the distribution of the luminous matter falls below an acceleration of the order of 10^(-10) m/s^2. In the standard model, which combines Newtonian gravity with dark matter, the origin of this acceleration scale is challenging and remains unsolved. On the contrary, the full set of observations can be neatly described, and were partly predicted, by a modification of Newtonian dynamics, dubbed MOND, that does not resort to the existence of dark matter. On the scale of galaxy clusters and beyond, however, MOND is not as successful as on the scale of galaxies, and the existence of some dark matter appears unavoidable. A model combining MOND with hot dark matter made of sterile neutrinos seems to be able to describe most of the astrophysical phenomenology, from the power spectrum of the cosmic microwave background anisotropies to the dynamics of dwarf galaxies. Whether there exists a yet unknown covariant theory that contains General Relativity and Newtonian gravity in the weak field limit, and MOND as the ultra-weak field limit is still an open question.
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A relativistic theory of modified gravity has been recently proposed by Bekenstein. The tensor field in Einsteins theory of gravity is replaced by a scalar, a vector, and a tensor field which interact in such a way to give Modified Newtonian Dynamics (MOND) in the weak-field non-relativistic limit. We study the evolution of the universe in such a theory, identifying its key properties and comparing it with the standard cosmology obtained in Einstein gravity. The evolution of the scalar field is akin to that of tracker quintessence fields. We expand the theory to linear order to find the evolution of perturbations on large scales. The impact on galaxy distributions and the cosmic microwave background is calculated in detail. We show that it may be possible to reproduce observations of the cosmic microwave background and galaxy distributions with Bekensteins theory of MOND.
A unique signature of the modified Newtonian dynamics (MOND) paradigm is its peculiar behavior in the vicinity of the points where the total Newtonian acceleration exactly cancels. In the Solar System, these are the saddle points of the gravitational potential near the planets. Typically, such points are embedded into low-acceleration bubbles where modified gravity theories a` la MOND predict significant deviations from Newtons laws. As has been pointed out recently, the Earth-Sun bubble may be visited by the LISA Pathfinder spacecraft in the near future, providing a unique occasion to put these theories to a direct test. In this work, we present a high-precision model of the Solar Systems gravitational potential to determine accurate positions and motions of these saddle points and study the predicted dynamical anomalies within the framework of quasi-linear MOND. Considering the expected sensitivity of the LISA Pathfinder probe, we argue that interpolation functions which exhibit a faster transition between the two dynamical regimes have a good chance of surviving a null result. An example of such a function is the QMOND analog of the so-called simple interpolating function which agrees well with much of the extragalactic phenomenology. We have also discovered that several of Saturns outermost satellites periodically intersect the Saturn-Sun bubble, providing the first example of Solar System objects that regularly undergo the MOND regime.
In this paper, we constrain the dimensionless Compton wavelength parameter $B_0$ of $f(R)$ gravity as well as the mass of sterile neutrino by using the cosmic microwave background observations, the baryon acoustic oscillation surveys, and the linear growth rate measurements. Since both the $f(R)$ model and the sterile neutrino generally predict scale-dependent growth rates, we utilize the growth rate data measured in different wavenumber bins with the theoretical growth rate approximatively scale-independent in each bin. The employed growth rate data come from the peculiar velocity measurements at $z=0$ in five wavenumber bins, and the redshift space distortions measurements at $z=0.25$ and $z=0.37$ in one wavenumber bin. By constraining the $f(R)$ model alone, we get a tight 95% upper limit of $log_{10}B_0<-4.1$. This result is slightly weakened to $log_{10}B_0<-3.8$ (at 2$sigma$ level) once we simultaneously constrain the $f(R)$ model and the sterile neutrino mass, due to the degeneracy between the parameters of the two. For the massive sterile neutrino parameters, we get the effective sterile neutrino mass $m_{ u,{rm{sterile}}}^{rm{eff}}<0.62$ eV (2$sigma$) and the effective number of relativistic species $N_{rm eff}<3.90$ (2$sigma$) in the $f(R)$ model. As a comparison, we also obtain $m_{ u,{rm{sterile}}}^{rm{eff}}<0.56$ eV (2$sigma$) and $N_{rm eff}<3.92$ (2$sigma$) in the standard $Lambda$CDM model.
Sterile neutrinos can affect the evolution of the universe, and thus using the cosmological observations can search for sterile neutrinos. In this work, we use the cosmic microwave background (CMB) anisotropy data from the Planck 2018 release, combined with the latest baryon acoustic oscillation (BAO), type Ia supernova (SN), and Hubble constant ($H_0$) data, to constrain the cosmological models with considering sterile neutrinos. In order to test the influences of the properties of dark energy on the constraint results of searching for sterile neutrinos, in addition to the $Lambda$ cold dark matter ($Lambda$CDM) model, we also consider the $w$CDM model and the holographic dark energy (HDE) model. We find that sterile neutrinos cannot be detected when the $H_0$ local measurement is not included in the data combination. When the $H_0$ measurement is included in the joint constraints, it is found that $Delta N_{rm eff}>0$ is detected at about 2.7$sigma$ level for the $Lambda$CDM model and at about 1--1.7$sigma$ level for the $w$CDM model. However, $m_{ u,{rm{sterile}}}^{rm{eff}}$ still cannot be well constrained and only upper limits can be given. In addition, we find that the HDE model is definitely ruled out by the current data. We also discuss the issue of the Hubble tension, and we conclude that involving sterile neutrinos in the cosmological models cannot truly resolve the Hubble tension.
We investigate the impacts of dark energy on constraining massive (active/sterile) neutrinos in interacting dark energy (IDE) models by using the current observations. We employ two typical IDE models, the interacting $w$ cold dark matter (I$w$CDM) model and the interacting holographic dark energy (IHDE) model, to make an analysis. To avoid large-scale instability, we use the parameterized post-Friedmann approach to calculate the cosmological perturbations in the IDE models. The cosmological observational data used in this work include the Planck cosmic microwave background (CMB) anisotropies data, the baryon acoustic oscillation data, the type Ia supernovae data, the direct measurement of the Hubble constant, the weak lensing data, the redshift-space distortion data, and the CMB lensing data. We find that the dark energy properties could influence the constraint limits of active neutrino mass and sterile neutrino parameters in the IDE models. We also find that the dark energy properties could influence the constraints on the coupling strength parameter $beta$, and a positive coupling constant, $beta>0$, can be detected at the $2.5sigma$ statistical significance for the IHDE+$ u_s$ model by using the all-data combination. In addition, we also discuss the Hubble tension issue in these scenarios. We find that the $H_0$ tension can be effectively relieved by considering massive sterile neutrinos, and in particular in the IHDE+$ u_s$ model the $H_0$ tension can be reduced to be at the $1.28sigma$ level.
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