Constraining Early Dark Energy with Large-Scale Structure
Mikhail M. Ivanov, Evan McDonough, J. Colin Hill, Marko Simonović, Michael W. Toomey, Stephon Alexander, Matias Zaldarriaga
备注:
26 pages, 12 figures. v2: Version to appear in Phys Rev D. Appendices B and C demonstrate that EDE provides a worse fit than LCDM to Planck+BOSS data, and that constraints are not driven by prior volume effects
An axion-like field comprising $\sim 10\%$ of the energy density of the universe near matter-radiation equality is a candidate to resolve the Hubble tension; this is the "early dark energy" (EDE) model. However, as shown in Hill et al. (2020), the model fails to simultaneously resolve the Hubble tension and maintain a good fit to both cosmic microwave background (CMB) and large-scale structure (LSS) data. Here, we use redshift-space galaxy clustering data to sharpen constraints on the EDE model. We perform the first EDE analysis using the full-shape power spectrum likelihood from the Baryon Oscillation Spectroscopic Survey (BOSS), based on the effective field theory (EFT) of LSS. The inclusion of this likelihood in the EDE analysis yields a $25\%$ tighter error bar on $H_0$ compared to primary CMB data alone, yielding $H_0 = 68.54^{+0.52}_{-0.95}$ km/s/Mpc ($68\%$ CL). In addition, we constrain the maximum fractional energy density contribution of the EDE to $f_{\rm EDE} < 0.072$ ($95\%$ CL). We explicitly demonstrate that the EFT BOSS likelihood yields much stronger constraints on EDE than the standard BOSS likelihood. Including further information from photometric LSS surveys,the constraints narrow by an additional $20\%$, yielding $H_0 = 68.73^{+0.42}_{-0.69}$ km/s/Mpc ($68\%$ CL) and $f_{\rm EDE}<0.053$ ($95\%$ CL). These bounds are obtained without including local-universe $H_0$ data, which is in strong tension with the CMB and LSS, even in the EDE model. We also refute claims that MCMC analyses of EDE that omit SH0ES from the combined dataset yield misleading posteriors. Finally, we demonstrate that upcoming Euclid/DESI-like spectroscopic galaxy surveys can greatly improve the EDE constraints. We conclude that current data preclude the EDE model as a resolution of the Hubble tension, and that future LSS surveys can close the remaining parameter space of this model.
We examine the effectiveness of the weak gravity conjecture in constraining the dark energy by comparing with observations. For general dark energy models with plausible phenomenological interactions between dark sectors, we find that although the weak gravity conjecture can constrain the dark energy, the constraint is looser than that from the observations.
A unification of dark matter and dark energy in terms of a logotropic perfect dark fluid has recently been proposed, where deviations with respect to the standard $Λ{\rm CDM}$ model are dependent on a single parameter $B$. In this paper we show that the requirement that the linear growth of cosmic structures on comoving scales larger than $8 h^{-1} \, {\rm Mpc}$ is not significantly affected with respect to the standard $Λ{\rm CDM}$ result provides the strongest constraint to date on the model ($B <6 \times 10^{-7}$), an improvement of more than three orders of magnitude over previous constrai…
We explore the phenomenology of scalar fields coupled to asymptotically safe quantum gravity, in light of their potential significance for dark matter, for the inflaton as well as dynamical dark energy, and in the Higgs sector in and beyond the Standard Model. This work is a step towards delineating the boundaries of the asymptotically safe swampland by exploiting the constraining power of the asymptotic-safety paradigm. Firstly, we strengthen indications that quantum gravitational fluctuations could drive scalar potentials towards flatness, with intriguing potential implications for inflation…
We briefly discuss the intriguing case of a phenomenological non-gravitational coupling in the dark sector, where the interaction is parameterized as an energy transfer either from dark matter to dark energy or the opposite. We show that a non-zero coupling with an energy flow from the latter to the former leads to a full reconciliation of the tension between high- and low-redshift observations present in the standard cosmological model.
Many extensions of Standard Model (SM) include a dark sector which can interact with the SM sector via a light mediator. We explore the possibilities to probe such a dark sector by studying the distortion of the CMB spectrum from the blackbody shape due to the elastic scatterings between the dark matter and baryons through a hidden light mediator. We in particular focus on the model where the dark sector gauge boson kinetically mixes with the SM and present the future experimental prospect for a PIXIE-like experiment along with its comparison to the existing bounds from complementary terrestri…
As an attractive candidate for dark matter, the primordial black holes (PBHs) in the mass range ($10^{15} \sim 10^{16}$)$\mathrm{g}$ could be detected via their Hawking radiation, including neutrinos and antineutrinos of three flavors. In this paper, we investigate the possibility to constrain the PBH as dark matter by measuring (anti)neutrino signals at the large liquid-scintillator detector of Jiangmen Underground Neutrino Observatory (JUNO). Among six available detection channels, the inverse beta decay $\overlineν^{}_e + p \to e^+ + n$ is shown to be most sensitive to the fraction $f^{}_{\…
In this paper we propose a mechanism that protects theories violating a holographic bound suggested in arXiv:1203.5476 from developing accelerated expansion. The mechanism builts on work on transplanckian physics, and a non-trivial choice of vacuum states. If correct, it lends further support for detectable signatures in the CMBR signalling new physics.
For a general dark-energy equation of state, we estimate the maximum possible radius of massive structures that are not destabilized by the acceleration of the cosmological expansion. A comparison with known stable structures constrains the equation of state. The robustness of the constraint can be enhanced through the accumulation of additional astrophysical data and a better understanding of the dynamics of bound cosmic structures.
Based on the assumption that the dark energy possessing bulk viscosity is homogenously and isotropically permeated in the universe, we propose three new viscous dark energy (VDE) models to characterize the accelerating universe. By constraining these three models with the latest cosmological observations, we find that they just deviate very slightly from the standard cosmological model and can alleviate effectively the current $H_0$ tension between the local observation by the Hubble Space Telescope and the global measurement by the Planck Satellite. Interestingly, we conclude that a spatially…
The constraints on non-minimal dark sectors involving ensembles of unstable dark-matter species are well established and quite stringent in cases in which these species decay to visible-sector particles. However, in cases in which these ensembles decay exclusively to other, lighter dark-sector states, the corresponding constraints are less well established. In this paper, we investigate how information about the expansion rate of the universe at low redshifts gleaned from observations of Type Ia supernovae can be used to constrain ensembles of unstable particles which decay primarily into dark…
In this work we have used the recent cosmic chronometers data along with the latest estimation of the local Hubble parameter value, $H_0$ at 2.4\% precision as well as the standard dark energy probes, such as the Supernovae Type Ia, baryon acoustic oscillation distance measurements, and cosmic microwave background measurements (PlanckTT $+$ lowP) to constrain a dark energy model where the dark energy is allowed to interact with the dark matter. A general equation of state of dark energy parametrized by a dimensionless parameter `$β$' is utilized. From our analysis, we find that the interaction…
Ultra-light dark matter may consist of axion-like particles with masses below 10^(-19) eV. Two-photon interactions of these particles affect the polarization of radiation propagating through the dark matter. Coherent oscillations of the Bose condensate of the particles induce periodic changes in the plane of polarisation of emission passing through the condensate. We estimate this effect and analyze MOJAVE VLBA polarization observations of bright downstream features in the parsec-scale jets of active galaxies. Through the non-observation of periodic polarization changes, we are able to constra…
We forecast constraints on cosmological parameters in the interacting dark energy models using the mock data generated for neutral hydrogen intensity mapping (IM) experiments. In this work, we only consider the interacting dark energy models with energy transfer rate $Q=βHρ_{\rm c}$, and take BINGO, FAST, SKA1-MID, and Tianlai as typical examples of the 21 cm IM experiments. We find that the Tianlai cylinder array will play an important role in constraining the interacting dark energy model. Assuming perfect foreground removal and calibration, and using the Tianlai-alone data, we obtain $σ(H_0…
One of the great endeavors of the past decade has been the evaluation of different observational techniques for measuring dark energy properties and of theoretical techniques for constraining models of cosmic acceleration given cosmological data. This chapter reviews a few of the key developments, promises, and cautions for revealing dark energy. We also present a few new calculations, on direct detection of acceleration through redshift drift, the minimum uncertainty in the equation of state, and testing gravity.
We study a model of interacting dark matter and dark energy, in which the two components are coupled. We calculate the predictions for the 21-cm intensity mapping power spectra, and forecast the detectability with future single-dish intensity mapping surveys (BINGO, FAST and SKA-I). Since dark energy is turned on at $z\sim 1$, which falls into the sensitivity range of these radio surveys, the HI intensity mapping technique is an efficient tool to constrain the interaction. By comparing with current constraints on dark sector interactions, we find that future radio surveys will produce tight an…
Astrophysical neutrinos travel long distances from their sources to the Earth traversing dark matter halos of clusters of galaxies and that of our own Milky Way. The interaction of neutrinos with dark matter may affect the flux of neutrinos. The recent multi-messenger observation of a high energy neutrino, IceCube-170922A, can give a robust upper bound $σ/M_{dm} \lesssim 5.1\times 10^{-23} {\rm cm}^2 /$GeV on the interaction between neutrino and dark matter at a neutrino energy of 290 TeV allowing 90\% suppression. Combining the constraints from CMB and LSS at different neutrino energies, we c…
Even if Dark Matter (DM) is neutral under electromagnetism, it can still interact with the Standard Model (SM) via photon exchange from higher-dimensional operators. Here we classify the general effective operators coupling DM to photons, distinguishing between Dirac/Majorana fermion and complex/real scalar DM. We provide model-independent constraints on these operators from direct and indirect detection. We also constrain various DM-lepton operators, which induce DM-photon interactions via RG running or which typically arise in sensible UV-completions. This provides a simple way to quickly as…
Using renormalization-group flow and cosmological constraints on inflation models, we exploit a unique connection between cosmological inflation and the dynamical mass of dark-matter particles in the luminogenesis model, a unification model with the gauge group $SU(3)_C \times SU(6) \times U(1)_Y$, which breaks to the Standard Model with an extra gauge group for dark matter when the inflaton rolls into the true vacuum. In this model, inflaton decay gives rise to dark matter, which in turn decays to luminous matter in the right proportion that agrees with cosmological data. Some attractive feat…
If ultralight $(\ll$ eV), bosonic dark matter couples to right handed neutrinos, active neutrino masses and mixing angles depend on the ambient dark matter density. When the neutrino Majorana mass, induced by the dark matter background, is small compared to the Dirac mass, neutrinos are "pseudo-Dirac" fermions that undergo oscillations between nearly degenerate active and sterile states. We present a complete cosmological history for such a scenario and find severe limits from a variety of terrestrial and cosmological observables. For scalar masses in the "fuzzy" dark matter regime ($\sim 10^{…
Sanchez and Lacombe have ever developed a lattice fluid theory based on a well-defined statistical mechanical model. Taking the lattice fluid as a candidate of dark energy, we investigate the cosmic evolution of this fluid. Using the combined observational data of Type Ia Supernova (SNe Ia), Baryon Acoustic Oscillations (BAO) and Observational Hubble Data (OHD), we find the best fit value of the parameter in the model, $A = -0.3_{-0.1}^{+0.1}$. Then the cosmological implications of the model are presented.
I present the first constraints on decaying cold dark matter (DCDM) models thanks to the effective field theory of large-scale structure (EFTofLSS) applied to BOSS-DR12 data. I consider two phenomenological models of DCDM: i) a model where a fraction $f_{\rm dcdm}$ of cold dark matter (CDM) decays into dark radiation (DR) with a lifetime $τ$; ii) a model (recently suggested as a potential resolution to the $S_8$ tension) where all the CDM decays with a lifetime $τ$ into DR and a massive warm dark matter (WDM) particle, with a fraction $\varepsilon$ of the CDM rest mass energy transferred to th…
We show that Big Bang Nucleosynthesis (BBN) significantly constrains axion-like dark matter. The axion acts like an oscillating QCD $θ$ angle that redshifts in the early universe, increasing the neutron-proton mass difference at neutron freeze-out. An axion-like particle that couples too strongly to QCD results in the underproduction of 4He during BBN and is thus excluded. The BBN bound overlaps with much of the parameter space that would be covered by proposed searches for time-varying neutron EDMs. The QCD axion does not couple strongly enough to affect BBN.
We use the measurement of gamma-ray burst (GRB) distances to constrain dark energy cosmological model parameters. We employ two methods for analyzing GRB data - fitting luminosity relation of GRBs in each cosmology and using distance measures computed from binned GRB data. Current GRB data alone cannot tightly constrain cosmological parameters and allow for a wide range of dark energy models.
Recently, the observed equation of state for dark energy appears to favor values below $-1$. The tendency implies that the nature of dark energy may be quite different from that of the cosmological constant. In view of the adjustment on the equation of state keeps decreasing, the introduction of the phantom energy seems inevitable. By employing observational constraints from supernovae and from the acoustic scale in which the accuracy of the data has become extraordinary, we apply a phenomenological scenario to be acquainted with the evolution of our universe. The demonstration on the constrai…
In a large class of models we show that the light scalar field responsible for the Sommerfeld enhancement in the annihilation of dark matter leads to observable direct detection rates, due to its mixing with the standard model Higgs. As a result the large annihilation cross-section of dark matter at present epoch, required to explain the observed cosmic ray anomalies, can be strongly constrained by direct searches. In particular Sommerfeld boost factors of order of a few hundred are already out of the CDMS-II upper bound at 90% confidence level for reasonable values of the model parameters.
The local measurement of $H_0$ is in tension with the prediction of $Λ$CDM model based on the Planck data. This tension may imply that dark energy is strengthened in the late-time Universe. We employ the latest cosmological observations on CMB, BAO, LSS, SNe, $H(z)$ and $H_0$ to constrain several interacting dark energy models. Our results show no significant indications for the interaction between dark energy and dark matter. The $H_0$ tension can be moderately alleviated, but not totally released.
We perform a forecast analysis of the capability of the eLISA space-based interferometer to constrain models of early and interacting dark energy using gravitational wave standard sirens. We employ simulated catalogues of standard sirens given by merging massive black hole binaries visible by eLISA, with an electromagnetic counterpart detectable by future telescopes. We consider three-arms mission designs with arm length of 1, 2 and 5 million km, 5 years of mission duration and the best-level low frequency noise as recently tested by the LISA Pathfinder. Standard sirens with eLISA give access …
We constrain scattering length parameters in a Bose-Einstein condensate dark matter model by using galaxy clusters radii, with the implementation of a method previously applied to galaxies. At the present work, we use a sample of 114 clusters radii in order to obtain the scattering lengths associated with a dark matter particle mass in the range $10^{-6}-10^{-4}\, {\rm eV}$. We obtain scattering lengths that are five orders of magnitude larger than the ones found in the galactic case, even when taking into account the cosmological expansion in the cluster scale by means of the introduction of …
We investigate the possibility of constraining the dark energy equation of state by measuring the ratio of Einstein radii in a strong gravitational lens system with two source planes. This quantity is independent of the Hubble parameter and directly measures the growth of angular diameter distances as a function of redshift. We investigate the prospects for a single double source plane system and for a forecast population of systems discovered by re-observing a population of single source lenses already known from a photometrically selected catalogue such as CASSOWARY or from a spectroscopical…
Observational growth rate data had been derived from observations of redshift distortions in galaxy redshift surveys. Here we use the growth rate data to place constraints on the dark energy model parameters. By performing a joint analysis with the Type Ia supernova, baryon acoustic oscillation and cosmic microwave background data, it is found that the growth rate data are useful for improving the constraints. The joint constraints show that the $Λ$CDM model is still in good agreement with current observations, although a time-variant dark energy still cannot be ruled out. It is argued that th…
The existence and detection of scalar fields could provide solutions to long-standing puzzles about the nature of dark matter, the dark compact objects at the centre of most galaxies, and other phenomena. Yet, self-interacting scalar fields are very poorly constrained by astronomical observations, leading to great uncertainties in estimates of the mass $m_ϕ$ and the self-interacting coupling constant $λ$ of these fields. To counter this, we have systematically employed available astronomical observations to develop new constraints, considerably restricting this parameter space. In particular, …
It has been long discussed that cosmic rays may contain signals of dark matter. In the last couple of years an anomaly of cosmic-ray positrons has drawn a lot of attentions, and recently an excess in cosmic-ray anti-proton has been reported by AMS-02 collaboration. Both excesses may indicate towards decaying or annihilating dark matter with a mass of around 1-10 TeV. In this article we study the gamma rays from dark matter and constraints from cross correlations with distribution of galaxies, particularly in a local volume. We find that gamma rays due to inverse-Compton process have large inte…
In this work we study the constraints on the dark matter interaction with the standard model particles, from the observations of dark matter relic density, the direct detection experiments of CDMS and XENON, and the indirect detection of the antiproton-to-proton ratio by PAMELA. A model independent way is adopted in the study by constructing the effective interaction operators between dark matter and standard model particles. The most general 4-fermion operators are investigated. We find that the constraints from different observations are complementary with each other. Especially the spin ind…
Ultralight dark photons predicted in several Standard Model extensions can trigger the superradiant instability around rotating black holes if their Compton wavelength is comparable to the Blackhole radius. Consequently, the angular momentum of the black hole is reduced to a value which depends upon the mass and spin of the black hole as well as the mass of the dark photon. We use the mass and spin measurements of the primary black holes in two recently observed binary black hole systems: GW190517 and GW190426_152155 to constrain dark photon mass in the ranges $1.7\times 10^{-14}{\rm\ eV}<m_{A…
We use the Chandra unresolved X-ray emission spectrum from a 12'-28' (2.8-6.4 kpc) annular region of the Andromeda galaxy to constrain the radiative decay of sterile neutrino warm dark matter. By excising the most baryon-dominated, central 2.8 kpc of the galaxy, we reduce the uncertainties in our estimate of the dark matter mass within the field of view and improve the signal-to-noise ratio of prospective sterile neutrino decay signatures relative to hot gas and unresolved stellar emission. Our findings impose the most stringent limit on the sterile neutrino mass to date in the context of the …
The recent observational evidence for the current cosmic acceleration have stimulated renewed interest in alternative cosmologies, such as scenarios with interaction in the dark sector (dark matter and dark energy). In general, such models contain an unknown negative-pressure dark component coupled with the pressureless dark matter and/or with the baryons that results in an evolution for the Universe rather different from the one predicted by the standard $Λ$CDM model. In this work we test the observational viability of such scenarios by using the most recent galaxy cluster gas mass fraction v…
The presence of a primordial magnetic field would have induced resonant conversions between photons and axion-like particles (ALPs) during the thermal history of the Universe. These conversions would have distorted the blackbody spectrum of the cosmic microwave background (CMB). In this context, we derive bounds on the photon-ALP resonant conversions using the high precision CMB spectral data collected by the FIRAS instrument on board of the Cosmic Background Explorer. We obtain upper limits on the product of the photon-ALP coupling constant g times the magnetic field strength B down to g B > …
In the inhomogeneous Universe, the cosmological conversion of dark photons into ordinary photons (and vice versa) may happen at a great number of resonance redshifts. This alters the CMB observed energy spectrum and degree of small-scale anisotropies. We utilize results from the EAGLE simulation to obtain the conversion probability along random line-of-sights to quantify these effects. We then apply our results to the case where dark photons are sourced by dark matter decay and their high-redshift conversion into ordinary photons modify the global 21 cm signal expected from the cosmic dawn era…
We investigate the primordial curvature perturbation by the observation of dark matter substructure. Assuming a bump in the spectrum of the curvature perturbation in the wavenumber of k>1 Mpc^{-1}, we track the evolution of the host halo and subhalos in a semi-analytic way. Taking into account possible uncertainties in the evaluation of the tidal stripping effect on the subhalo growth, we find a new robust bound on the curvature perturbation with a bump from the number of observed dwarf spheroidal galaxies in our Galaxy and the observations of the stellar stream. The upper limit on the amplitu…
We derive constraints on elastic scattering between baryons and dark matter using the cosmic microwave background (CMB) data from the Planck satellite and the Lyman-alpha forest data from the Sloan Digital Sky Survey. Elastic scattering allows baryons and dark matter to exchange momentum, affecting the dynamics of linear density perturbations in the early Universe. We derive constraints to scattering cross sections of the form sigma \propto v^n, allowing for a wide range of velocity dependencies with n between -4 and 2. We improve and correct previous estimates where they exist, including velo…
We present a spectroscopic catalog of (mostly) red galaxies in 24 galaxy clusters in the redshift range 0.17 < z < 0.92 obtained with the LRIS instrument on the Keck I telescope. Here we describe the observations and the galaxy spectra, including the discovery of three cD galaxies with LINER emission spectra, and the spectroscopic discovery of four new galaxy-galaxy lenses in cluster environments.
Cosmological observations are normally fit under the assumption that the dark sector can be decomposed into dark matter and dark energy components. However, as long as the probes remain purely gravitational, there is no unique decomposition and observations can only constrain a single dark fluid; this is known as the dark degeneracy. We use observations to directly constrain this dark fluid in a model-independent way, demonstrating in particular that the data cannot be fit by a dark fluid with a single constant equation of state. Parameterizing the dark fluid equation of state by a variety of …
Dark energy affects the Hubble expansion rate (namely, the expansion history) $H(z)$ by an integral over $w(z)$. However, the usual observables are the luminosity distances or the angular diameter distances, which measure the distance-redshift relation. Actually, dark energy affects the distances (and the growth factor) by a further integration over functions of $H(z)$. Thus, the direct measurements of the Hubble parameter $H(z)$ at different redshifts are of great importance for constraining the properties of dark energy. In this paper, we show how the typical dark energy models, for example,…
We study the gravothermal evolution of dark matter halos in the presence of dissipative dark matter self-interactions. Dissipative interactions are present in many particle-physics realizations of the dark-sector paradigm and can significantly accelerate the gravothermal collapse of halos compared to purely elastic dark matter self-interactions. This is the case even when the dissipative interaction timescale is longer than the free-fall time of the halo. Using a semianalytical fluid model calibrated with isolated and cosmological $N$-body simulations, we calculate the evolution of the halo pr…
Although most proposed dark matter candidates are stable, in order for dark matter to be present today, the only requirement is that its lifetime is longer than the age of the Universe, t_U ~ 4 10^17 s. Moreover, the dark matter particle could be produced via non-thermal processes and have a larger annihilation cross section from the canonical value for thermal dark matter, <sigma v> ~ 3 10^{-26} cm3/s. We propose a strategy to distinguish between dark matter annihilation and/or decay in the case that a clear signal is detected in future gamma-ray observations of Milky Way dwarf galaxies with …
The Figure of Merit Science Working Group (FoMSWG) recently forecast the constraints on dark energy that will be achieved prior to the Joint Dark Energy Mission (JDEM) by ground-based experiments that exploit baryon acoustic oscillations, type Ia supernovae, and weak gravitational lensing. We show that cluster counts from on-going and near-future surveys should provide robust, complementary dark energy constraints. In particular, we find that optimally combined optical and Sunyaev-Zel'dovich effect cluster surveys should improve the Dark Energy Task Force (DETF) figure of merit for pre-JDEM pr…
Constraining Dark Acoustic Oscillations with the High-Redshift UV Luminosity Function
C.N. Yang Institute for Theoretical Physics, Stony Brook University(纽约州立大学石溪分校杨振宁理论物理研究所);Department of Physics, University of Toronto(多伦多大学物理系);Theoretical Physics Department, CERN(欧洲核子研究中心理论物理部);Physics Department, Boston University(波士顿大学物理系);Department of Astronomy, The University of Texas at Austin(德克萨斯大学奥斯汀分校天文学系);Cosmic Frontier Center, The University of Texas at Austin(德克萨斯大学奥斯汀分校宇宙前沿中心);Texas Center for Cosmology & Astroparticle Physics(德克萨斯宇宙学与高能物理中心);Department of Astronomy & Astrophysics, University of California, San Diego(加州大学圣地亚哥分校天文与天体物理系)
In the cold dark matter scenario, galactic dark matter halos are populated with a large number of smaller subhalos. Previous work has shown that dark matter annihilations in subhalos can generate a distinctive, non-Poisson signal in the gamma-ray photon counts probability distribution function (PDF). Here we show that the gamma-ray PDF also carries information about the velocity dependence of the dark matter annihilation cross section. After calculating the PDF assuming $s$-wave and Sommerfeld-enhanced annihilation, we perform a mock data analysis to illustrate how current and future observati…
Starlight in the Universe impedes the passage of high energy (e.g. TeV) gamma rays due to positron-electron pair production. The history of this stellar radiation field depends upon observations of star formation rate which themselves can only be interpreted in the context of a particular cosmology. For different equations of state of dark energy, the star formation rate data suggests a different density of stellar photons at a particular redshift and a different probability of arrival of gamma rays from distant sources. In this work we aim to show that this effect can be used to constrain the…
We study the $B-L$ gauge extension of the Standard Model which contains a singlet scalar and three right-handed neutrinos. The vacuum expectation value of the singlet scalar breaks the $U(1)_{B-L}$ symmetry. Here the third generation right-handed neutrino is qualified as the dark matter candidate, as an artifact of $Z_2$-charge assignment. Relic abundance of the dark matter is consistent with WMAP9 and PLANCK data, only near scalar resonances where dark matter mass is almost half of the scalar boson masses. Requiring correct relic abundance, we restrict the parameter space of the scalar mixing…