arXiv subjects

Zhe Chang

Publications and source records attributed to Zhe Chang.

At least 91 records · Page 5Linked to original sources

arXiv2013

Finslerian perturbation for the $Λ$CDM model

We present Finslerian perturbation for the $Λ$CDM model, which breaks the isotropic symmetry of the universe. The analysis on the Killing vectors shows that the Randers-Finsler spacetime breaks the isotropic symmetry even if the scalar perturbations of the FRW metric vanish. In Randers-Finsler spacetime, the modified geodesic equation deduces a modified Boltzmann equation. We propose a perturbational version of the gravitational field equation in Randers-Finsler spacetime, where we have omitted the curvature tensor that does not belong to the base space of the tangent bundle. The gravitational field equations for the gravitational wave are also presented. The primordial power spectrum of the gravitational wave is investigated. We show that the primordial power spectrum for super-horizon perturbations is unchanged. For sub-horizon perturbations, however, the power spectrum is modified.

gr-qc↗

arXiv2013

Finslerian MOND versus the Strong Gravitational Lensing of the Early-type Galaxies

The gravitational lensing of Bullet Clusters and early-type galaxies pose serious challenges on the validity of MOND. Recently, Finslerian MOND, a generalization of MOND in the framework of Finsler gravity, has been proposed to explain the mass discrepancy problem of Bullet Cluster 1E 0657\ 558. In this paper, we check the validity of the Finslerian MOND in describing the strong gravitational lensing of early-type galaxies. The investigation on ten strong lenses of the CASTLES samples shows that there is no strong evidence for the existence of dark matter.

astro-ph.GA↗

arXiv2013

Cosmological model with local symmetry of very special relativity and constraints on it from supernovae

Based on Cohen \& Glashow's very special relativity [A. G. Cohen and S. L. Glashow, Phys. Rev. Lett. {\bf 97} (2006) 021601], we propose an anisotropic modification to the Friedmann-Robertson-Walker (FRW) line element. An arbitrarily oriented 1-form is introduced and the FRW spacetime becomes of the Randers-Finsler type. The 1-form picks out a privileged axis in the universe. Thus, the cosmological redshift as well as the Hubble diagram of the type Ia supernovae (SNe Ia) becomes anisotropic. By directly analyzing the Union2 compilation, we obtain the privileged axis pointing to $(l,b)=({304^\circ}\pm{43^\circ},{-27^\circ}\pm{13^\circ})$ ($68\%~\rm{C.L.}$). This privileged axis is close to those obtained by comparing the best-fit Hubble diagrams in pairs of hemispheres. It should be noticed that the result is consistent with isotropy at the $1σ$ level since the anisotropic magnitude is $D=0.03\pm 0.03$.

astro-ph.CO↗

arXiv2013

Effects of spacetime anisotropy on the galaxy rotation curves

The observations on galaxy rotation curves show significant discrepancies from the Newtonian theory. This issue could be explained by the effect of the anisotropy of the spacetime. Conversely, the spacetime anisotropy could also be constrained by the galaxy rotation curves. Finsler geometry is a kind of intrinsically anisotropic geometry. In this paper, we study the effect of the spacetime anisotropy at the galactic scales in the Finsler spacetime. It is found that the Finslerian model has close relations with the Milgrom's MOND. By performing the best-fit procedure to the galaxy rotation curves, we find that the anisotropic effects of the spacetime become significant when the Newtonian acceleration $GM/r^2$ is smaller than the critical acceleration $a_0$. Interestingly, the critical acceleration $a_0$, although varies between different galaxies, is in the order of magnitude $cH_0/2π\sim 10^{-10} \rm{m\,\, s^{-2}}$.

astro-ph.GA↗

arXiv2013

Constraints on spacetime anisotropy and Lorentz violation from the GRAAL experiment

The GRAAL experiment could constrain the variations of the speed of light. The anisotropy of the speed of light may imply that the spacetime is anisotropic. Finsler geometry is a reasonable candidate to deal with the spacetime anisotropy. In this paper, the Lorentz invariance violation (LIV) of the photon sector is investigated in the locally Minkowski spacetime. The locally Minkowski spacetime is a class of flat Finsler spacetime and refers a metric with the anisotropic departure from the Minkowski one. The LIV matrices used to fit the experimental data are represented in terms of these metric deviations. The GRAAL experiment constrains the spacetime anisotropy to be less than $10^{-14}$. In addition, we find that the simplest Finslerian photon sector could be viewed as a geometric representation of the photon sector in the minimal standard model extension (SME).

hep-ph↗

arXiv2013

Finsler geometric perspective on the bulk flow in the universe

Astronomical observations showed that there may exist a bulk flow with peculiar velocities in the universe, which contradicts with the (Λ)CDM model. The bulk flow reveals that the observational universe is anisotropic at large scales. In fact, a more reliable observation on the anisotropy of spacetime comes from the CMB power spectra. The WMAP and Planck satellites both show that there is a hemispherical power asymmetry at large-angular scales. In this paper, we propose a "wind" scenario to the bulk flow (or the anisotropy of spacetime). Under the influence of the "wind", the spacetime metric could become a Finsler structure. By resolving the null geodesic equation, we obtain the modified luminosity distance, which has a dipolar form at the leading order. Thus, the "wind" describes well the bulk flow. In addition, we perform a least-(χ^2) fit to the data of type Ia supernovae (SNe Ia) in the Union2.1 compilation. The peculiar velocity of the bulk flow has an upper limit (v_{bulk}\lesssim 4000 \rm{km/s}), which is compatible with all the existing observational values.

astro-ph.CO↗

arXiv2013

Constraints from Type IA Supernovae on λ-CDM Model in Randers-Finsler Space

Gravitational field equations in Randers-Finsler space of approximate Berwald type are investigated. A modified Friedmann equation and a new luminosity distance-redshift relation is proposed. A best-fit to the Type Ia supernovae (SNe) observations yields that the $Ω_Λ$ in the $Λ$-CDM model is suppressed to almost zero. This fact indicates that the astronomical observations on the Type Ia SNe can be described well without invoking any form of dark energy. The best-fit age of the universe is given. It is in agreement with the age of our galaxy.

astro-ph.CO↗

arXiv2013

Finslerian MOND vs. observations of Bullet Cluster 1E0657-558

It is known that theory of MOND with spherical symmetry cannot account for the convergence $κ$-map of Bullet Cluster 1E0657-558. In this paper, we try to set up a Finslerian MOND, a generalization of MOND in Finsler spacetime. We use $Ric=0$ to obtain the gravitational vacuum field equation in a four-dimensional Finsler spacetime. To leading order in the post-Newtonian approximation, we obtain the explicit form of the Finslerian line element. It is simply the Schwarzschild's metric except for the Finslerian rescaling coefficient $f(v)$ of the radial coordinate $r$, i.e. $R=f(v(r))r$. By setting $f(v(r))=(1-\sqrt{a_0r^2/GM})^{-1}$, we obtain the famous MOND in a Finslerian framework. Taking a dipole and a quadrupole term into consideration, we give the convergence $κ$ in gravitational lensing astrophysics in our model. Numerical analysis shows that our prediction is to a certain extent in agreement with the observations of Bullet Cluster 1E0657-558. With the theoretical temperature $T$ taking the observed value 14.8 keV, the mass density profile of the main cluster obtained in our model is the same order as that given by the best-fit King $β$-model.

astro-ph.GA↗

arXiv2013

Generalization of Rindler Potential at Cluster Scales in Randers-Finslerian Spacetime: a Possible Explanation of the Bullet Cluster 1E0657-558?

The data of the Bullet Cluster 1E0657-558 released on November 15, 2006 reveal that the strong and weak gravitational lensing convergence $κ$-map has an $8σ$ offset from the $Σ$-map. The observed $Σ$-map is a direct measurement of the surface mass density of the Intracluster medium(ICM) gas. It accounts for 83% of the averaged mass-fraction of the system. This suggests a modified gravity theory at large distances different from Newton's inverse-square gravitational law. In this paper, as a cluster scale generalization of Grumiller's modified gravity model (D. Grumiller, Phys. Rev. Lett. 105, 211303 (2010)), we present a gravity model with a generalized linear Rindler potential in Randers-Finslerian spacetime without invoking any dark matter. The galactic limit of the model is qualitatively consistent with the MOND and Grumiller's. It yields approximately the flatness of the rotational velocity profile at the radial distance of several kpcs and gives the velocity scales for spiral galaxies at which the curves become flattened. Plots of convergence $κ$ for a galaxy cluster show that the peak of the gravitational potential has chances to lie on the outskirts of the baryonic mass center. Assuming an isotropic and isothermal ICM gas profile with temperature $T=14.8$ keV (which is the center value given by observations), we obtain a good match between the dynamical mass $M_\textmd{T}$ of the main cluster given by collisionless Boltzmann equation and that given by the King $β$-model. We also consider a Randers+dark matter scenario \textbf{and a $Λ$-CDM model} with the NFW dark matter distribution profile. We find that a mass ratio $η$ between dark matter and baryonic matter about 6 fails to reproduce the observed convergence $κ$-map for the isothermal temperature $T$ taking the observational center value.

astro-ph.CO↗

arXiv2013

Galaxies Rotation Curves in the Grumiller's Modified Gravity

The effective potential in the Grumiller's modified gravity [D. Grumiller, Phys. Rev. Lett {\bf 105}, 211303 (2010)] includes the Newtonian potential and a Rindler term. The fitting to the rotation curve data of eight galaxies suggests a universal Rindler acceleration $a\approx 0.30\times 10^{-10}$ m s$^{-2}$. We do a two-parameter fit first, with the mass-to-light ratio ($Υ_*$) and the Rindler acceleration ($a$) as free parameters. It is found that the data of six out of the eight galaxies fit well with the prediction of theory in the range $0\lesssim r \lesssim 40$ kpc, although the theoretical curves show a tendency of arising beyond this range. The Rindler accelerations of the six well-fitted galaxies have the same magnitude, with an average value $\bar{a}\approx0.30\times 10^{-10}$ m s$^{-2}$. Inspired by this fact, we then carry out a one-parameter ($Υ_*$) fit to the six galaxies, with $a$ fixed at $\bar{a}$, and find that the theory can still reproduce the observation. The value of Rindler acceleration we get here is a quarter of that of Milgrom's MOND. For the rest two galaxies, NGC5055 and DDO154, the fitting results are significantly improved if the photometric scale length ($h$) is included as another free parameter.

astro-ph.CO↗

arXiv2013

A unified constraint on the Lorentz invariance violation from both short and long GRBs

Possible Lorentz invariance violation (LIV) has been investigated for a long time based on observations of GRBs . These arguments relied on the assumption that photons with different energy are emitted at the same place and time. In this work, we try to take account of the intrinsic time delay $Δt_{\rm int}$ between emissions of low and high energy photons by using the magnetic jet model. The possible LIV effects are discussed in a unified scenario both for long and short {\it Fermi}-detected GRBs. This leads to a unique quantum gravity energy scale $M_1c^2 \sim 1.0 \times 10^{20}$ GeV respecting the linear dispersion relation.

astro-ph.HE↗

arXiv2013

Constraining the Bulk Lorentz Factor of GRB Outflow in the Magnetic-dominated Jet Model

Recent observations by the Fermi-LAT showed that there are delayed arrivals of GeV photons relative to the onset of MeV photons in some GRBs. In order to avoid a large optical depth, the minimal value of the Lorentz factor has been estimated to be higher than 1000 in some brightest bursts. In this paper, we present a detailed calculation of the time delay between the MeV and GeV photons in the framework of the magnetic-dominated jet model. We find that the time delay strongly depends on the saturated bulk Lorentz factor of the jet. Inspired by this fact, we use this model to calculate the Lorentz factors of the four brightest Fermi bursts. The results indicate that the Lorentz factors are much smaller than that obtained from the "single-zone" scenario. The short GRB 090510 has a minimal Lorentz factor 385, while the three long bursts GRB 080916c, GRB090902b and GRB 090926 have almost the same Lorentz factors, with an average value near 260. Another interesting result is that, for long bursts, GeV photons are emitted after the bulk Lorentz factor saturates. For the short GRB, however, MeV and GeV photons are emitted at the same phase, i.e., either at the expansion phase or at the coast phase.

astro-ph.HE↗

arXiv2012

Lorentz and CPT violations in Finsler spacetime

Standard model with intrinsic Lorentz and CPT violations is proposed in a Finsler geometric framework. We present explicitly Lorentz and CPT--breaking Lagrangians of the matter fields and the gauge fields in locally Minkowski spacetime. The Lorentz invariance violation is found to be originated from the spacetime background deviating from the Minkowski one. Similarly, the CPT violation is determined by the behaviors of the locally Minkowski metric under the parity and time reversal operations. To help understanding phenomenologies, we compare the Finslerian model with the standard--model extension (SME) term by term at a first order approximation.

hep-ph↗

arXiv2012

Lorentz invariance violation and electromagnetic field in an intrinsically anisotropic spacetime

Recently, Kostelecky [V.A. Kostelecky, Phys. Lett. B 701, 137 (2011)] proposed that the spontaneous Lorentz invariance violation (sLIV) is related to Finsler geometry. Finsler spacetime is intrinsically anisotropic and induces naturally Lorentz invariance violation (LIV). In this paper, the electromagnetic field is investigated in locally Minkowski spacetime. The Lagrangian is presented explicitly for the electromagnetic field. It is compatible with the one in the standard model extension (SME). We show the Lorentz--violating Maxwell equations as well as the electromagnetic wave equation. The formal plane wave solution is obtained for the electromagnetic wave. The speed of light may depend on the direction of light and the lightcone may be enlarged or narrowed. The LIV effects could be viewed as influence from an anisotropic media on the electromagnetic wave. In addition, the birefringence of light will not emerge at the leading order in this model. A constraint on the spacetime anisotropy is obtained from observations on gamma--ray bursts (GRBs).

hep-ph↗

arXiv2012

The spacetime structure of MOND with Tully-Fisher relation and Lorentz invariance violation

It is believed that the modification of Newtonian dynamics (MOND) is possible alternate for dark matter hypothesis. Although Bekenstein's TeVeS supplies a relativistic version of MOND, one may still wish a more concise covariant formulism of MOND. In this paper, within covariant geometrical framwork, we present another version of MOND. We show the spacetime structure of MOND with properties of Tully-Fisher relation and Lorentz invariance violation.

gr-qc↗

arXiv2012

Gravitational wave in Lorentz violating gravity

By making use of the weak gravitational field approximation, we obtain a linearized solution of the gravitational vacuum field equation in an anisotropic spacetime. The plane-wave solution and dispersion relation of gravitational wave is presented explicitly. There is possibility that the speed of gravitational wave is larger than the speed of light and the casuality still holds. We show that the energy-momentum of gravitational wave in the ansiotropic spacetime is still well defined and conserved.

gr-qc↗

arXiv2012

Neutrino superluminality without Cherenkov-like processes in Finslerian special relativity

Recently, Cohen and Glashow [A.G. Cohen, S.L. Glashow, Phys. Rev. Lett. {\bf 107}, 181803 (2011)] pointed out that the superluminal neutrinos reported by the OPERA would lose their energy rapidly via the Cherenkov-like process. The Cherenkov-like process for the superluminal particles would be forbidden if the principle of special relativity holds in any frame instead violated with a preferred frame. We have proposed that the Finslerian special relativity could account for the data of the neutrino superluminality (arXiv:1110.6673[hep-ph]). The Finslerian special relativity preserves the principle of special relativity and involves a preferred direction while consists with the causality. In this paper, we prove that the energy-momentum conservation is preserved and the energy-momentum is well defined in Finslerian special relativity. The Cherenkov-like process is forbidden in the Finslerian special relativity. Thus, the superluminal neutrinos would not lose energy in their distant propagation.

hep-ph↗

arXiv2012

An Inflationary Scenario Taking into Account of Possible Dark Energy Effects in the Early Universe

We investigate the possible effect of cosmological-constant type dark energy during the inflation period of the early universe. This is accommodated by a new dispersion relation in de Sitter space. The modified inflation model of a minimally-coupled scalar field is still able to yield an observation-compatible scale-invariant primordial spectrum, simultaneously having potential to generate a spectrum with lower power at large scales. A qualitative match to the WMAP 7-year data is presented. We obtain an $Ω_Λ$ of the same order of that in the $Λ$-CDM model. Possible relations between the de Sitter scenario and the Doubly Special Relativity(DSR) are also discussed.

astro-ph.CO↗