Scalar Gravity and Higgs Mechanism

The role that the auxiliary scalar field φ plays in Brans–Dicke cosmology is discussed. If a constant vacuum energy is assumed to be the origin of dark energy, then the corresponding density parameter would be a quantity varying with φ; and almost all of the fundamental components of our universe can be unified into the dynamical equation for φ. As a generalization of Brans–Dicke theory, we propose a new gravity theory with a complex scalar field ϕ which is coupled to the cosmological curvature scalar. Through such a coupling, the Higgs mechanism is naturally incorporated into the evolution of the universe, and a running density of the field vacuum energy is obtained which may release the particle standard model from the rigorous cosmological constant problem in some sense. Our model predicts a running mass scale of the fundamental particles in which the gauge symmetry breaks spontaneously. The running speed of the mass scale in our case could survive all existing experiments.     

Is the evidence for dark energy secure?

Several kinds of astronomical observations, interpreted in the framework of the standard Friedmann–Robertson–Walker cosmology, have indicated that our universe is dominated by a Cosmological Constant. The dimming of distant Type Ia supernovae suggests that the expansion rate is accelerating, as if driven by vacuum energy, and this has been indirectly substantiated through studies of angular anisotropies in the cosmic microwave background (CMB) and of spatial correlations in the large-scale structure (LSS) of galaxies. However there is no compelling direct evidence yet for (the dynamical effects of) dark energy. The precision CMB data can be equally well fitted without dark energy if the spectrum of primordial density fluctuations is not quite scale-free and if the Hubble constant is lower globally than its locally measured value. The LSS data can also be satisfactorily fitted if there is a small component of hot dark matter, as would be provided by neutrinos of mass ∼0.5 eV. Although such an Einstein–de Sitter model cannot explain the SNe Ia Hubble diagram or the position of the “baryon acoustic oscillation” peak in the autocorrelation function of galaxies, it may be possible to do so, e.g. in an inhomogeneous Lemaitre–Tolman–Bondi cosmology where we are located in a void which is expanding faster than the average. Such alternatives may seem contrived but this must be weighed against our lack of any fundamental understanding of the inferred tiny energy scale of the dark energy. It may well be an artifact of an oversimplified cosmological model, rather than having physical reality.     

A Quantum Mechanical Relation Connecting Time,Temperature, and Cosmological Constant of the Universe: Gamow’S Relation Revisited as a Special Case

Considering our expanding universe as made up of gravitationally interacting particles which describe particles of luminous matter, dark matter and dark energy which is represented by a repulsive harmonic potential among the points in the flat 3-space and incorporating Mach’s principle into our theory, we derive a quantum mechanical relation connecting, temperature of the cosmic microwave background radiation, age, and cosmological constant of the universe. When the cosmological constant is zero, we get back Gamow’s relation with a much better coefficient. Otherwise, our theory predicts a value of the cosmological constant 2.0×10⁻⁵⁶ cm⁻² when the present values of cosmic microwave background temperature of 2.728 K and age of the universe 14 billion years are taken as input.     

Curvature Inspired Cosmological Scenario

Using modified gravity with non-linear terms of curvature, R ² and R ^(2+r) (with r being a positive real number and R being the scalar curvature), cosmological scenario, beginning at the Planck scale, is obtained. Here a unified picture of cosmology is obtained from f(R)-gravity. In this scenario, universe begins with power-law inflation followed by deceleration and acceleration in the late universe as well as possible collapse of the universe in future. It is different from f(R)-dark energy models with non-linear curvature terms assumed as dark energy. Here, dark energy terms are induced by linear as well as non-linear terms of curvature in Friedmann equation being derived from modified gravity. It is also interesting to see that, in this model, dark radiation and dark matter terms emerge spontaneously from the gravitational sector. It is found that dark energy, obtained here, behaves as quintessence in the early universe and phantom in the late universe. Moreover, analogous to brane-tension in brane-gravity inspired Friedmann equation, a tension term λ arises here being called as cosmic tension, It is found that, in the late universe, Friedmann equation (obtained here) contains a term −ρ ²/2λ (ρ being the phantom energy density) analogous to a similar term in Friedmann equation with loop quantum effects, if λ>0 and brane-gravity correction when λ<0.     

Phantom dark energy with varying-mass dark matter particles: Acceleration and cosmic coincidence problem

We investigate several varying-mass dark matter particle models in the framework of phantom cosmology. We examine whether there exist late-time cosmological solutions, corresponding to an accelerating universe and possessing dark energy and dark matter densities of the same order. Imposing exponential or power-law potentials and exponential or power-law mass dependence, we conclude that the coincidence problem cannot be solved or even alleviated. Thus, if dark energy is attributed to the phantom paradigm, varying-mass dark matter models cannot fulfill the basic requirement that led to their construction.     

Analytical solutions of accreting black holes immersed in a ΛCDM model

The evolution of the mass of a black hole embedded in a universe filled with dark energy and cold dark matter is calculated in a closed form within a test fluid model in a Schwarzschild metric, taking into account the cosmological evolution of both fluids. The result describes exactly how accretion asymptotically switches from the matter-dominated to the Λ-dominated regime. For early epochs, the black hole mass increases due to dark matter accretion, and on later epochs the increase in mass stops as dark energy accretion takes over. Thus, the unphysical behaviour of previous analyses is improved in this simple exact model.     

Interacting ghost dark energy in non-flat universe

A new dark energy model called “ghost dark energy” was recently suggested to explain the observed accelerating expansion of the universe. This model originates from the Veneziano ghost of QCD. The dark energy density is proportional to Hubble parameter, ρ _D  = α H, where α is a constant of order L_QCD³{\Lambda_{\rm QCD}^3} and Λ_QCD ~ 100 MeV is QCD mass scale. In this Letter, we extend the ghost dark energy model to the universe with spatial curvature in the presence of interaction between dark matter and dark energy. We study cosmological implications of this model in detail. In the absence of interaction the equation of state parameter of ghost dark energy is always w _D > −1 and mimics a cosmological constant in the late time, while it is possible to have w _D < −1 provided the interaction is taken into account. When k = 0, all previous results of ghost dark energy in flat universe are recovered. For the observational test, we use Supernova type Ia Gold sample, shift parameter of cosmic microwave background radiation and the correlation of acoustic oscillation on the last scattering surface and the baryonic acoustic peak from Sloan Digital Sky Survey are used to confine the value of free parameter of mentioned model.     

On Dark Energy,Weyl’s Geometry,Different Derivations of the Vacuum Energy Density and the Pioneer Anomaly

Two different derivations of the observed vacuum energy density are presented. One is based on a class of proper and novel generalizations of the (Anti) de Sitter solutions in terms of a family of radial functions R(r) that provides an explicit formula for the cosmological constant along with a natural explanation of the ultraviolet/infrared (UV/IR) entanglement required to solve this problem. A nonvanishing value of the vacuum energy density of the order of is derived in agreement with the experimental observations. A correct lower estimate of the mass of the observable universe related to the Dirac–Eddington–Weyl’s large number N = 10⁸⁰ is also obtained. The presence of the radial function R(r) is instrumental to understand why the cosmological constant is not zero and why it is so tiny. Finally, we rigorously prove why the proper use of Weyl’s Geometry within the context of Friedman–Lemaitre–Robertson–Walker cosmological models can account for both the origins and the value of the observed vacuum energy density (dark energy). The source of dark energy is just the dilaton-like Jordan–Brans–Dicke scalar field that is required to implement Weyl invariance of the most simple of all possible actions. The full theory involving the dynamics of Weyl’s gauge field A_μ is very rich and may explain also the anomalous Pioneer acceleration and the temporal variations (over cosmological scales) of the fundamental constants resulting from the expansion of the Universe. This is consistent with Dirac’s old idea of the plausible variation of the physical constants but with the advantage that it is not necessary to invoke extra dimensions. Dedicated to the loving memory of Rachael Bowers.     

Consequences of a Cosmological Phase Transition at the TeV Scale

A finite vacuum energy density implies the existence of a UV scale for gravitational modes. This gives a phenomenological scale to the dynamical equations governing the cosmological expansion that must satisfy constraints consistent with quantum measurability and spatial flatness. Examination of these constraints for the observed dark energy density establishes a time interval from the transition to the present, suggesting major modifications from the thermal equations of state far from Planck density scales. The assumption that a phase transition initiates the radiation dominated epoch is shown under several scenarios to be able to produce fluctuations to the CMB of the order observed. Quantum measurability constraints (eg. uncertainly relations) define cosmological scales bounded by luminal expansion rates. It is shown that the dark energy can consistently be interpreted as being due to the vacuum energy of collective gravitational modes which manifest as the zero-point motions of coherent Planck scale mass units prior to the UV scale onset of gravitational quantum de-coherence for the cosmology. A cosmological model with multiple scales, one of which replaces an apparent cosmological “constant”, is shown to reproduce standard cosmology during intermediate times, while making the exploration of the early and late time cosmology more accessible. Talk presented at the 2006 biennial conference of the International Association for Relativistic Dynamics, June 12–14, University of Connecticut (Storrs).     

Extending the Redshift-Distance Relation in Cosmological General Relativity to Higher Redshifts

The redshift-distance modulus relation, the Hubble Diagram, derived from Cosmological General Relativity has been extended to arbitrarily large redshifts. Numerical methods were employed and a density function was found that results in a valid solution of the field equations at all redshifts. The extension has been compared to 302 type Ia supernova data as well as to 69 Gamma-ray burst data. The latter however do not truly represent a ‘standard candle’ as the derived distance moduli are not independent of the cosmology used. Nevertheless the analysis shows a good fit can be achieved without the need to assume the existence of dark matter. The Carmelian theory is also shown to describe a universe that is always spatially flat. This results from the underlying assumption of the energy density of a cosmological constant Ω_Λ=1, the result of vacuum energy. The curvature of the universe is described by a spacevelocity metric where the energy content of the curvature at any epoch is Ω _K =Ω_Λ−Ω=1−Ω, where Ω is the matter density of the universe. Hence the total density is always Ω _K +Ω=1.     

Cosmological Consequences of Scale-Related Comoving Masses for Cosmic Pressure, Mass, and Vacuum Energy Density

According to ideas of Mach, Whitrow, Dirac, or Hoyle, inertial masses of particles should not be a genuine, predetermined quantity; rather they should represent a relational quantity which by its value somehow reflects the deposition and constellation of all other objects in their cosmic environment. In this paper we want to pick up suggestions given by Thirring and by Hoyle of how, due to requirements of the equivalence of rotations and of general relativistic conformal scale invariance, the particle masses of cosmic objects should vary with the cosmic length scale. We study cosmological consequences of comoving cosmic masses which co-evolve by mass with the expansion of the universe. The vanishing of the covariant divergence of the cosmic energy-momentum tensor under the new prerequisite that matter density only falls off with the reciproke of the squared cosmic scale S(t) then leads to the astonishing result that cosmic pressuredoes not fall off adiabatically but rather falls off in a quasi-isothermal behaviour, varying with S(t) as matter density does. Hence, as a new cosmological fact, it arises that, even in the late phases of cosmic expansion, pressure cannot be neglected what concerns its gravitational action on the cosmic dynamics. We then show that under these conditions the cosmological equations can, however, only be solved if, in addition to matter, also pressure and energy density of the cosmic vacuum are included in the calculation. An unaccelerated expansion with a Hubble parameter falling off with S(t)⁻¹ is obtained for a vacuum energy density decay according to S(t)⁻² with a well-tuned proportion of matter and vacuum pressures. As it appears from these results, a universe with particle masses increasing with the cosmic sale S(t) is in fact physically conceivable in an energetically consistent manner, if vacuum energy at the expansion of the universe is converted into mass density of real matter with no net energy loss occuring. This universe in addition also happens to be an economical one which has and keeps a vanishing total energy.     

第五讲暗能量和德西特时空

最近的天文观测表明，宇宙是在加速膨胀，而不是原来认为的减速膨胀．为解释加速膨胀，必须在宇宙的物质能量中引入暗能量这一成分，文章讨论了暗能量的可能侯选者，特别强调了宇宙常数问题、德西特时空问题以及和德西特时空相关的一些基本问题．     

Dark energy interacting with dark matter and a third fluid: Possible EoS for this component

A cosmological model of dark energy interacting with dark matter and another general component of the universe is considered. The equations for the coincidence parameters r and s, which represent the ratios between dark energy and dark matter and the other cosmic fluid respectively, are analyzed in terms of the stability of stationary solutions. The obtained general results allow to shed some light on the equations of state of the three interacting fluids, due to the constraints imposed by the stability of the solutions. We found that for an interaction proportional to the sum of the dark energy density and the third fluid density, the hypothetical fluid must have positive pressure, which leads naturally to a cosmological scenario with radiation, unparticle or even some form of warm dark matter as the third interacting fluid.     

Purely kinetic coupled gravity

Cosmic acceleration can be achieved not only with a sufficiently flat scalar field potential but through kinetic terms coupled to gravity. These derivative couplings impose a shift symmetry on the scalar field, aiding naturalness. We write the most general purely kinetic action not exceeding mass dimension 6 and obeying second order field equations. The result reduces to a simple form involving a coupling of the Einstein tensor with the kinetic term and can be interpreted as adding a new term to Galileon gravity in curved spacetime. We examine the cosmological implications of the effective dark energy and classify the dynamical attractor solutions, finding a quasistable loitering phase mimicking late time acceleration by a cosmological constant.     

R2 Correction and Its Implication of Present Cosmic Accelerating Behavior

In this work we show an R + αR2 model of the universe in which certain quadratic correction is considered. Our results indicate that the R2 term can act as the present impetus of cosmic acceleration, but there may be a future collapsing universe with this component damped. This model can also tolerate a negative cosmological constant A,although there seems to be no need for a non-vanishing one. In our simplification, this curvature component has a stationary equation of state, which is similar to radiation. Unlike other dark energy models, this "missing" energy has a negative density. Some details and effects on cold dark matter and A-relevant model have been discussed in the frame of curvature-squared gravity theories.     

Entanglement inside the cosmological apparent horizon

Possible connections between quantum entanglement and cosmological eras are considered. In particular, assuming that two epochs are each other entangling, by measuring the entanglement degree, it is possible to recover dynamical properties of the universe. In particular, the effects of dark energy could be due to the entanglement between states, since a negative pressure arises at late times. In this process, we choose as ruler to quantify the “entanglement weight”, the so-called negativity of entanglement. It follows that a natural anti-gravitational effect occurs when the cosmological eras are entangled. Thus, dark energy could be seen as a straightforward consequence of entanglement. Specifically, our results can be compared with observational data. In doing so, it is possible to show that a pressureless term is recovered at a certain epoch dominating over dark energy and ruling the structure formation.     

An inhomogeneous model universe behaving homogeneously

We present a new model universe based on the junction of FRW to flat Lemaitre–Tolman–Bondi (LTB) solutions of Einstein equations along our past light cone, bringing structures within the FRW models. The model is assumed globally to be homogeneous, i.e. the cosmological principle is valid. Local inhomogeneities within the past light cone are modeled as a flat LTB, whereas those outside the light cone are assumed to be smoothed out and represented by a FRW model. The model is singularity free, always FRW far from the observer along the past light cone, gives way to a different luminosity distance relation as for the CDM/FRW models, a negative deceleration parameter near the observer, and correct linear and non-linear density contrast. As a whole, the model behaves like a FRW model on the past light cone with a special behavior of the scale factor, Hubble and deceleration parameter, mimicking dark energy. Paper in honor of Bahram Mashhoon’s 60th birthday.     

Dark energy and viscous cosmology

Singularities in the dark energy universe are discussed, assuming that there is a bulk viscosity in the cosmic fluid. In particular, it is shown how the physically natural assumption of letting the bulk viscosity be proportional to the scalar expansion in a spatially flat FRW universe can drive the fluid into the phantom region (w < −1), even if it lies in the quintessence region (w > −1) in the non-viscous case.     

Perfect fluid dark matter

Taking the flat rotation curve as input and treating the matter content in the galactic halo region as perfect fluid we obtain a space–time metric at the galactic halo region in the framework of general relativity. We find that the resultant space–time metric is a non-relativistic dark matter induced space–time embedded in a static Friedmann–Lemaître–Robertson–Walker universe i.e. the flat rotation curve not only leads to the existence of dark matter but also suggests about the background geometry of the universe. Within its range of validity the flat rotation curve and the demand that the dark matter to be non-exotic together indicate for a (nearly) flat universe as favored by the modern cosmological observations. We obtain the expressions for energy density and pressure of dark matter there and consequently the equation of state of dark matter. Various other aspects of the solutions are also analyzed.