Evolution of Density Parameters on a Smooth Embedded Universe

In this paper we examine the evolution of cosmic density parameters in a four‐dimensional space‐time embedded in a five‐dimensional bulk space. We show that the extrinsic curvature is an independent spin‐2 field governed by the Gupta equations. Without evoking a dark energy fluid, the corresponding cosmological model is compared with the phenomenological XCDM model and shows a good concordance with recent cosmological datasets from Planck Collaboration and the latest Baryons Acoustic Oscillations/Cosmic Microwave Background (BAO/CMBR) + SNIa studying the evolution of density parameters. In addition, a discussion on the coincidence problem is also proposed.     

宇宙学常数疑难

当代天文学的一系列观测事实都支持应该存在一个非零的正的宇宙学常数，但是，人们发现当前宇宙学常数值太小，而且宇宙学常数即真空能量密度与现在的物质密度巧合地具有相同的量级，然而现有物理学理论还无法给出合理的解释，因此宇宙学常数问题成为物理学和天文学上最重大的疑难之一。文章综述了近年来宇宙在加速膨胀这一重大的天文发现和宇宙学常数的观测结果以及当前理论物理学在宇宙学常数问题上的一些尝试。     

Can brane dark energy model be probed observationally by distant supernovae?

The recent astronomical measurements of distant supernovae as well as other observations indicate that our Universe is presently accelerating. There are different proposals for the explanation of this acceleration, such as the cosmological constant Λ, decaying vacuum energy, an evolving scalar field (quintessence), phantom energy, etc. Most of these proposals require the existence of exotic matter with negative pressure violating the strong energy condition. On the other hand, there have appeared many models which offer dramatically different mechanisms for the current acceleration, in which dark energy emerges from the gravity sector rather than from the matter sector. In this Letter, we compare the concordance ΛCDM model with the Sahni–Shtanov brane-world models of dark energy by using the Akaike and Bayesian information criteria. We show that new parameters in the brane model are not statistically significant in terms of the information criteria, although the best fit method gives an improved fit to the SNIa data, because of the additional parameters. This is because the information criteria of model selection compensate for this advantage by penalizing models having more free parameters. We conclude that only new future observational data are accurate enough to give an advantage to dark-energy models of the brane origin, i.e., a very high-significance detection is required to justify the presence of new parameters. In our statistical analysis both Riess et al.'s and Astier et al.'s SNIa samples are used. For stringent constraining parameters of the models the baryon oscillation peak (BOP) test is used.     

Bianchi Type-I Anisotropic Dark Energy Model with Constant Deceleration Parameter

A new dark energy model in anisotropic Bianchi type-I (B-I) space-time with time dependent equation of state (EoS) parameter and constant deceleration parameter has been investigated in the present paper. The Einstein’s field equations have been solved by applying a variation law for generalized Hubble’s parameter (Berman in Il Nuovo Cimento B 74:182, 1983) which generates two types of solutions, one is of power-law type and other is of the exponential form. The existing range of the dark energy EoS parameter ω for derived model is found to be in good agreement with the three recent observations (i) SNe Ia data (Knop et al. in Astrophys. J. 598:102, 2003), (ii) SNe Ia data collaborated with CMBR anisotropy and galaxy clustering statistics (Tegmark et al. in Astrophys. J. 606:702, 2004) and (iii) a combination of cosmological datasets coming from CMB anisotropies, luminosity distances of high redshift type Ia supernovae and galaxy clustering (Hinshaw et al. in Astrophys. J. Suppl. Ser. 180:225, 2009 and Komatsu et al. in Astrophys. J. Suppl. Ser. 180:330, 2009). The cosmological constant Λ is found to be a decreasing function of time and it approaches a small positive value at the present epoch which is corroborated by results from recent supernovae Ia observations. It has also been suggested that the dark energy that explains the observed accelerating universe may arise due to the contribution to the vacuum energy of the EoS in a time dependent background. Geometric and kinematic properties of the model and the behaviour of the anisotropy of the dark energy have been carried out.     

On the cosmological constant problem and brane-world geometry

The cosmological constant problem is examined within the context of the covariant brane-world gravity, based on Nash’s embedding theorem for Riemannian geometries. We show that the vacuum structure of the brane-world is more complex than General Relativity’s because it involves extrinsic elements, in specific, the extrinsic curvature. In other words, the shape (or local curvature) of an object becomes a relative concept, instead of the “absolute shape” of General Relativity. We point out that the immediate consequence is that the cosmological constant and the energy density of the vacuum quantum fluctuations have different physical meanings: while the vacuum energy density remains confined to the four-dimensional brane-world, the cosmological constant is a property of the bulk’s gravitational field that leads to the conclusion that these quantities cannot be compared, as it is usually done in General Relativity. Instead, the vacuum energy density contributes to the extrinsic curvature, which in turn generates Nash’s perturbation of the gravitational field. On the other hand, the cosmological constant problem ceases to be in the brane-world geometry, reappearing only in the limit where the extrinsic curvature vanishes.     

Vacuum energy: Quantum hydrodynamics vs. quantum gravity

We compare quantum hydrodynamics and quantum gravity. They share many common features. In particular, both have quadratic divergences, and both lead to the problem of the vacuum energy, which, in quantum gravity, transforms to the cosmological constant problem. We show that, in quantum liquids, the vacuum energy density is not determined by the quantum zero-point energy of the phonon modes. The energy density of the vacuum is much smaller and is determined by the classical macroscopic parameters of the liquid, including the radius of the liquid droplet. In the same manner, the cosmological constant is not determined by the zero-point energy of quantum fields. It is much smaller and is determined by the classical macroscopic parameters of the Universe dynamics: the Hubble radius, the Newton constant, and the energy density of matter. The same may hold for the Higgs mass problem: the quadratically divergent quantum correction to the Higgs potential mass term is also cancelled by the microscopic (trans-Planckian) degrees of freedom due to the thermodynamic stability of the whole quantum vacuum.     

Stress-energy connection and cosmological constant problem

We study gravitational properties of vacuum energy by erecting a geometry on the stress-energy tensor of vacuum, matter and radiation. Postulating that the gravitational effects of matter and radiation can be formulated by an appropriate modification of the spacetime connection, we obtain varied geometrodynamical equations which properly comprise the usual gravitational field equations with, however, Planck-suppressed, non-local, higher-dimensional additional terms. The prime novelty brought about by the formalism is that, the vacuum energy does act not as the cosmological constant but as the source of the gravitational constant. The formalism thus deafens the cosmological constant problem by channeling vacuum energy to gravitational constant. Nevertheless, quantum gravitational effects, if any, restore the problem via the graviton and graviton-matter loops, and the mechanism proposed here falls short of taming such contributions to cosmological constant.     

The cosmological constant is back

A diverse set of observations now compellingly suggest that the universe possesses a nonzero cosmological constant. In the context of quantum-field theory a cosmological constant corresponds to the energy density of the vacuum, and the favored value for the cosmological constant corresponds to a very tiny vacuum energy density. We discuss future observational tests for a cosmological constant as well as the fundamental theoretical challenges — and opportunities — that this poses for particle physics and for extending our understanding of the evolution of the universe back to the earliest moments.This essay received the fifth award from the Gravity Research Foundation, 1995-Ed.     

The cosmological constant and dark energy in braneworlds

We review recent attempts to address the cosmological constant problem and the late-time acceleration of the Universe based on braneworld models. In braneworld models, the way in which the vacuum energy gravitates in the 4D spacetime is radically different from conventional 4D physics. It is possible that the vacuum energy on a brane does not curve the 4D spacetime and only affects the geometry of the extra-dimensions, offering a solution to the cosmological constant problem. We review the idea of supersymmetric large extra dimensions that could achieve this and also provide a natural candidate for a quintessence field. We also review the attempts to explain the late-time accelerated expansion of the universe from the large-distance modification of gravity based on the braneworld. We use the Dvali–Gabadadze–Porrati model to demonstrate how one can distinguish this model from dark energy models in 4D general relativity. Theoretical difficulties in this approach are also addressed.     

A dynamical approach to the cosmological constant

This Letter presents an exact analytic solution of a simple cosmological model in presence of both nonrelativistic matter and scalar field where Einstein's cosmological constant Λ appears as an integration constant. Unlike Einstein's cosmological constant ascribed to vacuum energy, the dark energy density and the energy density of the ordinary matter decrease at the same rate during the expansion of the universe. Therefore the model is free of the coincidence problem. Comparing the predictions using this model with the current cosmological observations shows that the results are consistent.     

Prospect for Cosmological Parameter Estimation Using Future Hubble Parameter Measurements

We constrain cosmological parameters using only Hubble parameter data and quantify the impact of future Hubble parameter measurements on parameter estimation for the most typical dark energy models. We first constrain cosmological parameters using 52 current Hubble parameter data including the Hubble constant measurement from the Hubble Space Telescope. Then we simulate the baryon acoustic oscillation signals from WFIRST (Wide-Field Infrared Survey Telescope) covering the redshift range of z ∈[0.5,2] and the redshift drift data from E-ELT (European Extremely Large Telescope) in the redshift range of z ∈[2,5]. It is shown that solely using the current Hubble parameter data could give fairly good constraints on cosmological parameters. Compared to the current Hubble parameter data, with the WFIRST observation the H(z) constraints on dark energy would be improved slightly, while with the E-ELT observation the H(z) constraints on dark energy is enormously improved.     

Running vacuum in the Universe and the time variation of the fundamental constants of Nature

We compute the time variation of the fundamental constants (such as the ratio of the proton mass to the electron mass, the strong coupling constant, the fine-structure constant and Newton’s constant) within the context of the so-called running vacuum models (RVMs) of the cosmic evolution. Recently, compelling evidence has been provided that these models are able to fit the main cosmological data (SNIa+BAO+H(z)+LSS+BBN+CMB) significantly better than the concordance \(\Lambda \)CDM model. Specifically, the vacuum parameters of the RVM (i.e. those responsible for the dynamics of the vacuum energy) prove to be nonzero at a confidence level \({\gtrsim } 3\sigma \). Here we use such remarkable status of the RVMs to make definite predictions on the cosmic time variation of the fundamental constants. It turns out that the predicted variations are close to the present observational limits. Furthermore, we find that the time evolution of the dark matter particle masses should be crucially involved in the total mass variation of our Universe. A positive measurement of this kind of effects could be interpreted as strong support to the “micro–macro connection” (viz. the dynamical feedback between the evolution of the cosmological parameters and the time variation of the fundamental constants of the microscopic world), previously proposed by two of us (HF and JS).     

Dark energy versus modified gravity: Impacts on measuring neutrino mass

In this paper,we make a comparison for the impacts of smooth dynamical dark energy,modified gravity,and interacting dark energy on the cosmological constraints on the total mass of active neutrinos.For definiteness,we consider theΛCDM model,the w CDM model,the f(R)model,and two typical interacting vacuum energy models,i.e.,the IΛCDM1 model with Q=βHρc and the IΛCDM2 model with Q=βHρΛ.In the cosmological fits,we use the Planck 2015 temperature and polarization data,in combination with other low-redshift observations including the baryon acoustic oscillations,the type Ia supernovae,the Hubble constant measurement,and the large-scale structure observations,such as the weak lensing as well as the redshift-space distortions.Besides,the Planck lensing measurement is also employed in this work.We find that,the w CDM model favors a higher upper limit on the neutrino mass compared to theΛCDM model,while the upper limit in the f(R)model is similar with that in theΛCDM model.For the interacting vacuum energy models,the IΛCDM1 model favors a higher upper limit on neutrino mass,while the IΛCDM2 model favors an identical neutrino mass with the case ofΛCDM.     

Semi-local cosmic strings and the cosmological constant problem

We study the cosmological constant problem in a three-dimensional N = 2 supergravity theory with gauge groupSU (2)_global × U(1)_local. The model we consider is known to admit string-like configurations, the so-called semi-local cosmic strings. We show that the stability of these solitonic solutions is provided by supersymmetry through the existence of a lower bound for the energy, even though the manifold of the Higgs vacuum does not contain non-contractible loops. Charged Killing spinors do exist over configurations that saturate the Bogomol'nyi bound, as a consequence of an Aharonov-Bohm-like effect. Nevertheless, there are no physical fermionic zero modes on these backgrounds. The exact vanishing of the cosmological constant does not imply, then, Bose-Fermi degeneracy. This provides a non-trivial example of the recent claim made by Witten on the vanishing of the cosmological constant in three dimensions without unphysical degeneracies.     

Quintessence Reconstruction of Interacting HDE in a Non-Flat Universe

In this paper we consider quintessence reconstruction of interacting holographic dark energy in a non-fiat background. As system＇s IR cutoff we choose the radius of the event horizon measured on the sphere of the horizon, defined as L = at（t）. To this end we construct a quintessence model by a real, single scalar field. Evolution of the potential, V（φ）, as well as the dynamics of the scalar field, φ, is obtained according to the respective holographic dark energy. The reconstructed potentials show a cosmological constant behavior for the present time. We constrain the model parameters in a fiat universe by using the observational data, and applying the Monte Carlo Markov chain simulation. We obtain the best fit values of the holographic dark energy model and the interacting parameters as c=1.0576-0.6632-0.6632^＋0.3010＋0.3052 and ζ =0.2433-0.2251-.2251^＋0.6373＋0.6373 , respectively. From the data fitting results we also find that the model can cross the phantom line in the present universe where the best fit value of the dark energy equation of state is WD=-1.2429.     

Conformal Invariance, Accelerating Universe and the Cosmological Constant Problem

We investigate a conformal invariant gravitational model which is taken to hold at early universe. The conformal invariance allows us to make a dynamical distinction between the two unit systems (or conformal frames) usually used in cosmology and elementary particle physics. In this model we argue that when the universe suffers phase transition, the resulting mass scale introduced by particle physics should have a variable contribution to vacuum energy density. This variation is controlled by the conformal factor which is taken as a dynamical field. We then deal with the cosmological consequences of this model. In particular, we shall show that there is an inationary phase at early times. At late times, on the other hand, it provides a mechanism which makes a large effective cosmological constant relax to a sufficiently small value. Moreover, we shall show that the conformal factor acts as a quintessence field that leads the universe to accelerate at late times.     

Gravitational coupling and dynamical reduction of the cosmological constant

We introduce a dynamical model to reduce a large cosmological constant to a sufficiently small value. The basic ingredient in this model is a distinction which has been made between the two unit systems used in cosmology and particle physics. We have used a conformal invariant gravitational model to define a particular conformal frame in terms of large scale properties of the universe. It is then argued that the contributions of mass scales in particle physics to the vacuum energy density should be considered in a different conformal frame. In this manner, a decaying mechanism is presented in which the conformal factor appears as a dynamical field and plays a key role to relax a large effective cosmological constant. Moreover, we argue that this model also provides a possible explanation for the coincidence problem.     

The Evolution of Primordial Black Hole Masses in the Radiation-Dominated Era

We discuss in this work the behaviour of primordial black holes (PBHs) in the radiation era. Taking into account the Hawking evaporation and the absorption of energy we revisit the complete differential equation for the evolution of the mass of a PBH. We show that the mass can grow in this cosmological phase in a very slow fashion (even when considering the very high temperature of the radiation) if at all, and give a strong upper limit to the maximum accretion of mass. We evaluate relativistic effects due to the peculiar motion relative to the CMBR and show that the existence of relativistic black holes with very high mass absorption is highly unlikely. Finally we demonstrate that thermodynamic equilibrium between black holes and the cosmic radiation can not exist for finite times, and therefore initially non-evaporating PBHs must jump to the evaporating regime. This analysis supports the several efforts performed to look for signatures of evaporating holes.