Dvali-Gabadadze-Porrati Research Articles

Cosmographic Constraints and Cosmic Fluids

The problem of reproducing dark energy effects is reviewed here with particular interest devoted to cosmography. We summarize some of the most relevant cosmological models, based on the assumption that the corresponding barotropic equations of state evolve as the universe expands, giving rise to the accelerated expansion. We describe in detail the ΛCDM (Λ-Cold Dark Matter) and ωCDM models, considering also some specific examples, e.g., Chevallier–Polarsky–Linder, the Chaplygin gas and the Dvali–Gabadadze–Porrati cosmological model. Finally, we consider the cosmological consequences of f(R) and f(T) gravities and their impact on the framework of cosmography. Keeping these considerations in mind, we point out the model-independent procedure related to cosmography, showing how to match the series of cosmological observables to the free parameters of each model. We critically discuss the role played by cosmography, as a selection criterion to check whether a particular model passes or does not present cosmological constraints. In so doing, we find out cosmological bounds by fitting the luminosity distance expansion of the redshift, z, adopting the recent Union 2.1 dataset of supernovae, combined with the baryonic acoustic oscillation and the cosmic microwave background measurements. We perform cosmographic analyses, imposing different priors on the Hubble rate present value. In addition, we compare our results with recent PLANCK limits, showing that the ΛCDM and ωCDM models seem to be the favorite with respect to other dark energy models. However, we show that cosmographic constraints on f(R) and f(T) cannot discriminate between extensions of General Relativity and dark energy models, leading to a disadvantageous degeneracy problem.

Testing Dvali–Gabadadze–Porrati gravity with Planck

Recently, the Planck Collaboration has released the first cosmological papers providing the highest resolution, full sky, maps of the cosmic microwave background (CMB) temperature anisotropies. It is crucial to understand that whether the accelerating expansion of our universe at present is driven by an unknown energy component (Dark Energy) or a modification to general relativity (Modified Gravity). In this Letter we study a phenomenological model which interpolates between the pure ΛCDM model and the Dvali–Gabadadze–Porrati (DGP) braneworld model with an additional parameter α. Firstly, we calculate the “distance information” of Planck data which includes the “shift parameter” R, the “acoustic scale” lA, and the photon decoupling epoch z⁎ in different cosmological models and find that this information is almost independent on the input models we use. Then, we compare the constraints on the free parameter α of the DGP model from the “distance information” of Planck and WMAP data and find that the Planck data with high precision do not improve the constraint on α, but give the higher median value and the better limit on the current matter density fraction Ωm. Then, combining the “distance information” of Planck measurement, baryon acoustic oscillations (BAO), Type Ia supernovae (SNIa) and the prior on the current Hubble constant (HST), we obtain the tight constraint on the parameter α<0.20 at 95% confidence level, which implies that the flat DGP model has been ruled out by the current cosmological data. Finally, we allow the additional parameter α<0 in our calculations and interestingly obtain α=−0.29±0.20 (68% C.L.), which means the current data slightly favor the effective equation of state weff<−1. More importantly, the tension between constraints on H0 from different observational data has been eased.

Observational constraints on non-minimally coupled Galileon model

As an extension of Dvali-Gabadadze-Porrati (DGP) model, the Galileon theory has been proposed to explain the "self-accelerating problem" and "ghost instability problem". In this Paper, we extend the Galileon theory by considering a non-minimally coupled Galileon scalar with gravity. The statefinder analysis, $Om(z)$ diagnostic and constraint the model parameters have been investigate , we find $\Omega_\text{m0}=0.263_{-0.031}^{+0.031}$, $n=1.53_{-0.37}^{+0.21}$ (at the $95\%$ confidence level) with $\chi^2_{\text{min}}=473.376$. Further we show that due to the SNe Ia + BAO data ,our model behaves like a phantom-like dark energy.

Testing modified gravity models with recent cosmological observations

We explore the cosmological implications of five modified gravity (MG) models by using the recent cosmological observational data, including the recently released SNLS3 type Ia supernovae sample, the cosmic microwave background anisotropy data from the Wilkinson Microwave Anisotropy Probe 7-yr observations, the baryon acoustic oscillation results from the Sloan Digital Sky Survey data release 7, and the latest Hubble constant measurement utilizing the Wide Field Camera 3 on the Hubble Space Telescope. The MG models considered include the Dvali-Gabadadze-Porrati(DGP) model, two $f(R)$ models, and two $f(T)$ models. We find that compared with the $\Lambda$CDM model, MG models can not lead to a appreciable reduction of the $\chi^2_{min}$. The analysis of AIC and BIC shows that the simplest cosmological constant model($\Lambda$CDM) is still most preferred by the current data, and the DGP model is strongly disfavored. In addition, from the observational constraints, we also reconstruct the evolutions of the growth factor in these models. We find that the current available growth factor data are not enough to distinguish these MG models from the $\Lambda$CDM model.

THEORETICAL MODELS OF DARK ENERGY

Mounting observational data confirm that about 73% of the energy density consists of dark energy which is responsible for the current accelerated expansion of the Universe. We present observational evidences and dark energy projects. We then review various theoretical ideas that have been proposed to explain the origin of dark energy; they contain the cosmological constant, modified matter models, modified gravity models and the inhomogeneous model. The cosmological constant suffers from two major problems: one regarding fine-tuning and the other regarding coincidence. To solve them there arose modified matter models such as quintessence, k-essence, coupled dark energy and unified dark energy. We compare those models by presenting attractive aspects, new rising problems and possible solutions. Furthermore, we review modified gravity models that lead to late-time accelerated expansion without invoking a new form of dark energy; they contain f(R) gravity and the Dvali–Gabadadze–Porrati (DGP) model. We also discuss observational constraints on those models and on future modified gravity theories. Finally we review the inhomogeneous Lemaître–Tolman–Bondi (LTB) model that drops an assumption of the spatial homogeneity of the Universe. We also present basics of cosmology and scalar field theory, which are useful especially for students and novices to understand dark energy models.

Stability analysis of the cosmological solutions with induced gravity and scalar field on the brane

We study cosmological dynamics and phase space of a scalar field localized on the Dvali–Gabadadze–Porrati brane. We consider both the minimally and non-minimally coupled scalar quintessence and phantom fields on the brane. In the non-minimal case, the scalar field couples with induced gravity on the brane. We present a detailed analysis of the critical points, their stability and late-time cosmological viability of the solutions in the phase space of the model.

Holographic induced gravity model with a Ricci dark energy: Smoothing the little rip and big rip through Gauss-Bonnet effects?

We present an holographic brane-world model of the Dvali-Gabadadze-Porrati (DGP) scenario with and without a Gauss-Bonnet term (GB) in the bulk. We show that an holographic dark energy component with the Ricci scale as the infrared cutoff can describe the late-time acceleration of the Universe. In addition, we show that the dimensionless holographic parameter is very important in characterizing the DGP branches, and in determining the behavior of the Ricci dark energy as well as the asymptotic behavior of the brane. On the one hand, in the DGP scenario the Ricci dark energy will exhibit a phantomlike behavior with no big rip if the holographic parameter is strictly larger than $1/2$. For smaller values, the brane hits a big rip or a little rip. On the other hand, we have shown that the introduction of the GB term avoids the big rip and little rip singularities on both branches but cannot avoid the appearance of a big freeze singularity for some values of the holographic parameter on the normal branch, however, these values are very unlikely because they lead to a very negative equation of state at the present and therefore we can speak in practice of singularity avoidance. At this regard, the equation of state parameter of the Ricci dark energy plays a crucial role, even more important than the GB parameter, in rejecting the parameter space where future singularities appear.

A Specific Case of Generalized Einstein-aether Theories

With the dark energy phenomena explored over a decade, in this present work we discuss a specific case of the generalized Einstein-aether theories, in which the modified Friedmann equation is similar to that in the Dvali—Gabadadze—Porrati (DGP) brane world model. We compute the joint statistic constraints on model parameters in this specific case by using the recent type Ia supernovae (SNe Ia) data, the cosmic microwave background (CMB) shift parameter data, and the baryonic acoustic oscillations (BAOs) data traced by the Sloan Digital Sky Survey (SDSS). Furthermore, we analyze other constrains from the observational Hubble parameter data (OHD). The comparison with the standard cosmological model (cosmological constant Λ cold dark matter (ΛCDM) model) is clearly shown; also we comment on the interesting relation between the coupling constant M in this model and the special accelerate scale in the modified Newtonian dynamics (MOND) model initially given by Milgrom with the hope for interpreting the galaxy rotation curves without introducing mysterious dark matter.

Cosmological probes of modified gravity: the nonlinear regime

We review the effects of modified gravity on large-scale structure in the nonlinear regime, focusing on f(R) gravity and the Dvali-Gabadadze-Porrati model, for which full N-body simulations have been performed. In particular, we discuss the abundance of massive halos, the nonlinear matter power spectrum and the dynamics within clusters and galaxies, with particular emphasis on the screening mechanisms present in these models.

Classical stability of the Galileon

We consider the classical equations of motion for a single Galileon field with generic parameters in the presence of non-relativistic sources. We introduce the concept of absolute stability of a theory: if one can show that a field at a single point---like infinity for instance---in spacetime is stable, then stability of the field over the rest of spacetime is guaranteed for any positive energy source configuration. The Dvali-Gabadadze-Porrati (DGP) model is stable in this manner, and previous studies of spherically symmetric solutions suggest that certain classes of the single field Galileon (of which the DGP model is a subclass) may have this property as well. We find, however, that when general solutions are considered this is not the case. In fact, when considering generic solutions there are no choices of free parameters in the Galileon theory that will lead to absolute stability except the DGP choice. Our analysis indicates that the DGP model is an exceptional choice among the large class of possible single field Galileon theories. This implies that if general solutions (non-spherically symmetric) exist they may be unstable. Given astrophysical motivation for the Galileon, further investigation into these unstable solutions may prove fruitful.

Measuring coherent motions in the universe

We present new measurements of the coherent motion of galaxies based on observations of the large-scale redshift-space distortions seen in the two-dimensional two-point correlation function of Luminous Red Galaxies in Data Release Seven of the Sloan Digital Sky Survey. We have developed a new methodology for estimating these coherent motions, which is less dependent on the details of galaxy bias and of the cosmological model to explain the late-time acceleration of the expansion of the Universe. We measure a one-dimensional velocity dispersion of galaxies on large-scales of σv = h-1 Mpc and σv = h-1 Mpc at a mean redshift of z = 0.25 and 0.38 respectively. These values are fully consistent with predictions for a WMAP7-normalised ΛCDM Universe and inconsistent at confidence of 3.8σ with a Dvali-Gabadadze-Porrati (DGP) model for the Universe. We can convert the units of these σv measurements to km/s and km/s respectively (assuming a ΛCDM universe), which are lower that expected based on recent low redshift (z < 0.2) measurements of the peculiar velocity field (or “bulk flows”). It is difficult to directly compare these measurements as they cover different redshift ranges and different areas of the sky. However, one possible cosmological explanation for this discrepancy is that our Galaxy is located in unusually over, or under, dense region of the Universe.

OBSERVATIONAL CONSTRAINTS ON PHANTOM CROSSING DGP GRAVITY

We study the observational constraints on the Phantom Crossing DGP model. We demonstrate that the crossing of the phantom divide does not occur within the framework of the original Dvali–Gabadadze–Porrati (DGP) model or the DGP model developed by Dvali and Turner. By extending their model in the framework of an extra dimension scenario, we study a model that realizes crossing of the phantom divide. We investigate the cosmological constraints obtained from the recent observational data of Type Ia supernovae, cosmic microwave background anisotropies, and baryon acoustic oscillations. The best-fit values of the parameters with 1σ (68%) errors for the Phantom Crossing DGP model are [Formula: see text]. We find that the Phantom Crossing DGP model is more compatible with the observations than the original DGP model or the DGP model developed by Dvali and Turner. Our model can realize late-time acceleration of the universe, similar to that of ΛCDM model, without dark energy due to the effect of DGP gravity. In our model, the crossing of the phantom divide occurs at a redshift of z ~ 0.2.

Modified holographic dark energy in DGP brane world

In this Letter, the cosmological dynamics of a modified holographic dark energy which is derived from the UV/IR duality by considering the black hole mass in higher dimensions as UV cutoff, is investigated in Dvali–Gabadadze–Porrati (DGP) brane world model. We choose Hubble horizon and future event horizon as IR cutoff respectively. And the two branches of the DGP model are both taken into account. When Hubble horizon is considered as IR cutoff, the modified holographic dark energy (HDE) behaves like an effect dark energy that modification of gravity in pure DGP brane world model acts and it can drive the expansion of the universe speed up at late time in ϵ=−1 branch which in pure DGP model cannot undergo an accelerating phase. When future event horizon acts as IR cutoff, the equation of state parameter of the modified HDE can cross the phantom divide.

Self-accelerating solutions in the cascading DGP braneworld

Abstract The self-accelerating branch of the Dvali–Gabadadze–Porrati (DGP) five-dimensional braneworld has provided a compelling model for the current cosmic acceleration. Recent observations, however, have not favored it so much. We discuss the solutions which contain a de Sitter 3-brane in the cascading DGP braneworld model, which is a kind of higher-dimensional generalizations of the DGP model, where a p-dimensional brane is placed on a ( p + 1 ) -dimensional one and the p-brane action contains the ( p + 1 ) -dimensional induced scalar curvature term. In the simplest six-dimensional model, we derive the solutions. Our solutions can be classified into two branches, which reduce to the self-accelerating and normal solutions in the limit of the original five-dimensional DGP model. In the presence of the six-dimensional bulk gravity, the ‘normal’ branch provides a new self-accelerating solution. The expansion rate of this new branch is generically lower than that of the original one, which may alleviate the fine-tuning problem.

Cosmic constraint to DGP brane model: Geometrical and dynamical perspectives

In this paper, the Dvali-Gabadadze-Porrati (DGP) brane model is confronted by current cosmic observational data sets from geometrical and dynamical perspectives. On the geometrical side, the recently released Union2 557 of type Ia supernovae (SN Ia), the baryon acoustic oscillation from the Sloan Digital Sky Survey and the Two Degree Galaxy Redshift Survey (transverse and radial to line-of-sight data points), the cosmic microwave background measurement given by the seven-year Wilkinson Microwave Anisotropy Probe observations [shift parameters $R$, ${l}_{a}({z}_{*})$ and redshift at the last scatter surface ${z}_{*}$], ages of high redshifts galaxies, i.e., the lookback time and the high redshift gamma ray bursts are used. On the dynamical side, data points about the growth function of matter linear perturbations are used. Using the same data set combination, we also constrain the flat $\ensuremath{\Lambda}\mathrm{CDM}$ model as a comparison. The results show that current geometrical and dynamical observational data sets much favor the flat $\ensuremath{\Lambda}\mathrm{CDM}$ model and the departure from it is above $4\ensuremath{\sigma}(6\ensuremath{\sigma})$ for the spatially flat DGP model with (without) SN systematic errors. The consistence of growth function data points is checked in terms of a relative departure of redshift-distance relation.

Growth of linear matter perturbations and current observational constraints

We discuss, using a recently proposed parametrization for the growth index of linear matter perturbations, the observational constraints on the wCDM model and the Dvali–Gabadadze–Porrati (DGP) model with all current growth factor data. We find that the wCDM model is allowed by the observations at the 1σ confidence level, while the DGP model is only consistent with observations at 2σ confidence level.

Crossing the phantom divide in extended Dvali–Gabadadze–Porrati gravity

We propose a phantom crossing Dvali--Gabadadze--Porrati (DGP) model. In our model, the effective equation of state of the DGP gravity crosses the phantom divide line. We demonstrate crossing of the phantom divide does not occur within the framework of the original DGP model or the DGP model developed by Dvali and Turner. By extending their model, we construct a model that realizes crossing of the phantom divide. We find that the smaller the value of the new introduced parameter $\beta$ is, the older epoch crossing of the phantom divide occurs in. Our model can account for late-time acceleration of the universe without dark energy. We investigate and show the property of Phantom crossing DGP model.

Dynamical masses in modified gravity

Differences in masses inferred from dynamics, such as velocity dispersions or x rays, and those inferred from lensing are a generic prediction of modified gravity theories. Viable models, however, must include some nonlinear mechanism to restore general relativity (GR) in dense environments, which is necessary to pass Solar System constraints on precisely these deviations. In this paper, we study the dynamics within virialized structures in the context of two modified gravity models, $f(R)$ gravity and Dvali-Gabadadze-Porrati (DGP). The nonlinear mechanisms to restore GR, which $f(R)$ and DGP implement in very different ways, have a strong impact on the dynamics in bound objects; they leave distinctive signatures in the dynamical mass-lensing mass relation as a function of mass and radius. We present measurements from $N$-body simulations of $f(R)$ and DGP, as well as semianalytical models that match the simulation results to surprising accuracy in both cases. The semianalytical models are useful for making the connection to observations. Our results confirm that the environment and scale dependence of the modified gravity effects have to be taken into account when confronting gravity theories with observations of dynamics in galaxies and clusters.

SPIN-2 GHOST IN BRANE GRAVITY

It is known that Dvali-Gabadadze-Porrati (DGP) braneworld model has a self-acceleration branch. However, this cosmological solution contains a spin-2 ghost. We study the possibility of avoiding the appearance of the ghost by slightly modifying the model, introducing the second brane. As a result we find we cannot avoid the appearance of ghost by two-branes model. Then we discuss whether spin-2 ghost is really harmful or not by evaluating the rate of spontaneous particle production due to ghost instability. We explain that non-covariant cutoff momentum arises rather naturally in the case of spin-2 ghost. As a result, the particle production rate is extremely suppressed and therefore the presence of a ghost might be harmless.

Validity of generalised second law in holographic DGP brane

In this paper we study the validity of the generalised second law of thermodynamics (GSLT) of the universe bounded by the event horizon on the Dvali–Gabadadze–Porrati (DGP) brane world. The radius of the event horizon is calculated by establishing a correspondence between holographic dark energy and the effective energy density in the DGP brane world. It is shown that in the absence of cold dark matter (CDM), GSLT is always respected. In the presence of CDM, we take three different DGP models and find conditions under which GSLT holds.