DGP Model Research Articles

Closed timelike curves in the Galileon model

It has long been known that generic solutions to the nonlinear DGP and Galileon models admit superluminal propagation. In this note we present a solution of these models which also admits closed timelike curves (CTCs). We observe that these CTCs only arise when, according to each observer, there exists some region in which the higher derivative terms are larger than the 2-derivative kinetic term.

Dynamic of the Accelerated Expansion of the Universe in the DGP Model

According to experimental data of SNe Ia (Supernovae type Ia), we will discuss in detial dynamics of the DGP model and introduce a simple parametrization of matter $\omega$, in order to analyze scenarios of the expanding universe and the evolution of the scale factor. We find that the dimensionless matter density parameter at the present epoch $\Omega^0_m=0.3$, the age of the universe $t_0= 12.48$ Gyr, $\frac{a}{a_0}=-2.4e^{\frac{-t}{25.56}}+2.45$. The next we study the linear growth of matter perturbations, and we assume a definition of the growth rate, $f \equiv \frac{dln\delta}{dlna}$. As many authors for many years, we have been using a good approximation to the growth rate $f \approx \Omega^{\gamma(z)}_m$, we also find that the best fit of the growth index, $\gamma(z)\approx 0.687 - \frac{40.67}{1 + e^{1.7. (4.48 + z)}}$, or $\gamma(z)= 0.667 + 0.033z$ when $z\ll1$. We also compare the age of the universe and the growth index with other models and experimental data. We can see that the DGP model describes the cosmic acceleration as well as other models that usually refers to dark energy and Cold Dark Matter (CDM).

ΛCDM, ΛDGP and extended phantom-like cosmologies

In this paper we compare outcomes of some extended phantom-like cosmologies with each other and also with $\Lambda$CDM\, and $\Lambda$DGP. We focus on the variation of the luminosity distances, the age of the universe and the deceleration parameter versus the redshift in these scenarios. In a dynamical system approach, we show that the accelerating phase of the universe in the $f(R)$-DGP scenario is stable if one consider the \emph{curvature fluid} as a phantom scalar field in the equivalent scalar-tensor theory, otherwise it is a transient and unstable phenomenon. Up to the parameters values adopted in this paper, the extended $F(R,\phi)$-DGP scenario is closer to the $\Lambda$CDM scenario than other proposed models. All of these scenarios explain the late-time cosmic speed-up in their normal DGP branches, but the redshift at which transition to the accelerating phase occurs are different: while the $\Lambda$DGP model transits to the accelerating phase much earlier, the $F(R,\phi)$-DGP model transits to this phase much later than other scenarios. Also, within the parameter spaces adopted in this paper, the age of the universe in the $f(R)$-DGP model is larger than $\Lambda$CDM, but this age in $F(G,\phi)$-DGP is smaller than $\Lambda$CDM.

Some adventures in the search for a modified gravity explanation of cosmic acceleration

The discovery of cosmic acceleration has raised the intriguing possibility that we are witnessing the first breakdown of General Relativity on cosmological scales. In this article I will briefly review current attempts to construct a theoretically consistent and observationally viable modification of gravity that is capable of describing the accelerating universe. I will discuss f(R) models, and their obvious extensions, and the DGP model as an example of extra-dimensional implementations. I will then briefly describe the Galileon models and their very recent multifield and curved space extensions - a class of four-dimensional effective field theories encoding extra dimensional modifications to gravity. This article is dedicated to the career of my friend and former colleague, Joshua Goldberg, and is written to appear in his festschrift.

On the cosmological viability of the Hu–Sawicki type modified induced gravity

It has been shown recently that the normal branch of a DGP braneworld scenario self-accelerates if the induced gravity on the brane is modified in the spirit of f(R) modified gravity. Within this viewpoint, we investigate cosmological viability of the Hu–Sawicki type modified induced gravity. Firstly, we present a dynamical system analysis of a general f(R)-DGP model. We show that in the phase space of the model, there exist three standard critical points; one of which is a de Sitter point corresponding to accelerating phase of the universe expansion. The stability of this point depends on the effective equation of state parameter of the curvature fluid. If we consider the curvature fluid to be a canonical scalar field in the equivalent scalar-tensor theory, the mentioned de Sitter phase is unstable, otherwise it is an attractor, stable phase. We show that the effective equation of state parameter of the model realizes an effective phantom-like behavior. A cosmographic analysis shows that this model, which admits a stable de Sitter phase in its expansion history, is a cosmologically viable scenario.

THE COSMOLOGICAL BULK FLOW: CONSISTENCY WITH ΛCDM ANDz≈ 0 CONSTRAINTS ON σ8AND γ

We derive estimates for the cosmological bulk flow from the SFI++ Tully-Fisher (TF) catalog. For a sphere of radius $40 \hmpc$ centered on the MW, we derive a bulk flow of $333 \pm 38\kms $ towards Galactic $ (l,b)=(276^\circ,14^\circ)$ within a $3^\circ$ $1\sigma$ error. Within a $ 100\hmpc$ we get $ 257\pm 44\kms$ towards $(l,b)=(279^\circ, 10^\circ)$ within a $6^\circ$ error. These directions are at a $40^\circ$ with the Supergalactic plane, close to the apex of the motion of the Local Group of galaxies after the Virgocentric infall correction. Our findings are consistent with the $\Lambda$CDM model with the latest WMAP best fit cosmological parameters. But the bulk flow allows independent constraints. For WMAP inferred Hubble parameter $h=0.71$ and baryonic mean density parameter $\Omega_b=0.0449$, the constraint from the bulk flow on the matter density $\Omega_m$, the normalization of the density fluctuations, $\sigma_8$, and the growth index, $\gamma$, can be expressed as $\sigma_8\Omega_m^{\gamma-0.55}(\Omega_m/0.266)^{0.28}=0.86\pm 0.11$ (for $\Omega_m\approx 0.266$). Fixing $\sigma_8=0.8$ and $\Omega_m=0.266$ as favored by WMAP, we get $\gamma=0.495\pm 0.096$. The constraint derived here rules out popular DGP models at more than the 99% confidence level. Our results are based on a method termed \ace\ (All Space Constrained Estimate) which reconstructs the bulk flow from an all space three dimensional peculiar velocity field constrained to match the TF measurements. At large distances \ace\ generates a robust bulk flow from the SFI++ that is insensitive to the assumed prior. For comparison, a standard straightforward maximum likelihood estimate leads to very similar results.

Braneworld Inflation with Induced Gravity and Curvature Effect

We construct a general braneworld inflation scenario where the inflaton field evolves on the DGP brane and curvature effects are taken into account via incorporation of the Gauss—Bonnet term in the bulk action. While induced gravity on the DGP brane modifies the IR limit of general relativity, the Gauss—Bonnet term in the bulk action modifies the UV sector of the theory. In this setup, the dynamics of perturbations on the brane are studied with details and some confrontation with recent observations are discussed. While the Einstein—Gauss—Bonnet inflation scenario favors only a red spectrum of the scalar perturbation, pure DGP and GBIG inflation models have the capacity to realize the blue spectrum too. In addition, the GBIG inflation scenario in the large field limit requires a smaller number of e-folds than other proposed scenarios in the same situation. For the tensor-to-scalar ratio, the GBIG inflation scenario gives a better fit with observationally supported value of R ≈ 0.24.

Nonlinear dynamics of 3D massive gravity

We explore the nonlinear classical dynamics of the three-dimensional theory of “New Massive Gravity” proposed by Bergshoeff, Hohm and Townsend. We find that the theory passes remarkably highly nontrivial consistency checks at the nonlinear level. In particular, we show that: (1) In the decoupling limit of the theory, the interactions of the helicity-0 mode are described by a single cubic term — the so-called cubic Galileon — previously found in the context of the DGP model and in certain 4D massive gravities. (2) The conformal mode of the metric coincides with the helicity-0 mode in the decoupling limit. Away from this limit the nonlinear dynamics of the former is described by a certain generalization of Galileon interactions, which like the Galileons themselves have a well-posed Cauchy problem. (3) We give a non-perturbative argument based on the presence of additional symmetries that the full theory does not lead to any extra degrees of freedom, suggesting that a 3D analog of the 4D Boulware-Deser ghost is not present in this theory. Last but not least, we generalize “New Massive Gravity” and construct a class of 3D cubic order massive models that retain the above properties.

Goldstone’s theorem and Hamiltonian of multi-Galileon modified gravity

The galileon model was recently proposed to locally describe a class of modified gravity theories, including the braneworld DGP model. We discuss spontaneous symmetry breaking of the self-accelerating branch in a multi-galileon theory with internal global symmetries. We show a modified version of Goldstone's theorem is applicable to the symmetry breaking pattern and discuss its implications. We also derive the Hamiltonian of a general multi-galileon theory and discuss its implications.

Testing a phenomenologically extended DGP model with upcoming weak lensing surveys

A phenomenological extension of the well-known brane-world cosmology of Dvali, Gabadadze and Porrati (eDGP) has recently been proposed. In this model, a cosmological-constant-like term is explicitly present as a non-vanishing tension σ on the brane, and an extra parameter α tunes the cross-over scale rc, the scale at which higher dimensional gravity effects become non negligible. Since the Hubble parameter in this cosmology reproduces the same ΛCDM expansion history, we study how upcoming weak lensing surveys, such as Euclid and DES (Dark Energy Survey), can confirm or rule out this class of models. We perform Monte Carlo Markov Chain simulations to determine the parameters of the model, using Type Ia Supernovæ, H(z) data, Gamma Ray Bursts and Baryon Acoustic Oscillations. We also fit the power spectrum of the temperature anisotropies of the Cosmic Microwave Background to obtain the correct normalisation for the density perturbation power spectrum. Then, we compute the matter and the cosmic shear power spectra, both in the linear and non-linear régimes. The latter is calculated with the two different approaches of Hu and Sawicki (2007) (HS) and Khoury and Wyman (2009) (KW). With the eDGP parameters coming from the Markov Chains, KW reproduces the ΛCDM matter power spectrum at both linear and non-linear scales and the ΛCDM and eDGP shear signals are degenerate. This result does not hold with the HS prescription. Indeed, Euclid can distinguish the eDGP model from ΛCDM because their expected power spectra roughly differ by the 3σ uncertainty in the angular scale range 700≲ℓ≲3000; on the contrary, the two models differ at most by the 1σ uncertainty over the range 500≲ℓ≲3000 in the DES experiment and they are virtually indistinguishable.

Non-Linear Equation of State and Effective Phantom Divide in Brane Models

Here, DGP model of brane-gravity is analyzed and compared with the standard general relativity and Randall-Sundrum cases using non-linear equation of state. Phantom fluid is known to violate the weak energy condition. In this paper, it is found that this characteristic of phantom energy is affected drastically by the negative brane-tension $\lambda$ of the RS-II model. It is found that in DGP model strong energy condition(SEC) is always violated and the universe accelerates only where as in RS-II model even SEC is not violated for $1 < \rho/\lambda < 2$ and the universe decelerates.

The stability of Einstein static universe in the DGP braneworld

The stability of an Einstein static universe in the DGP braneworld scenario is studied in this Letter. Two separate branches denoted by ϵ=±1 of the DGP model are analyzed. Assuming the existence of a perfect fluid with a constant equation of state, w, in the universe, we find that, for the branch with ϵ=1, there is no a stable Einstein static solution, while, for the case with ϵ=−1, the Einstein static universe exists and it is stable when −1<w<−13. Thus, the universe can stay at this stable state past-eternally and may undergo a series of infinite, non-singular oscillations. Therefore, the big bang singularity problem in the standard cosmological model can be resolved.

Schwinger-DeWitt technique for quantum effective action in brane induced gravity models

We develop the Schwinger-DeWitt technique for the covariant curvature expansion of the quantum effective action for brane induced gravity models in curved spacetime. This expansion has a part nonanalytic in DGP type scale parameter, leading to the cutoff scale which is given by the geometric average of the mass of the quantum field in the bulk and DGP scale. This cutoff is much higher than the analogous strong coupling scale of the DGP model treated by weak field expansion in the tree-level approximation. The lowest orders of this curvature expansion are calculated for the case of the scalar field in the $(d+1)$-dimensional bulk with the brane carrying the $d$-dimensional kinetic term of this field. The ultraviolet divergences in this model are obtained for a particular case of $d=4$.

COSMOLOGY FROM ANISOTROPIC DGP BRANEWORLD

We considered an anisotropic brane embedded in a five-dimensional bulk space–time. The Einstein equations and Friedmann equations are obtained. The corresponding Friedmann equations are modified with quadratic corrections to energy density. The anisotropic DGP model also admits a self-accelerating phase in the late universe. The acceleration conditions are obtained and they are consistent with the braneworld scenario. The acceleration condition for DGP model, in the late universe, is dependent on the crossover scale rc.

Improved parametrization of the growth index for dark energy and DGP models

We propose two improved parameterized form for the growth index of the linear matter perturbations: (I) γ(z)=γ0+(γ∞−γ0)zz+1 and (II) γ(z)=γ0+γ1zz+1+(γ∞−γ1−γ0)(zz+1)α. With these forms of γ(z), we analyze the accuracy of the approximation the growth factor f by Ωmγ(z) for both the wCDM model and the DGP model. For the first improved parameterized form, we find that the approximation accuracy is enhanced at the high redshifts for both kinds of models, but it is not at the low redshifts. For the second improved parameterized form, it is found that Ωmγ(z) approximates the growth factor f very well for all redshifts. For chosen α, the relative error is below 0.003% for the ΛCDM model and 0.028% for the DGP model when Ωm=0.27. Thus, the second improved parameterized form of γ(z) should be useful for the high precision constraint on the growth index of different models with the observational data. Moreover, we also show that α depends on the equation of state w and the fractional energy density of matter Ωm0, which may help us learn more information about dark energy and DGP models.

Cosmological simulations of normal-branch braneworld gravity

We introduce a cosmological model based on the normal branch of DGP braneworld gravity with a smooth dark energy component on the brane. The expansion history in this model is identical to LambdaCDM, thus evading all geometric constraints on the DGP cross-over scale r_c. This model can serve as a first approximation to more general braneworld models whose cosmological solutions have not been obtained yet. We study the formation of large scale structure in this model in the linear and non-linear regime using N-body simulations for different values of r_c. The simulations use the code presented in (F.S., arXiv:0905.0858) and solve the full non-linear equation for the brane-bending mode in conjunction with the usual gravitational dynamics. The brane-bending mode is attractive rather than repulsive in the DGP normal branch, hence the sign of the modified gravity effects is reversed compared to those presented in arXiv:0905.0858. We compare the simulation results with those of ordinary LambdaCDM simulations run using the same code and initial conditions. We find that the matter power spectrum in this model shows a characteristic enhancement peaking at k ~ 0.7 h/Mpc. We also find that the abundance of massive halos is significantly enhanced. Other results presented here include the density profiles of dark matter halos, and signatures of the brane-bending mode self-interactions (Vainshtein mechanism) in the simulations. Independently of the expansion history, these results can be used to place constraints on the DGP model and future generalizations through their effects on the growth of cosmological structure.

Boundary terms and junction conditions for the DGP π-Lagrangian and galileon

In the decoupling limit of DGP, π describes the brane-bending degree of freedom. It obeys second order equations of motion, yet it is governed by a higher derivative Lagrangian. We show that, analogously to the Einstein-Hilbert action for GR, the π-Lagrangian requires Gibbons-Hawking-York type boundary terms to render the variational principle well-posed. These terms are important if there are other boundaries present besides the DGP brane, such as in higher dimensional cascading DGP models. We derive the necessary boundary terms in two ways. First, we derive them directly from the brane-localized π-Lagrangian by demanding well-posedness of the action. Second, we calculate them directly from the bulk, taking into account the Gibbons-Hawking-York terms in the bulk Einstein-Hilbert action. As an application, we use the new boundary terms to derive Israel junction conditions for π across a sheet-like source. In addition, we calculate boundary terms and junction conditions for the galileons which generalize the DGP π-Lagrangian, showing that the boundary term for the n-th order galileon is the (n−1)-th order galileon.

Anisotropic cosmologies in warped DGP braneworld

The DGP braneworld scenario explains accelerated expansion of the Universe via leakage of gravity to extra dimensions without any need for dark energy. We study the behavior of homogeneous and anisotropic cosmologies on a warped DGP brane with perfect fluid as a matter source. Taking a conformally flat bulk, we obtain the general solutions of the field equations in an exact parametric form for Bianchi type I space-time with a pressureless fluid. Finally, the behavior of the observationally important parameters like shear, anisotropy, and the deceleration parameter is considered in detail. We find that isotropization can proceed slower in the warped DGP model than the generalized Randall-Sundrum II model.

Superluminality in DGP

We reconsider the issue of superluminal propagation in the DGP model of infrared modified gravity. Superluminality was argued to exist in certain otherwise physical backgrounds by using a particular, physically relevant scaling limit of the theory. In this paper, we exhibit explicit five-dimensional solutions of the full theory that are stable against small fluctuations and that indeed support superluminal excitations. The scaling limit is neither needed nor invoked in deriving the solutions or in the analysis of its small fluctuations. To be certain that the superluminality found here is physical, we analyze the retarded Green's function of the scalar excitations, finding that it is causal and stable, but has support on a widened light-cone. We propose to use absence of superluminal propagation as a method to constrain the parameters of the DGP model. As a first application of the method, we find that whenever the 4D energy density is a pure cosmological constant and a hierarchy of scales exists between the 4D and 5D Planck masses, superluminal propagation unavoidably occurs.

CHARGED ROTATING BLACK HOLES ON DGP BRANE

We consider charged rotating black holes localized on a three-brane in the DGP model. Assuming a Z2-symmetry across the brane and with a stationary and axisymmetric metric ansatz on the brane, a particular solution is obtained in the Kerr–Schild form. This solution belongs to the accelerated branch of the DGP model and has the characteristic of the Kerr–Newman–de Sitter-type solution in general relativity. Using a modified version of Boyer–Lindquist coordinates we examine the structures of the horizon and ergosphere.