We consider the Palatini formalism of the Born-Infeld gravity. In the Palatini formalism, the propagating mode is only graviton, whose situation is different from that in the metric formalism. We discuss about the FRW cosmology by using an effective potential. Especially we consider the condition that the bouncing could occur. We also give some speculations about the black hole formation
We study isotropic and anisotropic (Bianchi I) cosmologies in Palatini $f(R)$ and $f(R,R_{μν}R^{μν})$ theories of gravity and consider the existence of non-singular bouncing solutions in the early universe. We find that all $f(R)$ models with isotropic bouncing solutions develop shear singularities in the anisotropic case. On the contrary, the simple quadratic model $R+a R^2/R_P+R_{μν}R^{μν}/R_P$ exhibits regular bouncing solutions in both isotropic and anisotropic cases for a wide range of equations of state, including dust (for $a<0$) and radiation (for arbitrary $a$). It thus represents a p…
In a recent paper [Phys. Rev. D{\bf 85}, 023528 (2012)] the authors proposed a generalized Born-Infeld electrodynamics coupled to general relativity which produces a nonsingular bouncing universe. For a magnetic universe the resulting cosmic evolution inevitably interpolates between asymptotic de Sitter states. Here we shall show that (i) the above theory does not have the standard weak field Maxwell limit, (ii) a sudden curvature singularity -- not better than the big bang -- arises, (iii) the speed of sound squared is a negative quantity signaling instability against small perturbations of t…
We study the dynamics of a homogeneous and isotropic Friedmann-Robertson-Walker universe in the context of the Eddington-inspired Born-Infeld theory of gravity. We generalize earlier results, obtained in the context of a radiation dominated universe, to account for the evolution of a universe permeated by a perfect fluid with an arbitrary equation of state parameter $w$. We show that a bounce may occur for $κ>0$, if $w$ is time-dependent, and we demonstrate that it is free from tensor singularities. We argue that Eddington-inspired Born-Infeld cosmologies may be a viable alternative to the inf…
We show the existence of some bouncing cosmological solutions in the braneworld scenario. More specifically, we consider a dynamical three-brane in the background of Born-Infeld and electrically charged Gauss-Bonnet black hole. We find that, in certain range of parameter space, the brane universe, at least classically, never shrinks to a zero size, resulting in a singularity-free cosmology within the classical domain.
The scrutiny of black hole perturbations and its application to testing gravity theories have been a very crucial frontier in modern physics. In this paper we study the quasi-normal modes (QNM) of massless scalar perturbations for various charged black holes in the Palatini-type theories of gravity. Specifically, we consider the Palatini $f(R)$ theory coupled with Born-Infeld nonlinear electrodynamics and the Eddington-inspired-Born-Infeld gravity (EiBI) coupled with Maxwell electromagnetic fields. Special attention is paid to Einstein-Born-Infeld black holes, EiBI charged black holes and Born…
The Eddington-inspired-Born-Infeld (EiBI) model is reformulated within the mimetic approach. In the presence of a mimetic field, the model contains non-trivial vacuum solutions which could be free of spacetime singularity because of the Born-Infeld nature of the theory. We study a realistic primordial vacuum universe and prove the existence of regular solutions, such as primordial inflationary solutions of de Sitter type or bouncing solutions. Besides, the linear instabilities present in the EiBI model are found to be avoidable for some interesting bouncing solutions in which the physical metr…
We study the evolution of gravitational waves for non-singular cosmological solutions within the framework of Born-Infeld inspired gravity theories, with special emphasis on the Eddington-inspired Born-Infeld theory. We review the existence of two types of non-singular cosmologies, namely bouncing and asymptotically Minkowski solutions, from a perspective that makes their features more apparent. We study in detail the propagation of gravitational waves near these non-singular solutions and carefully discuss the origin and severity of the instabilities and strong coupling problems that appear. …
The so called $f(X)$ hybrid metric-Palatini gravity presents a unique viable generalisation of the $f(R)$ theories within the metric-affine formalism. Here the cosmology of the $f(X)$ theories is studied using the dynamical system approach. The method consists of formulating the propagation equation in terms of suitable (expansion-normalised) variables as an autonomous system. The fixed points of the system then represent exact cosmological solutions described by power-law or de Sitter expansion. The formalism is applied to two classes of $f(X)$ models, revealing both standard cosmological fix…
In this paper we constructed a semi-realistic cosmological model in a dynamic domain wall framework. Our universe is considered to be a (3+1) dimensional dynamic domain wall in a higher dimensional Einstein-Maxwell-Born-Infeld background. One of our interesting outcomes from the effective Hubble equation for the domain wall dynamics is that it contains an additional component of "dark matter" which is induced from the charge of the bulk Born-Infeld gauge field. In this background spacetime we have studied the cosmological dynamics of the domain wall. In addition to the Born-Infield gauge field…
We consider two types of modifications of Born-Infeld gravity in the Palatini formulation and explore their dynamics in the early universe. One of these families considers $f(R)$ corrections to the Born-Infeld Lagrangian, which can be seen as modifications of the dynamics produced by the quantum effects of matter, while the other consists on different powers of the elementary building block of the Born-Infeld Lagrangian, which we denote by $|\hatΩ|$. We find that the two types of nonsingular solutions that arise in the original Born-Infeld theory are also present in these extensions, being bou…
An introduction to extended theories of gravity formulated in metric-affine (or Palatini) spaces is presented. Focusing on spherically symmetric configurations with electric fields, we will see that in these theories the central singularity present in General Relativity is generically replaced by a wormhole structure. The resulting space-time becomes geodesically complete and, therefore, can be regarded as non-singular. We illustrate these properties considering two different models, namely, a quadratic $f(R)$ theory and a Born-Infeld like gravity theory.
In this Letter, we discuss the dynamics of a domain wall universe embedded into the charged black hole spacetime of the Einstein-Born-Infeld (EBI) theory. There are four kinds of possible spacetime structures, i.e., those with no horizon, the extremal one, those with two horizons (as the Reissner-Nordstr$\rm{\ddot o}$m black hole), and those with a single horizon (as the Schwarzshild black hole). We derive the effective cosmological equations on the wall. In contrast to the previous works, we take the contribution of the electrostatic energy on the wall into account. By examining the propertie…
We consider a magnetic flux pointing in the $z$ direction of an axially symmetric space-time (Melvin Universe) in a Born-Infeld-type extension of General Relativity (GR) formulated in the Palatini approach. Large magnetic fields could have been produced in the early Universe, and given rise to interesting phenomenology regarding wormholes and black hole remnants. We find a formal analytic solution to this problem that recovers the GR result in the appropriate limits. Our results set the basis for further extensions that could allow the embedding of pairs of black hole remnants in geometries wi…
We reconsider the problem of $f(R)$ theories of gravity coupled to Born-Infeld theory of electrodynamics formulated in a Palatini approach, where metric and connection are independent fields. By studying electrovacuum configurations in a static and spherically symmetric space-time, we find solutions which reduce to their Reissner-Nordström counterparts at large distances but undergo important non-perturbative modifications close to the center. Our new analysis reveals that the point-like singularity is replaced by a finite-size wormhole structure, which provides a geodesically complete and thu…
We study the dynamics of domain walls in Einstein-Born-Infeld-dilaton theory. Dilaton is non-trivially coupled with the Born-Infeld electromagnetic field. We find three different types of solutions consistent with the dynamic domain walls. For every case, the solutions have singularity. Further more, in these backgrounds, we study the dynamics of domain walls. We qualitatively plot various form of the bulk metrics and the potential encountered by the domain walls. In many cases, depending upon the value of the parameters, the domain walls show bouncing universe and also undergo inflationary ph…
The bouncing universe provides a possible solution to the Big Bang singularity problem. In this paper we study the bouncing solution in the universe dominated by the Quintom matter with an equation of state (EoS) crossing the cosmological constant boundary. We will show explicitly the analytical and numerical bouncing solutions in three types of models for the Quintom matter with an phenomenological EoS, the two scalar fields and a scalar field with a modified Born-Infeld action.
We review the recent literature on modified theories of gravity in the Palatini approach. After discussing the motivations that lead to consider alternatives to Einstein's theory and to treat the metric and the connection as independent objects, we review several topics that have been recently studied within this framework. In particular, we provide an in-depth analysis of the cosmic speedup problem, laboratory and solar systems tests, the structure of stellar objects, the Cauchy problem, and bouncing cosmologies. We also discuss the importance of going beyond the f(R) models to capture other …
The field equations associated with the Born-Infeld-Einstein action including matter are derived using a Palatini variational principle. Scalar, electromagnetic, and Dirac fields are considered. It is shown that an action can be chosen for the scalar field that produces field equations identical to the usual Einstein field equations minimally coupled to a scalar field. In the electromagnetic and Dirac cases the field equations reproduce the standard equations only to lowest order. The spherically symmetric electrovac equations are studied in detail. It is shown that the resulting Einstein equa…
We study Born-Infeld gravity coupled to a static, nonrotating electric field in $2+1$ dimensions and find exact analytical solutions. Two families of such solutions represent geodesically complete, and hence nonsingular, spacetimes. Another family represents a point-like charge with a singularity at the center. Despite the absence of rotation, these solutions resemble the charged, rotating BTZ solution of General Relativity but with a richer structure in terms of horizons. The nonsingular character of the first two families turn out to be attached to the emergence of a wormhole structure on th…
Universidad de Buenos Aires（布宜诺斯艾利斯大学）；CONICET - Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA)（阿根廷国家科学研究委员会-布宜诺斯艾利斯大学，布宜诺斯艾利斯物理研究所 (IFIBA)）；Instituto de Astronomía y Física del Espacio (IAFE, CONICET-UBA)（天文与空间物理研究所 (IAFE, 阿根廷国家科学研究委员会-布宜诺斯艾利斯大学)）
Motivated by the properties of matter quantum fields in curved space-times, we work out a gravity theory that combines the Born-Infeld gravity Lagrangian with an $f(R)$ piece. To avoid ghost-like instabilities, the theory is formulated within the Palatini approach. This construction provides more freedom to address a number of important questions such as the dynamics of the early universe and the cosmic accelerated expansion, among others. In particular, we consider the effect that adding an $f(R)=a R^2$ term has on the early-time cosmology. We find that bouncing solutions are robust against t…
In this paper, a modified Eddington-inspired-Born-Infeld (EiBI) theory with a pure trace term $g_{μν}R$ being added to the determinantal action is analysed from a cosmological point of view. It corresponds to the most general action constructed from a rank two tensor that contains up to first order terms in curvature. This term can equally be seen as a conformal factor multiplying the metric $g_{μν}$. This very interesting type of amendment has not been considered within the Palatini formalism despite the large amount of works on the Born-Infeld-inspired theory of gravity. This model can provi…
The recent direct detection of gravitational waves has highlighted the huge importance of the tensorial modes in any extended gravitational theory. One of the most appealing approaches to extend gravity beyond general relativity is the Eddington-inspired-Born-Infeld gravity which is formulated within the Palatini approach. This theory can avoid the Big Bang singularity in the physical metric although a Big Bang intrinsic to the affine connection is still there, which in addition couples to the tensorial sector and might jeopardize the viability of the model. In this paper, we suggest that a qu…
We consider $f(R)$ gravity and Born-Infeld-Einstein (BIE) gravity in formulations where the metric and connection are treated independently and integrate out the metric to find the corresponding models solely in terms of the connection, the archetypical treatment being that of Eddington-Schrödinger (ES) duality between cosmological Einstein and Eddington theories. For dimensions $D\ne2$, we find that this requires $f(R)$ to have a specific form which makes the model Weyl invariant, and that its Eddington reduction is then equivalent to that of BIE with certain parameters. For $D=2$ dimensions,…
We consider the transverse-traceless tensor perturbation of a spatial flat homogeneous and isotropic spacetime in Born-Infeld determinantal gravity, and investigate the evolution of the tensor mode for two solutions in the early universe. For the first solution where the initial singularity is replaced by a regular geometric de Sitter inflation of infinite duration, the evolution of the tensor mode is stable for the parameter spaces $α<-1$, $ω\geq-1/3$ and $α=-1$, $ω>0$. For the second solution where the initial singularity is replaced by a primordial brusque bounce, which suffers a sudden sin…
The Palatini $f(|\hatΩ|)$ gravity is a generalized theory of the Eddington-inspired Born-Infeld gravity, where $Ω_{~N}^{K}\equivδ_{~N}^{K}+bg^{KL}R_{LN}(Γ)$ is an auxiliary tensor constructed with the spacetime metric $g$ and independent connection $Γ$. In this paper, we study $f(|\hatΩ|)$ theory with $f(|\hatΩ|)=|\hatΩ|^{\frac{1}{2}+n}$ in the thick brane scenario and give some constraints on the brane model. We finally found an analytic solution of the thick brane generated by a single scalar field. The behavior of the negative energy density denotes the localization of the thick brane at th…
We generalize the ultraviolet sector of gravitation via a Born-Infeld action using lessons from massive gravity. The theory contains all of the elementary symmetric polynomials and is treated in the Palatini formalism. We show how the connection can be solved algebraically to be the Levi-Civita connection of an effective metric. The non-linearity of the algebraic equations yields several branches, one of which always reduces to General Relativity at low curvatures. We explore in detail a {\it minimal} version of the theory, for which we study solutions in the presence of a perfect fluid with s…
The quantum effects close to the classical big rip singularity within the Eddington-inspired-Born-Infeld theory (EiBI) are investigated through quantum geometrodynamics. It is the first time that this approach is applied to a modified theory constructed upon Palatini formalism. The Wheeler-DeWitt (WDW) equation is obtained and solved based on an alternative action proposed in Ref.[1], under two different factor ordering choices. This action is dynamically equivalent to the original EiBI action while it is free of square root of the spacetime curvature. We consider a homogeneous, isotropic and …
Motivated by the lack of rotating solutions sourced by matter in General Relativity as well as in modified gravity theories, we extend a recently discovered exact rotating solution of the minimal Einstein-scalar theory to its counterpart in Eddington-inspired Born-Infeld gravity coupled to a Born-Infeld scalar field. This is accomplished with the implementation of a well-developed mapping between solutions of Ricci-Based Palatini theories of gravity and General Relativity. The new solution is parametrized by the scalar charge and the Born-Infeld coupling constant apart from the mass and spin o…
