Publications

Title: Introduction to Palatini theories of gravity and nonsingular cosmologies.

Authors: Gonzalo J. Olmo

Journal-ref: Chapter of the book Open Questions in Cosmology , edited by Gonzalo J. Olmo. InTech Publishing, Rijeka, Croatia, (2012), ISBN 978-953-51-0880-1..

Abstract: These notes are a summary of lectures given at the Instituto de Astronomia of the Universidad Nacional Autonoma de Mexico (UNAM), the Dipartimento di Fisica of the Universita degli studi di Salerno (Italy), and the Instituto de Fisica Corpuscular of the Universitat de Valencia (Spain) during the year 2012. Basic mathematical aspects of Palatini theories of gravity, which are constructed assuming that metric and connection are independent geometrical entities, are briefly introduced and discussed, and followed by a detailed derivation of the field equations of some rather general Lagrangian theories. Applications to the early universe are considered paying special attention to the avoidance of the big bang singularity. The analysis of non-singular cosmologies carried out in arXiv:1005.4136 [gr-qc] is extended to include several perfect fluids.

Preprint

Title: The virial theorem and the dark matter problem in hybrid metric-Palatini gravity.

Authors: S. Capozziello, T. Harko, T. S. Koivisto, F. S. N. Lobo, Gonzalo J. Olmo

Journal-ref: arXiv.

Abstract: Hybrid metric-Palatini gravity is a recently proposed theory, consisting of the superposition of the metric Einstein-Hilbert Lagrangian with an $f(\cal R)$ term constructed \`{a} la Palatini. The theory predicts the existence of a long-range scalar field, which passes the Solar System observational constraints, even if the scalar field is very light, and modifies the cosmological and galactic dynamics. Thus, the theory opens new possibilities to approach, in the same theoretical framework, the problems of both dark energy and dark matter. In this work, we consider the generalized virial theorem in the scalar-tensor representation of the hybrid metric-Palatini gravity. More specifically, taking into account the relativistic collisionless Boltzmann equation, we show that the supplementary geometric terms in the gravitational field equations provide an effective contribution to the gravitational potential energy. We show that the total virial mass is proportional to the effective mass associated with the new terms generated by the effective scalar field, and the baryonic mass. This shows that the geometric origin in the generalized virial theorem may account for the well-known virial theorem mass discrepancy in clusters of galaxies. In addition to this, we also consider astrophysical applications of the model and show that the model predicts that the mass associated to the scalar field and its effects extend beyond the virial radius of the clusters of galaxies. In the context of the galaxy cluster velocity dispersion profiles predicted by the hybrid metric-Palatini model, the generalized virial theorem can be an efficient tool in observationally testing the viability of this class of generalized gravity models. Thus, hybrid metric-Palatini gravity provides an effective alternative to the dark matter paradigm of present day cosmology and astrophysics.

Preprint

Title: Stellar Structure Equations in Extended Palatini Gravity

Authors: Gonzalo J. Olmo, Helios Sanchis-Alepuz, Swapnil Tripathi

Journal-ref:

Abstract: We consider static spherically symmetric stellar configurations in Palatini theories of gravity in which the Lagrangian is an unspecified function of the form f(R,R_{\mu\nu}R^{\mu\nu}). We obtain the Tolman-Oppenheimer-Volkov equations corresponding to this class of theories and show that they recover those of f(R) theories and General Relativity in the appropriate limits. We show that the exterior vacuum solutions are of Schwarzschild-de Sitter type and comment on the possible expected modifications, as compared to GR, of the interior solutions.

Preprint

Title: Static Spherically Symmetric Solutions in Extended Palatini Gravity.

Authors: Gonzalo J. Olmo, Helios Sanchis-Alepuz, Swapnil Tripathi

Journal-ref:

Abstract: We consider static spherically symmetric stellar configurations in Palatini theories of gravity in which the Lagrangian is an unspecified function of the form f(R,R_{\mu\nu}R^{\mu\nu}). We obtain the Tolman-Oppenheimer-Volkov equations corresponding to this class of theories and show that they recover those of f(R) theories and General Relativity in the appropriate limits. We compute exterior vacuum solutions and comment on the possible expected modifications, as compared to GR, of the interior solutions.

Preprint

Title: Wormholes supported by hybrid metric-Palatini gravity.

Authors: S. Capozziello, T. Harko, T. S. Koivisto, F. S. N. Lobo, Gonzalo J. Olmo

Journal-ref: Phys.Rev.D86:127504,2012.

Abstract: Recently, a modified theory of gravity was presented, which consists of the superposition of the metric Einstein-Hilbert Lagrangian with an $f(\cal R)$ term constructed \`{a} la Palatini. The theory possesses extremely interesting features such as predicting the existence of a long-range scalar field, that explains the late-time cosmic acceleration and passes the local tests, even in the presence of a light scalar field. In this brief report, we consider the possibility that wormholes are supported by this hybrid metric-Palatini gravitational theory. We present here the general conditions for wormhole solutions according to the null energy conditions at the throat and find specific examples. In the first solution, we specify the redshift function, the scalar field and choose the potential that simplifies the modified Klein-Gordon equation. This solution is not asymptotically flat and needs to be matched to a vacuum solution. In the second example, by adequately specifying the metric functions and choosing the scalar field, we find an asymptotically flat spacetime.

Preprint

Title: Black hole formation from a null fluid in extended Palatini gravity.

Authors: J. Martinez-Asencio, Gonzalo J. Olmo, D. Rubiera-Garcia

Journal-ref: Phys.Rev. D86 (2012) 104010.

Abstract: We study the formation and perturbation of black holes by null fluxes of neutral matter in a quadratic extension of General Relativity formulated a la Palatini. Working in a spherically symmetric space-time, we obtain an exact analytical solution for the metric that extends the usual Vaidya-type solution to this type of theories. We find that the resulting space-time is formally that of a Reissner-Nordstrom black hole but with an effective charge term carrying the wrong sign in front of it. This effective charge is directly related to the luminosity function of the radiation stream. When the ingoing flux vanishes, the charge term disappears and the space-time relaxes to that of a Schwarzschild black hole. We provide two examples that illustrate the formation of a black hole from Minkowski space and the perturbation by a finite pulse of radiation of an existing Schwarzschild black hole.

Preprint

Title: Cosmology of hybrid metric-Palatini f(X)-gravity.

Authors: Salvatore Capozziello, Tiberiu Harko, Tomi S. Koivisto, Francisco S.N. Lobo, Gonzalo J. Olmo

Journal-ref: .

Abstract: A new class of modified theories of gravity, consisting of the superposition of the metric Einstein-Hilbert Lagrangian with an $f(\cal R)$ term constructed \`{a} la Palatini was proposed recently. The dynamically equivalent scalar-tensor representation of the model was also formulated, and it was shown that even if the scalar field is very light, the theory passes the Solar System observational constraints. Therefore the model predicts the existence of a long-range scalar field, modifying the cosmological and galactic dynamics. An explicit model that passes the local tests and leads to cosmic acceleration was also obtained. In the present work, it is shown that the theory can be also formulated in terms of the quantity $X\equiv \kappa^2 T+R$, where T and R are the traces of the stress-energy and Ricci tensors, respectively. The variable X represents the deviation with respect to the field equation trace of general relativity. The cosmological applications of this hybrid metric-Palatini gravitational theory are also explored, and cosmological solutions coming from the scalar-tensor representation of f(X)-gravity are presented. Criteria to obtain cosmic acceleration are discussed and the field equations are analyzed as a dynamical system. Several classes of dynamical cosmological solutions, depending on the functional form of the effective scalar field potential, describing both accelerating and decelerating Universes are explicitly obtained. Furthermore, the cosmological perturbation equations are derived and applied to uncover the nature of the propagating scalar degree of freedom and the signatures these models predict in the large-scale structure.

Preprint

Title: Black holes with electric charge in Palatini theories of gravity.

Authors: Gonzalo J. Olmo, D. Rubiera-Garcia.

Journal-ref: AIP Conf. Proc. 1458, pp. 511-514.

Abstract: We discuss the procedure of solving the field equations of Palatini f(R) and f(R,Q) theories coupled to an arbitrary nonlinear theory of electrodynamics as the matter source in spherically symmetric, static backgrounds. We provide a formal analytical solution for the metric in all such black hole spacetimes.

Preprint

Title: Reissner-Nordström black holes in extended Palatini theories.

Authors: Gonzalo J. Olmo

Journal-ref: Phys.Rev. D86 (2012) 044014.

Abstract: We study static, spherically symmetric solutions with an electric field in an extension of general relativity (GR) containing a Ricci-squared term and formulated in the Palatini formalism. We find that all the solutions present a central core whose area is proportional to the Planck area times the number of charges. Far from the core, curvature invariants quickly tend to those of the usual Reissner-Nordstr\"om solution, though the structure of horizons may be different. In fact, besides the structures found in the Reissner-Nordstr\"om solution of GR, we find black hole solutions with just one nondegenerate horizon (Schwarzschild-like), and nonsingular black holes and naked cores. The charge-to-mass ratio of the nonsingular solutions implies that the core matter density is independent of the specific amounts of charge and mass and of order the Planck density. We discuss the physical implications of these results for astrophysical and microscopic black holes, construct the Penrose diagrams of some illustrative cases, and show that the maximal analytical extension of the nonsingular solutions implies a bounce of the radial coordinate.

Preprint

Title: Cosmology in Palatini theories of gravity.

Authors: Gonzalo J. Olmo

Journal-ref: AIP Conf. Proc. 1458 (2011), 222-237.

Abstract: We discuss recent results on the cosmology of extended theories of gravity formulated in the Palatini approach, i.e., assuming that metric and connection are independent fields. In particular, we focus on the attempts to explain the cosmic speedup with f(R) theories and on models that avoid the big bang singularity. The field equations for gravity Lagrangians of the form f(g_{\mu\nu},{R^\alpha}_{\beta\mu\nu}) (including torsion) are explicitly derived and discussed.

Preprint

Title: Nonsingular charged black holes à la Palatini.

Authors: Gonzalo J. Olmo, Diego Rubiera-Garcia

Journal-ref: Int.J.Mod.Phys. D21 (2012) 1250067.

Abstract: We argue that the quantum nature of matter and gravity should lead to a discretization of the allowed states of the matter confined in the interior of black holes. To support and illustrate this idea, we consider a quadratic extension of General Relativity formulated \`{a} la Palatini and show that nonrotating, electrically charged black holes develop a compact core at the Planck density which is nonsingular if the mass spectrum satisfies a certain discreteness condition. We also find that the area of the core is proportional to the number of charges times the Planck area.

Preprint

Title: Birkhoff's theorem and perturbations in $f(R)$ theories

Authors: Gonzalo J. Olmo

Journal-ref: Annalen Phys. 524 (2012) 87-88.

Abstract: Invited contribution to Annalen der Physik (Expert Opinion).

Preprint

Title: Introduction to modified gravity: from the cosmic speedup problem to quantum gravity phenomenology.

Authors: Gonzalo J. Olmo

Journal-ref: Chapter in the book Aspects of Today's Cosmology, Edited by Antonio Alfonso-Faus, ISBN 978-953-307-626-3.

Abstract: These notes represent a summary of the introductory part of a course on modified gravity delivered at several Spanish Universities (Granada, Valencia, and Valladolid), at the University of Wisconsin-Milwaukee (WI, USA), and at the Karl-Franzens Universitaet (Graz, Austria) during the period 2008-2011. We begin with a discussion of the classical Newtonian framework and how special relativity boosted the interest on new theories of gravity. Then we focus on Nordstr\"om's scalar theories of gravity and their influence on Einstein's theory of general relativity. We comment on the meaning of the Einstein equivalence principle and its implications for the construction of alternative theories of gravity. We present the cosmic speedup problem and how $f(R)$ theories can be constrained attending to their weak-field behavior. We conclude by showing that Palatini $f(R)$ and $f(R,Q)$ theories can be used to address different aspects of quantum gravity phenomenology and singularity problems.

Preprint

Title: Palatini Approach Beyond Einstein's Gravity.

Authors: Gonzalo J. Olmo

Journal-ref: Proceedings of FFP12. To appear.

Abstract: I review recent results obtained for extensions of general relativity formulated within the Palatini formalism, an approach in which metric and connection are treated as independent geometrical entities. The peculiar dynamics of these theories, governed by second-order equations and having no new degrees of freedom, makes them specially suitable to address certain aspects of quantum gravity phenomenology, construct nonsingular bouncing cosmologies, and explore black hole interiors, which in the Reissner-Nordstr\"om case develop a compact core of finite density instead of a point-like singularity.

Preprint

Title: Nonsingular Black Holes

Authors: Gonzalo J. Olmo and Diego Rubiera-García

Journal-ref: Eur.Phys.J. C72 (2012) 2098.

Abstract: We find that if general relativity is modified at the Planck scale by a Ricci-squared term, electrically charged black holes may be nonsingular. These objects concentrate their mass in a microscopic sphere of radius $r_{core}\approx N_q^{1/2}l_P/3$, where $l_P$ is the Planck length and $N_q$ is the number of electric charges. The singularity is avoided if the mass of the object satisfies the condition $M_0^2\approx m_P^2 \alpha_{em}^{3/2} N_q^3/2$, where $m_P$ is the Planck mass and $\alpha_{em}$ is the fine-structure constant. For astrophysical black holes this amount of charge is so small that their external horizon almost coincides with their Schwarzschild radius. We work within a first-order (Palatini) approach.

Preprint

Title: Palatini approach to bouncing cosmologies and DSR-like effects.

Authors: Gonzalo J. Olmo

Journal-ref: J.Phys.Conf.Ser. 360 (2012) 012034.

Abstract: It is shown that a quadratic gravitational Lagrangian in the Palatini formulation is able to capture different aspects of quantum gravity phenomenology in a single framework. In particular, in this theory field excitations propagating with different energy-densities perceive different background metrics, a fundamental characteristic of the DSR and Rainbow Gravity approaches. This theory, however, avoids the so-called soccer ball problem. Also, the resulting isotropic and anisotropic cosmologies are free from the big bang singularity. This singularity avoidance occurs non-perturbatively and shares some similitudes with the effective dynamics of loop quantum cosmology.

Preprint

Title: Metric-Palatini gravity unifying local constraints and late-time cosmic acceleration

Authors: Tiberiu Harko, Tomi S. Koivisto, Francisco S.N. Lobo, Gonzalo J. Olmo

Journal-ref: Phys.Rev. D85 (2012) 084016.

Abstract: We present a novel approach to modified theories of gravity that consists of adding to the Einstein-Hilbert Lagrangian an f(R) term constructed a la Palatini. Using the respective dynamically equivalent scalar-tensor representation, we show that the theory can pass the Solar System observational constraints even if the scalar field is very light. This implies the existence of a long-range scalar field, which is able to modify the cosmological and galactic dynamics, but leaves the Solar System unaffected. We also verify the absence of instabilities in perturbations and provide explicit models which are consistent with local tests and lead to the late-time cosmic acceleration.

Preprint

Title: Palatini f(R) Black Holes in Nonlinear Electrodynamics.

Authors: Gonzalo J. Olmo, D. Rubiera-Garcia.

Journal-ref: Phys.Rev. D84 (2011) 124059.

Abstract: The electrically charged Born-Infeld black holes in the Palatini formalism for $f(R)$ theories are analyzed. Specifically we study those supported by a theory $f(R)=R\pm R^2/R_P$, where $R_P$ is Planck's curvature. These black holes only differ from their General Relativity counterparts very close to the center, but may give rise to different geometrical structures in terms of inner horizons. The nature and strength of the central singularities are also significantly affected. In particular, for the model $f(R)=R - R^2/R_P$ the singularity is shifted to a finite radius, $r_+$, and the Kretschmann scalar diverges only as $1/(r-r_+)^{2}$.

Preprint

Title: Remarks on the renormalization of primordial cosmological perturbations.

Authors: Ivan Agullo, Jose Navarro-Salas, Gonzalo J. Olmo, Leonard Parker

Journal-ref: Phys. Rev. D 84, 107304 (2011) .

Abstract: We briefly review the need to perform renormalization of inflationary perturbations to properly work out the physical power spectra. We also summarize the basis of (momentum-space) renormalization in curved spacetime and address several misconceptions found in recent literature on this subject.

Preprint

Title: Non-singular Universes a la Palatini

Authors: Gonzalo J. Olmo

Journal-ref: J.Phys.Conf.Ser.314, 012054 (2011) .

Abstract: It has recently been shown that f(R) theories formulated in the Palatini variational formalism are able to avoid the big bang singularity yielding instead a bouncing solution. The mechanism responsible for this behavior is similar to that observed in the effective dynamics of loop quantum cosmology and an f(R) theory exactly reproducing that dynamics has been found. I will show here that considering more general actions, with quadratic contributions of the Ricci tensor, results in a much richer phenomenology that yields bouncing solutions even in anisotropic (Bianchi I) scenarios. Some implications of these results are discussed.

Preprint

Title: Palatini Approach to Modified Gravity: f(R) Theories and Beyond

Authors: Gonzalo J. Olmo

Journal-ref: Int.J.Mod.Phys.D20, 413-462 (2011) .

Abstract: 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 phenomenological aspects related with dark matter/energy and quantum gravity.

Preprint

Title: Hamiltonian Formulation of Palatini f(R) theories a la Brans-Dicke.

Authors: Gonzalo J. Olmo and Hélios Sanchis-Alepuz

Journal-ref: Phys.Rev.D83, 104036 (2011) .

Abstract: We study the Hamiltonian formulation of f(R) theories of gravity both in metric and in Palatini formalism using their classical equivalence with Brans-Dicke theories with a non-trivial potential. The Palatini case, which corresponds to the w=-3/2 Brans-Dicke theory, requires special attention because of new constraints associated with the scalar field, which is non-dynamical. We derive, compare, and discuss the constraints and evolution equations for the ww=-3/2 and w\neq -3/2 cases. Based on the properties of the constraint and evolution equations, we find that, contrary to certain claims in the literature, the Cauchy problem for the w=-3/2 case is well-formulated and there is no reason to believe that it is not well-posed in general.

Preprint

Title: Palatini Actions and Quantum Gravity Phenomenology.

Authors: Gonzalo J. Olmo

Journal-ref: JCAP 10 (2011) 018 .

Abstract: We show that a quadratic gravitational Lagrangian in the Palatini formulation is able to capture different aspects of quantum gravity phenomenology in a single framework. In particular, we show that in this theory field excitations propagating with different energy-densities perceive different background metrics, which is a fundamental characteristic of the DSR and Rainbow Gravity approaches. Also, the resulting isotropic and anisotropic cosmologies are free from the big bang singularity. This singularity avoidance occurs non-perturbatively and shares some similitudes with the effective dynamics of loop quantum cosmology.

Preprint

Title: Acceleration radiation, transition probabilities, and trans-Planckian physics.

Authors: I. Agullo, J. Navarro-Salas, G.J. Olmo, L. Parker

Journal-ref: New J.Phys. 12, 095017(2010)

Abstract: An important question in the derivation of the acceleration radiation, which also arises in Hawking's derivation of black hole radiance, is the need to invoke trans-Planckian physics for the quantum field that originates the created quanta. We point out that this issue can be further clarified by reconsidering the analysis in terms of particle detectors, transition probabilities, and local two-point functions. By writing down separate expressions for the spontaneous- and induced-transition probabilities of a uniformly accelerated detector, we show that the bulk of the effect comes from the natural (non trans-Planckian) scale of the problem, which largely diminishes the importance of the trans-Planckian sector. This is so, at least, when trans-Planckian physics is defined in a Lorentz invariant way. This analysis also suggests how to define and estimate the role of trans-Planckian physics in the Hawking effect itself.

Preprint

Title: Hawking radiation by Kerr black holes and conformal symmetry.

Authors: Ivan Agullo, Jose Navarro-Salas, Gonzalo J. Olmo, Leonard Parker.

Journal-ref: Phys.Rev.Lett. 105, 211305 (2010).

Abstract: The exponential blueshift associated with the event horizon of a black hole makes conformal symmetry play a fundamental role in accounting for its thermal properties. Using a derivation based on two-point functions, we show that the spectrum of thermal radiation of scalar particles by Kerr (and Schwarzschild) black holes can be explicitly derived on the basis of a $2$-dimensional conformal symmetry arising in the wave equation near the horizon. This result reinforces the recently conjectured relation between Kerr geometry and a $2$-dimensional conformal field theory.

Preprint

Title: Isotropic and Anisotropic Bouncing Cosmologies in Palatini Gravity.

Authors: Carlos Barragan, Gonzalo J. Olmo.

Journal-ref: Phys.Rev. D82, 084015 (2010).

Abstract: We study isotropic and anisotropic (Bianchi I) cosmologies in Palatini $f(R)$ and $f(R,R_{\mu\nu}R^{\mu\nu})$ 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 $R+a R^2/R_P+R_{\mu\nu}R^{\mu\nu}/R_P$ 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 purely gravitational solution to the big bang singularity and anisotropy problems of general relativity without the need for exotic ($w>1$) sources of matter/energy.

Preprint

Title: Reply to "Comment on 'Insensitivity of Hawking radiation to an invariant Planck-scale cutoff' "

Authors: Ivan Agullo, Jose Navarro-Salas, Gonzalo J. Olmo, Leonard Parker.

Journal-ref: Phys.Rev. D81, 108502 (2010)

Abstract: We clarify the relationship between the conclusions of the previous Comment of A. Helfer [1] and that of our Brief Report [arXiv:0906.5315].

Preprint

Title: Inflation, Quantum Field Renormalization, and CMB Anisotropies.

Authors: Ivan Agullo, Jose Navarro-Salas, Gonzalo J. Olmo, Leonard Parker.

Journal-ref: Talk given in the 12th Marcel Grossman Meeting (Paris, July 2009). To appear in the proceedings.

Abstract: We point out that if quantum field renormalization is taken into account the predictions of slow-roll inflation for both the scalar and tensorial power spectra change significantly for wavelengths that today are at observable scales.

Preprint

Title: Inflation, Renormalization, and CMB Anisotropies.

Authors: Ivan Agullo, Jose Navarro-Salas, Gonzalo J. Olmo, Leonard Parker.

Journal-ref: J.Phys.Conf.Ser. 229, 012058 (2010).

Abstract: In single-field, slow-roll inflationary models, scalar and tensorial (Gaussian) perturbations are both characterized by a zero mean and a non-zero variance. In position space, the corresponding variance of those fields diverges in the ultraviolet. The requirement of a finite variance in position space forces its regularization via quantum field renormalization in an expanding universe. This has an important impact on the predicted scalar and tensorial power spectra for wavelengths that today are at observable scales. In particular, we find a non-trivial change in the consistency condition that relates the tensor-to-scalar ratio "r" to the spectral indices. For instance, an exact scale-invariant tensorial power spectrum, n_t=0, is now compatible with a non-zero ratio r= 0.12 +/- 0.06, which is forbidden by the standard prediction (r=-8n_t). Forthcoming observations of the influence of relic gravitational waves on the CMB will offer a non-trivial test of the new predictions.

Preprint

Title: Avoiding the Big Bang Singularity with Palatini f(R) Theories.

Authors: Carlos Barragan, Gonzalo J. Olmo, Helios Sanchis-Alepuz

Journal-ref: to appear in the Proceedings of 12th Marcel Grossmann Meeting, Paris (France)

Abstract: We show that there exist modified theories of gravity in which the metric satisfies second-order equations and in which the Big Bang singularity is replaced by a cosmic bounce without violating any energy condition. In fact, the bounce is possible even for presureless dust. We give a characterization of such theories, which are formulated in the Palatini formalism, and discuss their dynamics in the region near the bounce. We consider spatially flat and non-flat homogeneous and isotropic universes.

Preprint

Title: Enriched Phenomenology in Extended Palatini Theories

Authors: Gonzalo J. Olmo, Helios Sanchis-Alepuz, Swapnil Tripathi

Journal-ref: to appear in the Proceedings of 12th Marcel Grossmann Meeting, Paris (France)

Abstract: We show that extended theories of gravity with Lagrangian f(R,R_{\mu\nu}R^{\mu\nu}) in the Palatini formulation possess a phenomenology much richer than the simpler f(R) or f(R_{\mu\nu}R^{\mu\nu}) theories. In fact, we find that the scalars R and Q=R_{\mu\nu}R^{\mu\nu} can be written as algebraic functions of the energy density and pressure of the energy momentum tensor. In the simpler cases of f(R) or f(R_{\mu\nu}R^{\mu\nu}) theories, R and Q are just functions of the trace T of the energy-momentum tensor. As a result, in radiation dominated universes f(R) and f(R_{\mu\nu}R^{\mu\nu}) theories exhibit the same dynamics as general relativity with an effective cosmological constant. This is not the case of f(R,R_{\mu\nu}R^{\mu\nu}) models, in which R=R(\rho,P) and Q=Q(\rho,P) and, therefore, modified dynamics exists even for traceless sources.

Preprint

Title: Revising the observable consequences of slow-roll inflation.

Authors: Ivan Agullo, Jose Navarro-Salas, Gonzalo J. Olmo, Leonard Parker.

Journal-ref: Phys.Rev.D 81, 043514(2010)

Abstract: We study the generation of primordial perturbations in a (single-field) slow-roll inflationary universe. In momentum space, these (Gaussian) perturbations are characterized by a zero mean and a non-zero variance D²(k, t). However, in position space the variance diverges in the ultraviolet. The requirement of a finite variance in position space forces one to regularize D²(k, t). This can (and should) be achieved by proper renormalization in an expanding universe in a unique way. This affects the predicted scalar and tensorial power spectra (evaluated when the modes acquire classical properties) for wavelengths that today are at observable scales. As a consequence, the imprint of slow-roll inflation on the CMB anisotropies is significantly altered. We find a non-trivial change in the consistency condition that relates the tensor-to-scalar ratio r to the spectral indices. For instance, an exact scale-invariant tensorial power spectrum, n_t=0, is now compatible with a non-zero ratio $r\approx 0.12\pm0.06$, which is forbidden by the standard prediction (r=-8n_t). The influence of relic gravitational waves on the CMB may soon come within the range of planned measurements, offering a non-trivial test of the new predictions.

Preprint

Title: New Phenomenology for Palatini f(R) Theories: Non-singular Universes.

Authors: Gonzalo J. Olmo

Journal-ref: AIP proceedings series. "The Invisible Universe International Conference", Paris (France) June 29 - July 03, 2009.

Abstract: We study modified theories of gravity of the f(R) type in Palatini formalism. We first consider the stability of atoms when the Palatini gravitational interaction is taken into account in the derivation of the non-relativistic Schrodinger equation. We show that theories with infrared curvature corrections are ruled out by the mere existence of atoms. In particular, we carry out fully perturbative calculations that, for the first time, convincingly rule out the 1/R model of Carroll et al. in its Palatini version. We then study the Planck scale corrected quadratic model f(R)=R+R^2/R_P and show that it can avoid the big bang singularity for matter sources which satisfy all the energy conditions. We comment on the mechanisms that cure this singularity and point out that they are closely related to non- perturbative terms also present in the atomic Hamiltonian of infrared corrected models.

Preprint

Title: Inflation, quantum fields, and CMB anisotropies.

Authors: I.Agulló, J.Navarro-Salas, Gonzalo J. Olmo, Leonard Parker.

Journal-ref: Gen.Rel.Gravit.

Abstract: Inflationary cosmology has proved to be the most successful at predicting the properties of the anisotropies observed in the cosmic microwave background (CMB). In this essay we show that quantum field renormalization significantly influences the generation of primordial perturbations and hence the expected measurable imprint of cosmological inflation on the CMB. However, the new predictions remain in agreement with observation, and in fact favor the simplest forms of inflation. In the near future, observations of the influence of gravitational waves from the early universe on the CMB will test our new predictions.

Preprint

Title: Dynamical Aspects of Generalized Palatini Theories of Gravity.

Authors: Gonzalo J. Olmo, Helios Sanchis-Alepuz, Swapnil Tripathi

Journal-ref: Phys. Rev. D 80, 024013 (2009)

Abstract: We study the field equations of modified theories of gravity in which the lagrangian is a general function of the Ricci scalar and Ricci-squared terms in Palatini formalism. We show that the independent connection can be expressed as the Levi-Civita connection of an auxiliary metric which, in particular cases of interest, is related with the physical metric by means of a disformal transformation. This relation between physical and auxiliary metric boils down to a conformal transformation in the case of f(R) theories. We also show with explicit models that the inclusion of Ricci squared terms in the action can impose upper bounds on the accessible values of pressure and density, which might have important consequences for the early time cosmology and black hole formation scenarios. Our results indicate that the phenomenology of f(R_{ab}R^{ab}) theories is much richer than that of f(R) and f(R_{ab}R^{ab}) theories and that they also share some similarities with Bekenstein's relativistic theory of MOND.

Preprint

Title: Bouncing Cosmologies in Palatini f(R) Gravity

Authors: Carlos Barragan, Gonzalo J. Olmo, Helios Sanchis-Alepuz.

Journal-ref: Phys.Rev.D 80, 024016, (2009)

Abstract: We consider the early time cosmology of f(R) theories in Palatini formalism and study the conditions that guarantee the existence of homogeneous and isotropic models that avoid the Big Bang singularity. We show that for such models the Big Bang singularity can be replaced by a cosmic bounce without violating any energy condition. In fact, the bounce is possible even for pressureless dust. We give a characterization of such models and discuss their dynamics in the region near the bounce. We also find that power-law lagrangians with a finite number of terms may lead to non-singular universes, which contrasts with the infinite-series Palatini f(R) lagrangian that one needs to fully capture the effective dynamics of Loop Quantum Cosmology. We argue that these models could also avoid the formation of singularities during stellar gravitational collapse.

Preprint

Title: Insensitivity of Hawking radiation to an invariant Planck- scale cutoff.

Authors: Ivan Agullo, Jose Navarro-Salas, Gonzalo J. Olmo, Leonard Parker

Journal-ref: To appear in Phys.Rev.D

Abstract: A disturbing aspect of Hawking's derivation of black hole radiance is the need to invoke extreme conditions for the quantum field that originates the emitted quanta. It is widely argued that the derivation requires the validity of the conventional relativistic field theory to arbitrarily high, trans-Planckian scales. We stress in this note that this is not necessarily the case if the question is presented in a covariant way. We point out that Hawking radiation is immediately robust against an invariant Planck-scale cutoff. This important feature of Hawking radiation is relevant for a quantum gravity theory that preserves, in some way, the Lorentz symmetry.

Preprint

Title: Revising the predictions of inflation for the cosmic microwave background anisotropies.

Authors: Ivan Agullo, Jose Navarro-Salas, Gonzalo J. Olmo, Leonard Parker

Journal-ref:

Abstract: Inflationary cosmology predicts that, due to quantum effects, small density perturbations are generated in the very early universe with a nearly "scale-free" spectrum. The detection and analysis of anisotropies in the cosmic microwave background has spectacularly confirmed this prediction. Moreover, inflation also predicts the creation of primordial gravitational waves, which still remain undetectable. Forthcoming high-precision measurements of the cosmic microwave background may measure effects of relic gravitational waves, and this will be crucial to test the inflationary paradigm and strongly constrain inflationary models. Therefore, it is particularly important to scrutinize, from all points of view, the quantitative predictions of inflation. In this work we point out that if quantum field renormalization is taken into account, the predictions of slow- roll inflation for both the scalar and tensorial power spectrum change significantly. This leads, in particular, to a change in the consistency condition that relates the tensor-to-scalar amplitude ratio r with spectral indices. Moreover, a reexamination of the chaotic potentials \phi^2, \phi^4, shows that both fall well inside the 68% confidence level region in the plane (n_s, r) of the five-year WMAP data. In contrast, the standard predictions rule out the potential \phi^4. The alternative predictions presented in this work may soon come within the range of measurement of near-future experiments.

Preprint

Title: Reexamination of Polytropic Spheres in Palatini f(R) Gravity.

Authors: Gonzalo J. Olmo

Journal-ref: Phys.Rev.D 78, 104026 (2008)

Abstract: We investigate spherically symmetric, static matter configurations with polytropic equation of state for a class of f(R) models in Palatini formalism and show that the surface singularities recently reported in the literature are not physical in the case of Planck scale modified lagrangians. In such cases, they are just an artifact of the idealized equation of state used. In fact, we show that for the models f(R)=R\pm\lambda R^2, with \lambda on the order of the Planck length squared, the presence of a single electron in the Universe would be enough to cure all stellar singularities of this type. From our analysis it also follows that the stellar structure derived from these lagrangians is virtually undistinguishable from that corresponding to General Relativity. For ultraviolet corrected models far from the Planck scale, however, the surface singularities may indeed arise in the region of validity of the polytropic equation of state. This fact can be used to place constraints on the parameters of particular models.

Preprint

Title: The role of Planck scale in black hole radiance.

Authors: Iván Agulló, José Navarro-Salas, Gonzalo J. Olmo, and Leonard Parker.

Journal-ref: Int.J.Mod.Phys.D17:489-494,2008.

Abstract:Lorentz invariance plays a pivotal role in the derivation of the Hawking effect, which crucially requires an integration in arbitrarily small distances or, equivalently, in unbounded energies. New physics at the Planck scale could, therefore, potentially modify the emission spectrum. We show, however, that the kinematic invariance can be deformed in such a way that the thermal spectrum remains insensitive to trans-Planckian physics.

No preprint available

Title: Effective Action for Loop Quantum Cosmology a la Palatini

Authors: Gonzalo J. Olmo, Parampreet Singh

Journal-ref: JCAP01 (2009)030

Abstract: The resolution of the big bang singularity in loop quantum cosmology can be described by quantum gravitational modifications to the Friedman dynamics without introducing any new degrees of freedom. A challenging question is to construct a covariant effective action able to reproduce that new physics emergent at the Planck scale. By enlarging our scope to the realm of non-metric theories, we show that apparent tensions with conventional approaches can be overcome. We provide an algorithm to construct an effective action for loop quantum cosmology in the Palatini framework and obtain an action which involves an infinite series in the scalar curvature of the independent connection. This effective action successfully captures non-local quantum geometric effects and the non-singular bounce at the Planck scale and leads to general relativity at low curvatures.

Preprint

Title: Reexamination of the Power Spectrum in de Sitter Inflation.

Authors: Ivan Agullo, Jose Navarro-Salas, Gonzalo J. Olmo, Leonard Parker

Journal-ref: Phys.Rev.Lett. 101,171301(2008)

Abstract: We find that the amplitude of quantum fluctuations of the invariant de Sitter vacuum coincides exactly with that of the vacuum of a comoving observer for a massless scalar (inflaton) field. We propose redefining the actual physical power spectrum as the difference between the amplitudes of the above vacua. An inertial particle detector continues to observe the Gibbons-Hawking temperature. However, although the resulting power spectrum is still scale-free, its amplitude can be drastically reduced since now, instead of the Hubble's scale at the inflationary period, it is determined by the square of the mass of the inflaton fluctuation field.

Preprint

Title: Two-point functions with an invariant Planck scale and thermal effects

Authors: Ivan Agullo, Jose Navarro-Salas, Gonzalo J. Olmo, Leonard Parker

Journal-ref: Phys.Rev.D77,124032, 2008.

Abstract: Nonlinear deformations of relativistic symmetries at the Planck scale are usually addressed in terms of modified dispersion relations. We explore here an alternative route by directly deforming the two-point functions of an underlying field theory. The proposed deformations depend on a length parameter (Planck length) and preserve the basic symmetries of the corresponding theory. We also study the physical consequences implied by these modifications at the Planck scale by analyzing the response function of an accelerated detector in Minkowski space, an inertial one in de Sitter space, and also in a black hole spacetime.

Preprint

Title: Hydrogen atom in Palatini theories of gravity

Authors: Gonzalo J. Olmo

Journal-ref: Phys.Rev.D77,084021, 2008

Abstract: We study the effects that the gravitational interaction of $f(R)$ theories of gravity in Palatini formalism has on the stationary states of the Hydrogen atom. We show that the role of gravity in this system is very important for lagrangians $f(R)$ with terms that grow at low curvatures, which have been proposed to explain the accelerated expansion rate of the universe. We find that new gravitationally induced terms in the atomic Hamiltonian generate a strong backreaction that is incompatible with the very existence of bound states. In fact, in the 1/R model, Hydrogen disintegrates in less than two hours. The universe that we observe is, therefore, incompatible with that kind of gravitational interaction. Lagrangians with high curvature corrections do not lead to such instabilities.

Preprint

Title: Acceleration radiation and the Planck scale

Authors: Iván Agulló, José Navarro-Salas, Gonzalo J. Olmo, and Leonard Parker.

Journal-ref: Phys.Rev.D77,104034, 2008

Abstract: A uniformly accelerating observer perceives the Minkowski vacuum state as a thermal bath of radiation. We point out that this field-theory effect can be derived, for any dimension higher than two, without actually invoking very high energy physics. This supports the view that this phenomenon is robust against Planck-scale physics and, therefore, should be compatible with any underlying microscopic theory.

Preprint

Title:Short distances, black holes, and TeV gravity.

Authors: Iván Agulló, José Navarro-Salas, Gonzalo J. Olmo

Journal-ref: Proceedings of the 11th Marcel Grossman Meeting

Abstract:The Hawking effect can be rederived in terms of two- point functions and in such a way that it makes it possible to estimate, within the conventional semiclassical theory, the contribution of ultrashort distances at I^+ to the Planckian spectrum. Thermality is preserved for black holes with \kappa l_P much smaller than 1. However, deviations from the Planckian spectrum can be found for mini black holes in TeV gravity scenarios, even before reaching the Planck phase.

Preprint

Title: Limit to General Relativity in f(R) theories of gravity

Authors: Gonzalo J. Olmo

Journal-ref: Phys.Rev.D. 75, 023511 (2007)

Abstract:We discuss two aspects of f(R) theories of gravity in metric formalism. We first study the reasons to introduce a scalar- tensor representation for these theories and the behavior of this representation in the limit to General Relativity, f(R) going to R. We find that the scalar-tensor representation is well behaved even in this limit. Then we work out the exact equations for spherically symmetric sources using the original f(R) representation, solve the linearized equations, and compare our results with recent calculations of the literature. We observe that the linearized solutions are strongly affected by the cosmic evolution, which makes very unlikely that the cosmic speedup be due to f(R) models with correcting terms relevant at low curvatures.

Preprint - Published version

Title: Violation of the Equivalence Principle in Modified Theories of Gravity

Authors: Gonzalo J. Olmo - See this article in the news.

Journal-ref: Phys. Rev. Lett. 98, 061101 (2007)

Abstract:We show that the metric in f(R) theories of gravity in Palatini formalism can be solved as the product of a rank-two tensor times a scalar function which is very sensitive to the local energy- momentum densities. This local dependence of the metric generates new gravitationally-induced microscopic interactions, which eventually would lead to self-accelerated test body trajectories. These facts make very unlikely the viability of Palatini f(R) models designed to change the late-time cosmic evolution.

Preprint - Published version

Title:Short-distance contribution to the spectrum of Hawking radiation

Authors: I. Agullo, J. Navarro-Salas, Gonzalo J. Olmo, Leonard Parker

Journal-ref: Phys.Rev.D 76,044018(2007)

Abstract:The Hawking effect can be rederived in terms of two- point functions and in such a way that it makes it possible to estimate, within the conventional semiclassical theory, the contribution of ultrashort distances to the Planckian spectrum. For Schwarzschild black holes of three solar masses the analysis shows that Hawking radiation is very robust up to frequencies of 96 T_H or 270 T_H for bosons and fermions, respectively. For primordial black holes (with masses around 10^{15} g) these frequencies turn out to be of order 52T_H and 142 T_H. Only at these frequencies and above do we find that the contribution of Planck distances is of order of the total spectrum itself. Below this scale, the contribution of ultrashort distances to the spectrum is negligible. This suggests that only above these frequencies could an underlying quantum theory of gravity potentially predict significant deviations from Hawking's semiclassical result

Preprint

Title:Black hole radiance, short distances, and TeV gravity

Authors: Iván Agulló, José Navarro-Salas, Gonzalo J. Olmo

Journal-ref: Phys.Rev.Lett. 97 (2006) 041302

Abstract:Using a derivation of black hole radiance in terms of two-point functions one can provide a quantitative estimate of the contribution of short distances to the spectrum. Thermality is preserved for black holes with \kappa l_P much smaller than 1. However, deviations from the Planckian spectrum can be found for mini black holes in TeV gravity scenarios, even before reaching the Planck phase.

Preprint - Published version

Title:Semiclassical zero-temperature corrections to Schwarzschild spacetime and holography

Authors: A. Fabbri, S. Farese, J. Navarro-Salas, Gonzalo J. Olmo, H. Sanchis-Alepuz

Journal-ref: Phys.Rev. D73 (2006) 104023

Abstract: Motivated by the quest for black holes in AdS braneworlds, and in particular by the holographic conjecture relating 5D classical bulk solutions with 4D quantum corrected ones, we numerically solve the semiclassical Einstein equations (backreaction equations) with matter fields in the (zero temperature) Boulware vacuum state. In the absence of an exact analytical expression for T_mn in four dimensions we work within the s-wave approximation. Our results show that the quantum corrected solution is very similar to Schwarzschild till very close to the horizon, but then a bouncing surface for the radial function appears which prevents the formation of an event horizon. We also analyze the behavior of the geometry beyond the bounce, where a curvature singularity arises. In the dual theory, this indicates that the corresponding 5D static classical braneworld solution is not a black hole but rather a naked singularity.

Preprint - Published version

Title: Static quantum corrections to the Schwarzschild spacetime

Authors: A. Fabbri, S. Farese, J. Navarro-Salas, Gonzalo J. Olmo, H. Sanchis-Alepuz

Journal-ref: J.Phys.Conf.Ser.33:457-462,2006

Abstract: We study static quantum corrections of the Schwarzschild metric in the Boulware vacuum state. Due to the absence of a complete analytic expression for the full semiclassical Einstein equations we approach the problem by considering the s-wave approximation and solve numerically the associated backreaction equations. The solution, including quantum effects due to pure vacuum polarization, is similar to the classical Schwarzschild solution up to the vicinity of the classical horizon. However, the radial function has a minimum at a time-like surface close to the location of the classical event horizon. There the g_{00} component of the metric reaches a very small but non-zero value. The analysis unravels how a curvature singularity emerges beyond this bouncing point. We briefly discuss the physical consequences of these results by extrapolating them to a dynamical collapsing scenario.

Preprint - Published version

Title: Post-Newtonian constraints on f(R) cosmologies in metric and Palatini formalism

Authors: Gonzalo J. Olmo

Journal-ref: Phys.Rev.D72, 083505, (2005)

Abstract: We compute the complete post-Newtonian limit of both the metric and Palatini formulations of f(R) gravities using a scalar- tensor representation. By comparing the predictions of these theories with laboratory and solar system experiments, we find a set of inequalities that any lagrangian f(R) must satisfy. The constraints imposed by those inequalities allow us to find explicit bounds to the possible nonlinear terms of the lagrangian. We conclude that in both formalisms the lagrangian f(R) must be almost linear in R and that corrections that grow at low curvatures are incompatible with observations. This result shows that modifications of gravity at very low cosmic densities cannot be responsible for the observed cosmic speed-up.

Prep-0505135 - Prep-0505136 - Published version

Title:The gravity lagrangian according to solar system experiments

Authors: Gonzalo J. Olmo

Journal-ref: Phys.Rev.Lett. 95 (2005) 261102

Abstract: In this work we show that the gravity lagrangian f(R) at relatively low curvatures in both metric and Palatini formalisms is a bounded function that can only depart from the linearity within the limits defined by well known functions. We obtain those functions by analysing a set of inequalities that any f(R) theory must satisfy in order to be compatible with laboratory and solar system observational constraints. This result implies that the recently suggested f(R) gravity theories with nonlinear terms that dominate at low curvatures are incompatible with observations and, therefore, cannot represent a valid mechanism to justify the cosmic speed-up.

Preprint - Published version

Title: Nonlinear Gravity Theories in the Metric and Palatini Formalisms

Authors: Gonzalo J. Olmo and William Komp

Journal-ref:

Abstract: We study nonlinear gravity theories in both the metric and the Palatini (metric-affine) formalisms. The nonlinear character of the gravity lagrangian in the metric formalism causes the appearance of a scalar source of matter in Einstein's equations that can be interpreted as a quintessence field. However, in the Palatini case no new energy sources appear, though the equations of motion get modified in such a way that usual matter can lead to repulsive gravity at very low densities. Thus, the Palatini formalism could provide a mechanism to explain the recent acceleration of the universe without the necessity of dark energy sources. We also show that in contrast to the metric formalism where only the Einstein frame should be considered as physical, the Palatini formalism allows both the Einstein and the Jordan frames to be physically acceptable.

Preprint

Title: Particles and energy fluxes from a CFT perspective

Authors: A. Fabbri, J. Navarro-Salas, Gonzalo J. Olmo

Journal-ref: Phys.Rev. D70 (2004) 064022

Abstract: We analyze the creation of particles in two dimensions under the action of conformal transformations. We focus our attention on Möbius transformations and compare the usual approach, based on the Bogolubov coefficients, with an alternative but equivalent viewpoint based on correlation functions. In the latter approach the absence of particle production under full Möbius transformations is manifest. Moreover, we give examples, using the moving-mirror analogy, to illustrate the close relation between the production of quanta and energy.

Preprint - Published version

Title: Late-time correlators in semiclassical particle-black- hole scattering

Authors: A. Fabbri, D.J. Navarro, J. Navarro-Salas, Gonzalo J. Olmo

Journal-ref: Phys.Rev.D68,041502(R), (2003)

Abstract: We analyze the quantum corrected geometry and radiation in the scattering of extremal black holes by low-energy neutral matter. We point out the fact that the correlators of local observables inside the horizon are the same as those of the vacuum. Outside the horizon the correlators at late times are much bigger than those of the (thermal) case obtained neglecting the back reaction. This suggests that the corrected Hawking radiation could be compatible with unitarity.

Preprint - Published version

Title: A note on Möbius transformations and Bogolubov coefficients

Authors: A. Fabbri, J. Navarro-Salas and Gonzalo J. Olmo

Journal-ref: Proceedings of "Symmetries in Gravity and Field Theory", Workshop in honour of Prof. J. A. de Azcarraga. June 9-11, 2003. Salamanca (Spain)

Abstract: We analyze the creation of scalar massless particles in two dimensions under the action of conformal transformations. We focus our attention to Möbius transformation and clarify an apparent tension between the results obtained with the Bogolubov coefficients and those obtained within the conformal field theory approach.

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