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In this work, we explore wormhole geometries in a recently proposed modified gravity theory arising from a non-conservative gravitational theory, tentatively denoted action-dependent Lagrangian theories. The generalized gravitational field equation essentially depends on a background four-vector $\lambda^\mu$, that plays the role of a coupling parameter associated with the dependence of the gravitational Lagrangian upon the action, and may generically depend on the spacetime coordinates. Considering wormhole configurations, by using "Buchdahl coordinates", we find that the four-vector is given by $\lambda_{\mu}=\left(0,0,\lambda_{\theta},0\right)$, and that the spacetime geometry is severely restricted by the condition $g_{tt}g_{uu}=-1$, where $u$ is the radial coordinate. We find a plethora of specific asymptotically flat, symmetric and asymmetric, solutions with power law choices for the function $\lambda$, by generalizing the Ellis-Bronnikov solutions and the recently proposed black bounce geometries, amongst others. We show that these compact objects possess a far richer geometrical structure than their general relativistic counterparts., Comment: 11 pages, 5 figures, V2: version accepted for publication in PRD

K. G. Arun et al., The Laser Interferometer Space Antenna (LISA) has the potential to reveal wonders about the fundamental theory of nature at play in the extreme gravity regime, where the gravitational interaction is both strong and dynamical. In this white paper, the Fundamental Physics Working Group of the LISA Consortium summarizes the current topics in fundamental physics where LISA observations of gravitational waves can be expected to provide key input. We provide the briefest of reviews to then delineate avenues for future research directions and to discuss connections between this working group, other working groups and the consortium work package teams. These connections must be developed for LISA to live up to its science potential in these areas., E. Berti is supported by NSF Grants No. PHY-1912550 and AST-2006538, NASA ATP Grants No. 17-ATP17-0225 and 19-ATP19-0051, NSF-XSEDE Grant No. PHY-090003, and NSF Grant PHY-20043. D. Blas is supported by a ‘Ayuda Beatriz Galindo Senior’ from the Spanish ‘Ministerio de Universidades’, grant BG20/00228. IFAE is partially funded by the CERCA program of the Generalitat de Catalunya. The research leading of to these results has received funding from the Spanish Ministry of Science and Innovation (PID2020-115845GB-I00/AEI/10.13039/501100011033). K. Clough is supported by funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 693024). A. Cárdenas-Avendaño acknowledges funding from the Fundación Universitaria Konrad Lorenz (Project 5INV1) and from Will and Kacie Snellings. M. Crisostomi and E. Barausse are supported by the European Union’s H2020 ERC Consolidator Grant “GRavity from Astrophysical to Microscopic Scales” (Grant No. GRAMS-815673). P. Fleury received the support of a fellowship from “la Caixa” Foundation (ID 100010434). The fellowship code is LCF/BQ/PI19/11690018. C. Herdeiro thanks the support of the Center for Research and Development in Mathematics and Applications (CIDMA) through the Portuguese Foundation for Science and Technology (FCT - Fundação para a Ciência e a Tecnologia), references UIDB/04106/2020 and UIDP/04106/2020, the projects PTDC/FIS-OUT/28407/2017, CERN/FIS-PAR/0027/2019, PTDC/FIS-AST/3041/2020 and the European Union’s Horizon 2020 research and innovation (RISE) programme H2020-MSCA-RISE-2017 Grant No. FunFiCO-777740. P. Pani and E. Maggio acknowledge financial support provided under the European Union’s H2020 ERC, Starting Grant agreement no. DarkGRA–757480, and under the MIUR PRIN and FARE programmes (GW-NEXT, CUP: B84I20000100001), and support from the Amaldi Research Center funded by the MIUR program “Dipartimento di Eccellenza” (CUP: B81I18001170001). N.Frusciante was supported by Fundação para a Ciência e a Tecnologia (FCT) through the research grants UIDB/04434/2020, UIDP/04434/2020, PTDC/FIS-OUT/29048/2017, CERN/FIS-PAR/0037/2019, the FCT project “CosmoTests—Cosmological tests of gravity theories beyond General Relativity” with ref. number CEECIND/00017/2018 and the FCT project “BEYLA –BEYond LAmbda” with ref. number PTDC/FIS-AST/0054/2021. L.Lombriser was supported by a Swiss National Science Foundation Professorship grant (No. 170547). S.N. acknowledges support from the Alexander von Humboldt Foundation. D.N. acknowledges support from the NSF Grant No. PHY-2011784. R.B. acknowledges financial support from FCT – Fundação para a Ciência e a Tecnologia, I.P., under the Scientific Employment Stimulus - Individual Call - 2020.00470.CEECIND. V. Paschalidis acknowledges support from NSF Grant PHY-1912619 and NASA Grant 80NSSC20K1542 to the University of Arizona. B.S.S. is supported by NSF grants No. AST-2006384 and PHY-2012083. C.F.S. is supported by contracts ESP2017-90084-P and PID2019-106515GB-I00/AEI/10.13039/501100011033 (Spanish Ministry of Science and Innovation) and 2017-SGR-1469 (AGAUR, Generalitat de Catalunya). T. P. S. acknowledges partial support from the STFC Consolidated Grant No. ST/P000703/1. M. Ruiz acknowledges support from NASA Grant 80NSSC17K0070 to the University of Illinois at Urbana-Champaign. I.D. Saltas is supported by the Czech Science Foundation GAČR, Grant No. 21-16583M. N. Stergioulas is supported by the ESA Prodex grant PEA:4000132310 “LISA Stochastic Signals Analysis Pipeline”. F.V. acknowledges partial support from CNES. K.Y. acknowledges support from NSF Grant PHY-1806776, NASA Grant 80NSSC20K0523, a Sloan Foundation Research Fellowship and the Owens Family Foundation. K.Y. would like to also acknowledge support by the COST Action GWverse CA16104 and JSPS KAKENHI Grants No. JP17H06358. N. Yunes acknowledges support from NASA Grants No. NNX16AB98G, 80NSSC17M0041 and 80NSSC18K1352, NSF Award No. 1759615, and the Simons Foundation through MPS Award Number 896696. D.D. acknowledge financial support via an Emmy Noether Research Group funded by the German Research Foundation (DFG) under grant no. DO 1771/1-1.

Redshift drift is the phenomenon whereby the observed redshift between an emitter and observer comoving with the Hubble flow in an expanding FLRW universe will slowly evolve -- on a timescale comparable to the Hubble time. There are nevertheless serious astrometric proposals for actually observing this effect. We shall however pursue a more abstract theoretical goal, and perform a general cosmographic analysis of this effect, eschewing (for now) dynamical considerations in favour of purely kinematic symmetry considerations and Taylor series expansions based on FLRW spacetimes. We shall develop various exact results and series expansions for the redshift drift (and its derivative) in terms of the present day Hubble, deceleration, jerk, snap, crackle, and pop parameters, as well as the present day redshift of the source. In particular, potential observation of this redshift drift effect is intimately related to the universe exhibiting a nonzero deceleration parameter., Comment: V1: 24 pages. V2: 25 pages, 2 references added, no physics changes; V3: Now 24 Pages; this version closely resembles the final published version. (Reformatted; some discussion added; several references added.)

In this work, we seek a cosmological mechanism that may define the sign of the effective gravitational coupling constant, {\em G}. To this end, we consider general scalar-tensor gravity theories as they provide the field theory natural framework for the variation of the gravitational coupling. We find that models with a quadratic potential naturally stabilize the value of {\em G} into the positive branch of the evolution and further, that de Sitter inflation and a relaxation to General Relativity is easily attained., Comment: 16 pages, 16 figures

The TOV equation appears as the relativistic counterpart of the classical condition for hydrostatic equilibrium. In the present work we aim at showing that a generalised TOV equation also characterises the equilibrium of models endowed with other symmetries besides spherical. We apply the dual null formalism to spacetimes with two dimensional spherical, planar and hyperbolic symmetries with a perfect fluid as the source. We also assume a Killing vector field orthogonal to the surfaces of symmetry, which gives us static solutions, in the timelike Killing field case, and homogeneous dynamical solutions in the case the Killing field is spacelike. In order to treat equally all the aforementioned cases, we discuss the definition of a quasi-local energy for the spacetimes with planar and hyperbolic foliations, since the Hawking-Hayward definition only applies to compact foliations. After this procedure, we are able to translate our geometrical formalism to the fluid dynamics language in a unified way, to find the generalized TOV equation, for the three cases when the solution is static, and to obtain the evolution equation, for the homogeneous spacetime cases. Remarkably, we show that the static solutions which are not spherically symmetric violate the weak energy condition (WEC). We have also shown that the counterpart of the TOV equation for the spatially homogeneous models is just the familiar equation \r{ho} + P = 0, defining a cosmological constant-type behaviour, both in the hyperbolic and spherical cases. This implies a violation of the strong energy condition in both cases, added to the above mentioned violation of the weak energy condition in the hyperbolic case. We illustrate our unified treatment obtaining analogs of Schwarzschild interior solution, for an incompressible fluid $\rho = \rho_0$ constant., Comment: 10 pp, 1 fig

The Birkhoff theorem is a well-known result in general relativity and it is used in many applications. However, its most general version, due to Bona, is almost unknown and presented in a form less accessible to the relativist and cosmologist community. Moreover, many wield it mistakenly as a simple transposition of Newton's iron sphere theorem. In the present work, we propose a modern, dual null, presentation --- useful in many explorations, including black holes --- of the theorem that renders accessible most of the results of Bona's version. In addition, we discuss the fluid contents admissible for the application of the theorem, beyond a vacuum, and we demonstrate how the formalism greatly simplifies solving the dynamical equations and allows one to express the solution as a power expansion in $r$. We present a family of solutions that share the properties predicted by the Birkhoff theorem and discuss the existence of trapped and antitrapped regions. The formalism manifestly shows how the type of region --- trapped or untrapped --- determines the character of the Killing vector., 10 pages. The version published on PRD

Adopting the Landau-Lifshiftz method of classical fluctuations we determine the statistical average strength of the fluctuations of the energy flux on the apparent horizon of a homogeneous and isotropic universe described by Einstein gravity. We find that the fluctuations increase with the temperature of the horizon and decrease with its area, in accordance with the features of systems where gravity can be neglected. %is absent. We further find, on the one hand, that the fluctuations vanish in the cosmological constant dominated de Sitter expansion, and, on the other hand, that the domination of phantom fields is excluded. The reasonableness of the results we have obtained lend support to the view that the universe behaves as a normal thermodynamic system., Comment: 4 pages, no figures. Key words: Mathematical cosmology, statistical physics. It matches published version

This work studies the behavior of entropy in recent cosmological models that start with an initial de Sitter expansion phase, go through the conventional radiation and matter dominated eras to be followed by a final de Sitter epoch. In spite of their seemingly similarities (observationally they are close to the Λ-CDM model), different models deeply differ in their physics. The second law of thermodynamics encapsulates the underlying microscopic, statistical description, and hence we investigate it in the present work. Our study reveals that the entropy of the apparent horizon plus that of matter and radiation inside it, increases and is a concave function of the scale factor. Thus thermodynamic equilibrium is approached in the last de Sitter era, and this class of models is thermodynamically correct. Cosmological models that do not approach equilibrium appear in conflict with the second law of thermodynamics. (Based on Mimoso & Pavon 2013)

A common feature in the thermodynamic analysis of homogeneous and isotropic world models is the assumption that the temperature of the fluids inside the cosmic horizon (including dark energy) coincides with the temperature of the latter, whether it be either the event or the apparent horizon. We examine up to what extent this assumption may be justified, given that these temperatures evolve under different time-temperature laws. We argue that while radiation cannot reach thermal equilibrium with the horizon, non-relativistic matter may, and dark energy might though only approximately., Comment: 4 pages, two columns, no figures, matches version published in the Physical Review

In this work we revisit the definition of Matter Trapping Surfaces (MTS) introduced in previous investigations and show how it can be expressed in the so-called dual null formalism developed for Trapping Horizons (TH). With the aim of unifying both approaches, we construct a 2+2 threading from the 1+3 flow, and thus isolate one prefered spatial direction, that allows straightforward translation into a dual nul subbasis, and to deduce the geometric apparatus that follows. We remain as general as possible, reverting to spherical symmetry only when needed, and express the MTS conditions in terms of 2-expansion of the flow, then in purely geometric form of the dual null expansions. The Raychadhuri equations that describe both MTS and TH are written and interpreted using the previously defined gTOV (generalized Tolman-Oppenheimer-Volkov) functional introduced in previous work. Further using the Misner-Sharp mass and its previous perfect fluid definition, we relate the spatial 2-expansion to the fluid pressure, density and acceleration. The Raychaudhuri equations also allows us to define the MTS dynamic condition with first order differentials so the MTS conditions are now shown to be all first order differentials. This unified formalism allows one to realise that the MTS can only exist in normal regions, and so it can exist only between black hole horizons and cosmological horizons. Finally we obtain a relation yielding the sign, on a TH, of the non-vanishing null expansion which determines the nature of the TH from fluid content, and flow characteristics. The 2+2 unified formalism here investigated thus proves a powerful tool to reveal, in the future extensions, more of the very rich and subtle relations between MTS and TH., 10pp 1 fig. corrected for equation labels, cross listing corrected

In this work we present a phase-space analysis of the cosmological relaxation of generalized gravity theories where the gravitational constant G varies towards general relativity. We assess the interplay of the two main mechanisms that yield general relativity as the cosmological attractor: (i) the vanishing of the coupling function α(φ), and (ii) the existence of a minimum of the scalar field potential. The latter mechanism is shown to supersede the first. We classify the fixed points associated to different types of potentials and discuss the late time self-similar solutions that arise when the scalar field potential exhibits an asymptotic exponential behaviour from the viewpoint of the relaxation mechanism.

We consider the possibility of a gravitationally induced particle production through the mechanism of a nonminimal curvature-matter coupling. An interesting feature of this gravitational theory is that the divergence of the energy-momentum tensor is nonzero. As a first step in our study we reformulate the model in terms of an equivalent scalar-tensor theory, with two arbitrary potentials. By using the formalism of open thermodynamic systems, we interpret the energy balance equations in this gravitational theory from a thermodynamic point of view, as describing irreversible matter creation processes. The particle number creation rates, the creation pressure, and the entropy production rates are explicitly obtained as functions of the scalar field and its potentials, as well as of the matter Lagrangian. The temperature evolution laws of the newly created particles are also obtained. The cosmological implications of the model are briefly investigated, and it is shown that the late-time cosmic acceleration may be due to particle creation processes. Furthermore, it is also shown that due to the curvature--matter coupling, during the cosmological evolution a large amount of comoving entropy is also produced., Comment: 15 pages; accepted for publication in the European Physical Journal C

We consider generalized energy conditions in modified theories of gravity by taking into account the further degrees of freedom related to scalar fields and curvature invariants. The latter are usually recast as generalized {\it geometrical fluids} that have different meanings with respect to the standard matter fluids generally adopted as sources of the field equations. More specifically, in modified gravity the curvature terms are grouped in a tensor $H^{ab}$ and a coupling $g(\Psi^i)$ that can be reorganized in effective Einstein field equations, as corrections to the energy-momentum tensor of matter. The formal validity of such inequalities does not assure some basic requirements such as the attractive nature of gravity, so that the energy conditions have to be considered in a wider sense., Comment: 4 pages. V2: 5 pages; version to appear in Physics Letters B. V3: typo in Eq. (4) corrected

We investigate the relaxation of general scalar-tensor gravity theories towards general relativity. We extend Damour and Nordtvedt's work [Phys. Rev. Lett. 70 (1993) 2217; Phys. Rev. D 48 (1993) 3436] by including a cosmological potential. We find that Einstein's gravity is indeed a cosmological attractor both for isotropic and anisotropic universes, and that the universe exhibits inflationary expansion during the relaxation process.

We investigate the conditions under which general scalar-tensor gravity theories relax towards General Relativity. We extend the work of Damour and Nordtvedt [2] by studying the effects of the inclusion of a cosmological potential term. When the universe is either radiation dominated or vacuum, we find that Einstein’s gravity is indeed a cosmological attractor and, also, that the universe exhibits inflationary expansion. This latter feature provides another striking argument in favour of the inflationary paradigm, which in the present setting arises without the intervention of the usual inflaton field.

Theories of physics can be considered viable if the initial value problem and the energy conditions are formulated self-consistently. The former allow a uniquely determined dynamical evolution of the system, and the latter guarantee that causality is preserved and that "plausible" physical sources have been considered. In this work, we consider the further degrees of freedom related to curvature invariants and scalar fields in Extended Theories of Gravity (ETG). These new degrees of freedom can be recast as effective perfect fluids that carry different meanings with respect to the standard matter fluids generally adopted as sources of the field equations. It is thus somewhat misleading to apply the standard general relativistic energy conditions to this effective energy-momentum, as the latter contains the matter content and a geometrical quantity, which arises from the ETG considered. Here, we explore this subtlety, extending on previous work, in particular, to cases with the contracted Bianchi identities with diffeomorphism invariance and to cases with generalized explicit curvature-matter couplings, which imply the non-conservation of the energy-momentum tensor. Furthermore, we apply the analysis to specific ETGs, such as scalar-tensor gravity, $f(R)$ gravity and modified Gauss-Bonnet gravity. Interesting results appear such as matter that may exhibit unusual thermodynamical features, for instance, and gravity that retains its attractive character in the presence of negative pressures; or alternatively, we verify that repulsive gravity may occur for standard matter., Comment: 12 pages, version accepted for publication in Phys.Rev.D

We report here on the results of Brax et al. (Phys. Rev. D 85:123516, 2012) where we consider the dynamics of a 3-brane embedded in an extra-dimensional Tolman–Bondi Universe where the origin of space plays a special role. We study the mirage cosmology on the probe brane, resulting in an inhomogeneous and anisotropic four dimensional cosmology where the origin of space is also special. We show that the induced geometry, which is initially inhomogeneous and anisotropic, converges to an isotropic and homogeneous Friedmann–Lemaitre 4d space-time around the origin of the spatial geometry. For example, when a 3-brane is embedded in a 5d matter dominated model, the 4d dynamics around the origin converge to a Friedmann–Lemaitre Universe in a radiation dominated epoch. We analyse this isotropisation process and show that it is a late time attractor.

We investigate spherically symmetric spacetimes with an anisotropic fluid and discuss the existence and stability of a dividing shell separating expanding and collapsing regions. We resort to a 3 + 1 splitting and obtain gauge invariant conditions relating intrinsic spacetimes quantities to properties of the matter source. We find that the dividing shell is defined by a generalization of the Tolman- Oppenheimer-Volkoff equilibrium condition. The latter establishes a balance between the pressure gradients, both isotropic and anisotropic, and the strength of the fields induced by the Misner- Sharp mass inside the separating shell and by the pressure fluxes. This defines a local equilibrium condition, but conveys also a non-local character given the definition of the Misner-Sharp mass. By the same token, it is also a generalized thermodynamical equation of state as usually interpreted for the perfect fluid case, which now has the novel feature of involving both the isotropic and the anisotropic stress. We have cast the governing equations in terms of local, gauge invariant quantities which are revealing of the role played by the anisotropic pressures and inhomogeneous electric part of the Weyl tensor. We analyse a particular solution with dust and radiation that provides an illustration of our conditions. In addition, our gauge invariant formalism not only encompasses the cracking process from Herrera and coworkers but also reveals transparently the interplay and importance of the shear and of the anisotropic stresses., The authors wish to thank the anonymous referee for many enlightening comments and suggestions and Jose Fernando Pascual-Sanchez for helpful discussions. M. Le D. also wishes to thank Michele Fontanini, Daniel Guariento and Elcio Abdalla for helpful discussions. The work of M. Le D. has been supported by CSIC (JAEDoc072), CICYT (FPA2006-05807) in Spain and FAPESP (2011/24089-5) in Brazil. F.C.M. thanks CMAT, Univ. Minho, for support through FEDER Funds COMPETE and FCT Projects No. Est-C/MAT/UI0013/2011, No. PTDC/MAT/108921/2008 and No. CERN/FP/123609/2011. M. Le D. and J. P. M. acknowledge the CAAUL's Project No. PEst-OE/FIS/UI2751/2011. J. P. M. also wishes to thank FCT for Grants No. CERN/FP/123615/2011 and No. CERN/FP/123618/2011.

This brief report studies the behavior of entropy in two recent models of cosmic evolution by J.A.S. Lima, S. Basilakos, and F.E.M. Costa [Phys. Rev. D \underline{86}, 103534 (2012)], and J. A. S. Lima, S. Basilakos, and J. Sol\'{a} [arXiv:1209.2802]. Both start with an initial de Sitter expansion, go through the conventional radiation and matter dominated eras to be followed by a final and everlasting de Sitter expansion. In spite of their outward similarities (from the observational viewpoint they are arbitrary close to the conventional $\Lambda$CDM model), they deeply differ in the physics behind them. Our study reveals that in both cases the universe approaches thermodynamic equilibrium in the last de Sitter era in the sense that the entropy of the apparent horizon plus that of matter and radiation inside it increases and is concave. Accordingly, they are consistent with thermodynamics. Cosmological models that do not approach equilibrium at the last phase of their evolution appear in conflict with the second law of thermodynamics., Comment: 12 pages, no figures. Key words: Early and late universe, thermodynamics. This version matches the published one in Phys. Rev. D

In this paper we consider spherically symmetric general fluids with heat flux, motivated by causal thermodynamics, and give the appropriate set of conditions that define separating shells defining the divide between expansion and collapse. To do so we add the new requirement that heat flux and its evolution vanish at the separating surface. We extend previous works with a fully nonlinear analysis in the 1+3 splitting, and present gauge-invariant results. The definition of the separating surface is inspired by the conservation of the Misner-Sharp mass, and is obtained by generalizing the Tolman-Oppenheimer-Volkoff equilibrium and turnaround conditions. We emphasize the nonlocal character of these conditions as found in previous works and discuss connections to the phenomena of spacetime cracking and thermal peeling., Comment: 5pp. Updated to match published version

We investigate spherically symmetric spacetimes with an anisotropic fluid and discuss the existence and stability of a dividing shell separating expanding and collapsing regions. We find that the dividing shell is defined by a relation between the pressure gradients, both isotropic and anisotropic, and the strength of the fields induced by the Misner-Sharpe mass inside the separating shell and by the pressure fluxes. This balance is a generalization of the Tolman-Oppenheimer- Volkoff equilibrium condition which defines a local equilibrium condition, but conveys also a non- local character given the definition of the Misner-Sharpe mass. We present a particular solution with dust and radiation that provides an illustration of our results., Comment: 4pp Towards New Paradigms: Proceeding Of The Spanish Relativity Meeting 2011. AIP Conference Proceedings, Volume 1458, pp. 487-490 (2012). Published in AIP Conf.Proc. 1458 (2011) 487-490

In the search for an explanation for the current acceleration of the Universe, scalar fields are the most simple and useful tools to build models of dark energy. This field, however, must in principle couple with the rest of the world and not necessarily in the same way to different particles or fluids. We provide the most complete dynamical system analysis to date, consisting of a canonical scalar field conformally and disformally coupled to both dust and radiation. We perform a detailed study of the existence and stability conditions of the systems and comment on constraints imposed on the disformal coupling from Big-Bang Nucleosynthesis and given current limits on the variation of the fine-structure constant., Comment: 45 pages, 11 figures

We explore the dynamics and evolution of the Universe at early and late times, focusing on both dark energy and extended gravity models and their astrophysical and cosmological consequences. Modified theories of gravity not only provide an alternative explanation for the recent expansion history of the universe, but they also offer a paradigm fundamentally distinct from the simplest dark energy models of cosmic acceleration. In this review, we perform a detailed theoretical and phenomenological analysis of different modified gravity models and investigate their consistency. We also consider the cosmological implications of well motivated physical models of the early universe with a particular emphasis on inflation and topological defects. Astrophysical and cosmological tests over a wide range of scales, from the solar system to the observable horizon, severely restrict the allowed models of the Universe. Here, we review several observational probes -- including gravitational lensing, galaxy clusters, cosmic microwave background temperature and polarization, supernova and baryon acoustic oscillations measurements -- and their relevance in constraining our cosmological description of the Universe., 94 pages, 14 figures. Review paper accepted for publication in a Special Issue of Symmetry. "Symmetry: Feature Papers 2016". V2: Matches published version, now 79 pages (new format)

A method is investigated which enables exact solutions to be found for k=0 Friedmann cosmological models with a perfect fluid satisfying the equation of states p=(γ-1)ρ, where γ is constant and 0≤γ≤2, in scalar-tensor gravity theories with an arbitrary form for the gravitational coupling function ω(φ), which defines the theory. A number of explicit solutions are investigated for p=0 universes and inflationary universes, including those for theories in which ω(φ) has a power-law dependence on the scalar field φ. When p=-ρ new varieties of inflation arise in which a(t)∝tnexp(H0tm).

New exact solutions of Einstein's gravity coupled to a self-interacting conformal scalar field are derived in this work. Our approach extends a solution-generating technique originally introduced by Bekenstein for massless conformal scalar fields. Solutions are obtained for a Friedmann-Robertson-Walker geometry both for the cases of zero and non-zero curvatures, and a variety of interesting features are found. It is shown that one class of solutions tends asymptotically to a power-law inflationary behaviour $S(t)\sim t^p$ with $p>1$, while another class exhibits a late time approach to the $S(t)\sim t$ behaviour of the coasting models. Bouncing models which avoid an initial singularity are also obtained. A general discussion of the asymptotic behaviour and of the possibility of occurrence of inflation is provided., Latex, 27 pages plus 16 figures (not included, available from the authors upon request) DFFCUL-94-01-01

We present a brief summary of the results of Charters et al. [1] where a simple model of a massive inflation field ϕ coupled to another scalar filed χ with interaction term g 2ϕ2χ2 for the first stage of preheating, and we give a full description of the dynamics of the χ field modes, including the behaviour of the phase, in terms of the iteration of a simple family of circle maps.

Scalar-tensor (ST) gravity theories provide an appropriate theoretical framework for the variation of Newton’s fundamental constant, conveyed by the dynamics of a scalar-field non-minimally coupled to the space-time geometry. The experimental scrutiny of scalar-tensor gravity theories has led to a detailed analysis of their post-newtonian features, and is encapsulated into the so-called parametrised post-newtonian formalism (PPN). Of course this approach can only be applied whenever there is a newtonian limit, and the latter is related to the GR solution that is generalized by a given ST solution under consideration. This procedure thus assumes two hypothesis: On the one hand, that there should be a weak field limit of the GR solution; On the other hand that the latter corresponds to the limit case of given ST solution. In the present work we consider a ST solution with negative spatial curvature. It generalizes a general relativistic solution known as being of a degenerate class (A) for its unusual properties. In particular, the GR solution does not exhibit the usual weak field limit in the region where the gravitational field is static. The absence of a weak field limit for the hyperbolic GR solution means that such limit is also absent for comparison with the ST solution, and thus one cannot barely apply the PPN formalism. We therefore analyse the properties of the hyperbolic ST solution, and discuss the question o defining a generalised newtonian limit both for the GR solution and for the purpose of contrasting it with the ST solution. This contributes a basic framework to build up a parametrised pseudo-newtonian formalism adequate to test ST negatively curved space-times.

Scalar field models have been a focal point in cosmology during the last two decades or so. They play a central role in inflationary models, they arise in modified gravity theories that extend Einstein’s General Relativity (GR) which are, often, quantum motivated, and, recently, they have been put forward as a dark component of the universe. Here we analyse their dynamics in the framework of isotropic cosmologies presenting an unified approach that encompasses models both in Einstein’s GR and more general metric gravity theories. We perform a qualitative analysis of the major dynamical features of these models, discussing the existence of asymptotic regimes and their connection to a classification of the scalar fields potentials and couplings. A special interest is devoted to the interplay between scalar fields and matter which gives rise to scaling behaviour.

The gravitational wave equation for a spatially flat Friedmann-Robertson-Walker universe is derived in the context of scalar-tensor theories of gravity, which have the Brans-Dicke theory as a particular case. This equation is solved for several cosmological scenarios, including the expansions governed by the Nariai as well as the Gurevich-Finkelstein-Ruban solutions of Brans-Dicke theory and for a new set of exact solutions of other scalar-tensor theories. The amplification of gravitational waves is studied in comparison to what happens in the general relativistic case. It is shown how the coupling with the scalar field changes the scales defining very large and very small wave numbers, and consequently the value of the amplification coefficient. It is found that very small values for the coupling parameter could lead to amplification of subhorizon waves. The creation of the corresponding high-frequency gravitons is explained as a response to the rapid time variation of the gravitational "constant," which can occur near the singularity in some models. It is also shown that there could be amplification of waves even in a radiation-dominated universe in some cases, because the wave equation is not conformally invariant, except for the case of Nariai's solution in the Brans-Dicke theory.

A class of orthogonal, spatially homogeneous shear-free cosmological models with an imperfect liquid matter content is considered. It is shown that, for these models, the anisotropic stresses are related to the anisotropic curvature of the spatial hypersurfaces through the electric part of the Weyl tensor. This creates a counterbalance effect which has important consequences for the evolution of the cosmological models. Such features are discussed, and, as an application, some eternally anisotropic models with an imperfect fluid stress tensor which exhibit FRW-like behaviour are given.

In considering alternative higher-order gravity theories, one is liable to be motivated in pursuing models consistent and inspired by several candidates of a fundamental theory of quantum gravity. Indeed, motivations from string/M-theory predict that scalar field couplings with the Gauss-Bonnet invariant, G, are important in the appearance of non-singular early time cosmologies. In this work, we discuss the viability of an interesting alternative gravitational theory, namely, modified Gauss-Bonnet gravity or f(G) gravity. We consider specific realistic forms of f(G) analyzed in the literature that account for the late-time cosmic acceleration and that have been found to cure the finite-time future singularities present in the dark energy models. We present the general inequalities imposed by the energy conditions and use the recent estimated values of the Hubble, deceleration, jerk and snap parameters to examine the viability of the above-mentioned forms of f(G) imposed by the weak energy condition., 9 pages, 8 figures. V2: minor additions and corrections; to appear in PRD

Traversable wormhole are primarily useful as "gedanken-experiments" and as a theoretician's probe of the foundations of general relativity. In this work, we analyse the possibility of having tunnels in a hyperbolic spacetime. We obtain exact solutions of static and pseudo-spherically symmetric spacetime tunnels by adding exotic matter to a vacuum solution referred to as a degenerate solution of class A. The physical properties and characteristics of these intriguing solutions are explored, and through the mathematics of embedding it is shown that particular constraints are placed on the shape function, that differ significantly from the Morris-Thorne wormhole. In particular, it is shown that the energy density is always negative and the radial pressure is positive, at the throat, contrary to the Morris-Thorne counterpart. Specific solutions are also presented by considering several equations of state, and by imposing restricted choices for the shape function or the redshift function., Comment: 7 pages, 1 figure. V2: 8 pages, changes in title and throughout the text; to appear in PRD

We investigate a mechanism that generates the exact solutions of scalar field cosmologies in a unified way. The procedure investigated here permits to recover allmost all known solutions, and allows one to derive new solutions as well. In particular, we derive and discuss one novel solution defined in terms of the Lambert function. The solutions are organized in a classification which depends on the choice of a generating function which we have denoted by $x(\phi)$ that reflects the underlying thermodynamics of the model. We also analyse and discuss the existence of form invariances and dualities between solutions. A general way of defining the latter in an appropriate fashion for scalar fields is put forward., Comment: 6 figures, 30 pages

We investigate spherically symmetric perfect-fluid spacetimes and discuss the existence and stability of a dividing shell separating expanding and collapsing regions. We perform a 3+1 splitting and obtain gauge invariant conditions relating the intrinsic spatial curvature of the shells to the Misner-Sharp mass and to a function of the pressure that we introduce and that generalizes the Tolman-Oppenheimer-Volkoff equilibrium condition. We find that surfaces fulfilling those two conditions fit, locally, the requirements of a dividing shell and we argue that cosmological initial conditions should allow its global validity. We analyze the particular cases of the Lema\^itre-Tolman-Bondi dust models with a cosmological constant as an example of a cold dark matter model with a cosmological constant (\Lambda-CDM) and its generalization to contain a central perfect-fluid core. These models provide simple, but physically interesting illustrations of our results., Comment: 17pp, 9 figures, accepted by PRD

We investigate a static solution with an hyperbolic nature, characterised by a pseudo-spherical foliation of space. This space-time metric can be perceived as an anti-Schwarzschild solution, and exhibits repulsive features. It belongs to the class of static vacuum solutions termed "a degenerate static solution of class A". In the present work we review its fundamental features, discuss the existence of generalised wormholes, and derive its extension to scalar-tensor gravity theories in general., 3 pages, contribution to the proceedings of the Spanish Relativity Meeting-ERE2009

5 pages, 4 figures.-- PACS: 98.80.-k, 98.80.Cq, 98.80.Jk, 95.30.Sf , 04.40.Nr, 04.20.Jb, We discuss the existence of a dividing shell separating expanding and collapsing regions in spherically symmetric solutions with pressure. We obtain gauge invariant conditions relating not only the intrinsic spatial curvature of the shells to the ADM mass, but also a function of the pressure which we introduce that generalises the Tolman-Oppenheimer-Volkoff equilibrium condition, in the framework of a 3+1 spacetime splitting. We consider the particular case of a Lemaître-Tolman- Bondi dust models with a cosmological constant (a L-CDM model) as an example of our results., The work of MLeD is supported by CSIC (Spain) under the contract JAEDoc072, with partial support from CICYT project FPA2006-05807, at the IFT, Universidad Autonoma de Madrid, Spain, and was also supported by FCT (Portugal) under the grant SFRH/BD/16630/2004, at the CFTC, Lisbon University, Portugal. Financial support from the Foundation of the University of Lisbon and the Portuguese Foundation for Science and Technology (FCT) under contract POCTI/ISFL/2/618 is also gratefully acknowledged. FCM is supported by CMAT, Univ. Minho, and FCT project PTDC/MAT/108921/2008.

We present here an extended abstract of the results derived in [1], We study the decay of the inflaton field to another scalar field χ in the parametric resonance preheating mechanism. We consider the presence of several simultaneous couplings between the fields. We show that the contribution for the χ field energy density of the higher harmonic is a small fraction of that of the fundamental frequency, and so the presence of a finite number of higher harmonics has limited cosmological implications

We investigate spherically symmetric solutions with pressure and discuss the existence of a dividing shell separating expanding and collapsing regions. We perform a 3+1 splitting and obtain gauge invariant conditions relating not only the intrinsic spatial curvature of the shells to the ADM mass, but also a function of the pressure which we introduce that generalises the Tolman-Oppenheimer-Volkoff equilibrium condition. We consider the particular case of a Lema\^itre-Tolman dust models with a cosmological constant (a $\Lambda$-CDM model) as an example of our results., Comment: 4pp, 1fig, AIP Conference: Proc. XXXI Spanish Relat. Meeting, ERE08, Salamanca, Spain, 15-19 Sept., 2008 Septembre, Salamanca, Espagne

We address the problem of studying the decay of the inflaton field $\phi$ to another scalar field $\chi$ through parametric resonance in the case of a coupling that involves several decay modes. This amounts to the presence of extra harmonic terms in the perturbation of the $\chi$ field dynamics. For the case of two frequencies we compute the geometry of the resonance regions, which is significantly altered due to the presence of non-cuspidal resonance regions associated to higher harmonics and to the emergence of instability `pockets'. We discuss the effect of this change in the efficiency of the energy transfer process for the simplest case of a coupling given by a combination of the two interaction terms of homogeneous degree usually considered in the literature. We find that the presence of higher harmonics has limited cosmological implications., Comment: 14 pages, 4 figures Added references. Corrected typos

We study the model of a massive inflaton field $\phi$ coupled to another scalar filed $\chi$ with interaction term $g^2\phi^2\chi^2$ for the first stage of preheating. We obtain the the behavior of the phase in terms of the iteration of a simple family of circle maps. When expansion of the universe is taken into account the qualitative behavior of the phase and growth number evolution is reminiscent of the behavior found in the case without expansion., Comment: 4 pages, 4 figures, LaTeX; submitted to the Proceedings of Eleventh Marcel Grossmann Meeting

We address the problem of the energy conditions in modified gravity taking into account the additional degrees of freedom related to scalar fields and curvature invariants. The latter are usually interpreted as generalized {\it geometrical fluids} that differ in meaning with respect to the matter fluids generally considered as sources of the field equations. In extended gravity theories the curvature terms are encapsulated in a tensor $H^{ab}$ and a coupling $g(\Psi^i)$ that can be recast as effective Einstein field equations, with corrections to the energy-momentum tensor of matter. The formal validity of standard energy inequalities does not assure basic requirements such as the attractive nature of gravity, so we argue that the energy conditions have to be considered in a wider sense., Comment: Sumbitted to the Proceedings of the Spanish Relativity Meeting- ERE2014"Amost 100 years after Einstein revolution", to appear in the Journal of Physics: Conference Series

The decay of the inflaton into radiation and particles during the slow-roll suggests that these may interact with each other and that the latter may also decay into subproducts before inflation is completed. As a consequence, the fluid is no longer perfect and a non-negligible bulk viscosity necessarily sets in. We write the corresponding equations as an autonomous system and study the asymptotic behavior, the conditions for the existence of scaling solutions, and show that the late time effect of fluid dissipation alleviates the depletion of matter and increases the duration of inflation., Comment: 3 pages, uses World Sci. style; submitted to the Proceedings of Eleventh Marcel Grossmann Meeting