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We study the effects of dark energy (DE) anisotropic stress on features of the matter power spectrum (PS). We employ the Parametrized Post-Friedmannian (PPF) formalism to emulate an effective DE, and model its anisotropic stress properties through a two-parameter equation that governs its overall amplitude ($g_0$) and transition scale ($c_g$). For the background cosmology, we consider different equations of state to model DE including a constant $w_0$ parameter, and models that provide thawing (CPL) and freezing (nCPL) behaviors. We first constrain these parameters by using the Pantheon, BAO, $H_0$ and CMB Planck data. Then, we analyze the role played by these parameters in the linear PS. In order for the anisotropic stress not to provoke deviations larger than $10\%$ and $5\%$ with respect to the $��$CDM PS at $k \sim 0.01 \,h/\text{Mpc}$, the parameters have to be in the range $-0.30< g_0 < 0.32$, $0 \leq c_g^2 < 0.01$ and $-0.15 < g_0 < 0.16$, $0 \leq c_g^2 < 0.01$, respectively. Additionally, we compute the leading nonlinear corrections to the PS using standard perturbation theory in real and redshift space, showing that the differences with respect to the $��$CDM are enhanced, especially for the quadrupole and hexadecapole RSD multipoles., 19 pages, 13 figures, 1 table

A hundred years ago, two British expeditions measured the deflection of starlight by the sun's gravitational field, confirming the prediction made by Einstein's General theory of Relativity. One hundred years later many physicists around the world are involved in studying the consequences and use as a research tool, of the deflection of light by gravitational fields, a discipline that today receives the generic name of Gravitational Lensing. The present review aims to commemorate the centenary of Einstein's Eclipse expeditions by presenting a historical perspective of the development and milestones on gravitational light bending, covering from early XIX century speculations, to its current use as an important research tool in astronomy and cosmology., 45 pages, 26 figures, Feature Papers 2019 - Gravitational Physics

We present a formalism to compute Lagrangian displacement fields for a wide range of cosmologies in the context of perturbation theory up to third order. We emphasize the case of theories with scale dependent gravitational strengths, such as chameleons, but our formalism can be accommodated to other modified gravity theories. In the non-linear regime two qualitative features arise. One, as is well known, is that nonlinearities lead to a screening of the force mediated by the scalar field. The second is a consequence of the transformation of the Klein-Gordon equation from Eulerian to Lagrangian coordinates, producing frame-lagging terms that are important especially at large scales, and if not considered, the theory does not reduce to the $\Lambda$CDM model in that limit. We apply our formalism to compute the 1-loop power spectrum and the correlation function in $f(R)$ gravity by using different resummation schemes. We further discuss the IR divergences of these formalisms., Comment: 32 pages, 10 figures. v2: CLPT scheme added, IR divergences discussed. v3: Matches published version

We explore ways to obtain the very existence of a space-time metric from an action principle that does not refer to it a priori. Although there are reasons to believe that only a non-local theory can viably achieve this goal, we investigate here local theories that start with Schroedinger's purely affine theory [21], where he gave reasons to set the metric proportional to the Ricci curvature aposteriori. When we leave the context of unified field theory, and we couple the non-gravitational matter using some weak equivalence principle, we can show that the propagation of shock waves does not define a lightcone when the purely affine theory is local and avoids the explicit use of the Ricci tensor in realizing the weak equivalence principle. When the Ricci tensor is substituted for the metric, the equations seem to have only a very limited set of solutions. This backs the conviction that viable purely affine theories have to be non-local., 13 pages

In this work we extend the perturbation theory for modified gravity (MG) in two main aspects. First, the construction of matter overdensities from Lagrangian displacement fields is shown to hold in a general framework, allowing us to find Standard Perturbation Theory (SPT) kernels from known Lagrangian Perturbation Theory (LPT) kernels. We then develop a theory of biased tracers for generalized cosmologies, extending already existing formalisms for $\Lambda$CDM. We present the correlation function in Convolution-LPT and the power spectrum in SPT for $\Lambda$CDM, $f(R)$ Hu-Sawicky, and DGP braneworld models. Our formalism can be applied to many generalized cosmologies and to facilitate it, we are making public a code to compute these statistics. We further study the relaxation of bias with the use of a simple model and of excursion set theory, showing that in general the bias parameters have smaller values in MG than in General Relativity., Comment: 38 pages, 8 figures. v2: matches the published version

A family of potential--density pairs has been found for spherical halos and bulges of galaxies in the Newtonian limit of scalar--tensor theories of gravity. The scalar field is described by a Klein--Gordon equation with a source that is coupled to the standard Poisson equation of Newtonian gravity. The net gravitational force is given by two contributions: the standard Newtonian potential plus a term stemming from massive scalar fields. General solutions have been found for spherical systems. In particular, we compute potential--density pairs of spherical galactic systems, and some other astrophysical quantities that are relevant to generating initial conditions for spherical galaxy simulations., Comment: Paper accepted for publication in MNRAS, with four figures

We review the hydrodynamics of the dark sector components in Cosmology. For this purpose we use the approach of Newtonian gravitational instability, and thereafter we add corrections to arrive to a full relativistic description. In Cosmology and Astrophysics, it is usual to decompose the dark sector into two species, dark matter and dark energy. We will use instead a unified approach by describing a single unified dark fluid with very simple assumptions, namely that the dark fluid is barotropic and that its sound speed vanishes.

Using galactic rotation curves, we test a -quantum motivated- gravity model that at large distances modifies the Newtonian potential when spherical symmetry is considered. In this model one adds a Rindler acceleration term to the rotation curves of disk galaxies. Here we consider a standard and a power-law generalization of the Rindler modified Newtonian potential that are hypothesized to play the role of dark matter in galaxies. The new, universal acceleration has to be -phenomenologically- determined. Our galactic model includes the mass of the integrated gas and stars for which we consider a free mass model. We test the model by fitting rotation curves of thirty galaxies that has been employed to test other alternative gravity models. We find that the Rindler parameters do not perform a suitable fit to the rotation curves in comparison to the Burkert dark matter profile, but the models achieve a similar fit as the NFW's profile does. However, the computed parameters of the Rindler gravity show some spread, posing the model to be unable to consistently explain the observed rotation curves., Comment: 7 pages, a few figures and tables are added as supplementary material

It is shown some exact solutions in the Brans-Dicke (BD) theory for a Bianchi V metric having the property of inflationary expansion, graceful exit, and asymptotic evolution to a Friedmann-Robertson-Walker (FRW) open model. It is remarkable that an inflationary behaviour can occur, even without a cosmological potential or constant. However, the horizon and flatness problems cannot be solve within the standard BD theory because the inflationary period is severely restricted by the value of the BD parameter $\omega$., Comment: 28 pages, 6 figuras

We discuss the dynamics of anisotropic Bianchitype IX models in Jordan-Brans-Dicke cosmological theoryrendering the evolution of a universe model with closedspace near its beginning before inflation sets in. This paper displays how, when writtenin terms of reduced variables, the field equations allowstraightforward partial integration. The mean expansionH, the scalar field, and the three scale factors aregiven in terms of the volume expansion.

We review the role of fluids in cosmology by first introducing them in General Relativity and then by applying them to a FRW model of the Universe. We describe how relativistic and non-relativistic components evolve in the background dynamics.We also introduce scalar fields to show that they are able to yield an inflationary dynamics at very early times (inflation) and late times (quintessence). Then, we proceed to study the thermodynamical properties of the fluids and, lastly, its perturbed kinematics. We make emphasis on the constrictions of parameters by recent cosmological probes.

Dark matter and dark energy are essential in the description of the late Universe, since at least the epoch of equality. On the other hand, the inflation is also necessary and demands a "dark" component, usually associated to a scalar field that dominated the dynamics and kinematics in the very early Universe. Yet, these three dark components of standard model of cosmology are independent from each other, although there are alternative models that pursue to achieve a triple unification, or at least a double. In the present work we present an update of two models that we have considered in recent years. The first is the "dark fluid" model in which dark matter and dark energy are the same thing, achieving a double unification with specific properties that exactly emulate the standard model of cosmology, given the dark degeneracy that exists in the LCDM model. The second model is given by a single F(X) scalar field Lagrangian, with which one is able to model the whole cosmological dynamics, from inflation to today, representing a triple unification model. We highlight the main properties of these models, as well as we test them against known cosmological probes., Comment: 20 pages, 5 figures, 1 table. arXiv admin note: substantial text overlap with arXiv:1108.2457

Recently a new -quantum motivated- theory of gravity has been proposed that modifies the standard Newtonian potential at large distances when spherical symmetry is considered. Accordingly, Newtonian gravity is altered by adding an extra Rindler acceleration term that has to be phenomenologically determined. Here we consider a standard and a power-law generalization of the Rindler modified Newtonian potential. The new terms in the gravitational potential are hypothesized to play the role of dark matter in galaxies. Our galactic model includes the mass of the integrated gas, and stars for which we consider three stellar mass functions (Kroupa, diet-Salpeter, and free mass model). We test this idea by fitting rotation curves of seventeen low surface brightness galaxies from The HI Nearby Galaxy Survey (THINGS). We find that the Rindler parameters do not perform a suitable fit to the rotation curves in comparison to standard dark matter profiles (Navarro-Frenk-White and Burkert) and, in addition, the computed parameters of the Rindler gravity show a high spread, posing the model as a nonacceptable alternative to dark matter., 21 pages, 4 figures, 7 tables. V2 matches the Phys. Rev. D version in which we added some discussions

We analyze the phase space of a particular unified model of dark matter, dark energy, and inflation that we recently studied in [Phys. Rev. D 83, 063502 (2011)] whose Lagrangian is of the form L(X,phi) = F(X) - V(phi). We show that this model possesses a large set of initial conditions consistent with a successful cosmological model in which an inflationary phase is possible, followed by a matter era to end with dark energy domination. In order to understand the success of the model, we study the general features that unified dark matter (UDM) models should comply and then we analyze some particular models and find their constrictions., 9 pages, 1 figure, v2 clarified discussions and formulae to match the accepted version to appear in the proceedings of "IX Taller DGFM-SMF"

We summarize our studies on the determination of the mass of the dark matter halo, based on observations of rotation curves of test particles or of the gravitational lensing. As we show, it is not uncommon that some studies on the nature of dark matter include extra assumptions, some even on the very nature of the dark matter, what we want to determine!, and that bias the studies and the results obtained from the observation and, in some cases, imply an inconsistent system altogether., 12 pages, 2 figures

We study some properties of the dark degeneracy, which is the fact that what we measure in gravitational experiments is the energy momentum tensor of the total dark sector, and any split into components (as in dark matter and dark energy) is arbitrary. In fact, just one dark fluid is necessary to obtain exactly the same cosmological and astrophysical phenomenology as the LCDM model. We work explicitly the first order perturbation theory and show that beyond the linear order the dark degeneracy is preserved under some general assumptions. Then, we construct the dark fluid from a collection of interacting fluids. Finally, we try to break the degeneracy with a general class of couplings to baryonic matter. Nonetheless, we show that these interactions can also be understood in the context of the LCDM model as between dark matter and baryons. For this last investigation we choose two independent parameterizations for the interactions, one inspired in electromagnetism and the other in Chameleon theories. Then, we constrain them with a joint analysis of CMB and Supernovae observational data., 15 pages, 9 figures, Version 2: Extended discussion of Sec. IV B and some references added

We study a unification model for dark energy, dark matter, and inflation with a single scalar field with non canonical kinetic term. In this model the kinetic term of the Lagrangian accounts for the dark matter and dark energy, and at early epochs a quadratic potential accounts for slow roll inflation. The present work is an extension to the work by Bose and Majumdar [1] with a more general kinetic term that was proposed by Chimento in [2]. We demonstrate that the model is viable at the background and linear perturbation levels., Comment: 8 pages, 2 figures. Minor changes to text and formulae, and added 3 references to match the published version in Phys. Rev. D

This is a brief review of the standard model of cosmology. We first introduce the FRW models and their flat solutions for energy fluids playing an important role in the dynamics at different epochs. We then introduce different cosmological lengths and some of their applications. The later part is dedicated to the physical processes and concepts necessary to understand the early and very early Universe and observations of it., 25 pages, 2 figures, v2: a typo corrected

The dynamics of the production of relative high frequency gravitational waves by astrophysical events taking place within the galaxies in the cosmological context can be well represented by a phenomenological description of the generating processes through a “radiation energy profile” that contains two adjustable parameters. This profile gives a relation between the total pressure and energy density of the matter generating gravitational radiation together with the “waves” themselves, both treated as ordinary hydrodynamic fluids. The resulting cosmological models then represent, in a descriptive way only, universes filled with two interacting fluids: on the one hand gravitational radiation, and the matter which emits it but does not reabsorb it, on the other. It is shown that the dynamic effects of the model can be significant, even if the conversion rate of matter into gravitational radiation is relatively small.

We present a scenario in which a scalar field dark energy is coupled to the trace of the energy momentum tensor of the baryonic matter fields. In the slow-roll regime, this interaction could give rise to the cosmological features of dark matter. We work out the cosmological background solutions and fit the parameters of the model using the Union 2 supernovae data set. Then, we develop the cosmological perturbations up to linear order, and we find that the perturbed variables have an acceptable behavior, in particular the density contrast of baryonic matter grows similar to that in the $\Lambda$CDM model for a suitable choice of the strength parameter of the coupling., Comment: 10 pages, 8 figures, in this version small typos are corrected and it matches the published version in Phys. Rev. D15, January 2011

Attractor solutions that give dynamical reasons for dark energy to act like the cosmological constant, or behavior close to it, are interesting possibilities to explain cosmic acceleration. Coupling the scalar field to matter or to gravity enlarges the dynamical behavior; we consider both couplings together, which can ameliorate some problems for each individually. Such theories have also been proposed in a Higgs-like fashion to induce gravity and unify dark energy and dark matter origins. We explore restrictions on such theories due to their dynamical behavior compared to observations of the cosmic expansion. Quartic potentials in particular have viable stability properties and asymptotically approach general relativity., We gratefully acknowledge a UC-MEXUS-CONACYT Visiting Fellowship for JLCC to spend a sabbatical at Berkeley. JLCC thanks the Berkeley Center for Cosmological Physics for hospitality and CONACYT for grant No. 84133-F. This work has been supported in part by the Director, Office of Science, Office of High Energy Physics, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231, and the World Class University grant R32-2009-000-10130-0 through the National Research Foundation, Ministry of Education, Science and Technology of Korea.

There are two observations of galaxies that can offer some insight into the nature of the dark matter (DM), namely the rotation curves and the gravitational lensing. While the first one can be studied using the Newtonian limit, the second one is completely relativistic. Each one separately can not determine the nature of DM, but both together give us key information about this open problem. In this work we use a static and spherically symmetric metric to model the DM halo in a galaxy or in a galaxy cluster. The metric contains two free functions, one associated with the distribution of mass and the other one with the gravitational potential. We use galactic, typical rotation curves to univocally determine the kinematics of the halos. We compute separately the mass functions for a perfect fluid and a scalar field, and demonstrate that both models can be fitted to the observations, though with different masses. We then employ lensing to discriminate between these models. This procedure represents a test of models using two measurements: rotation curves and lensing., 5 pages, 2 figures, accepted in Phys. Rev. D

The space-space field equations of the Jordan Brans-Dicke theory describing a spatially homogeneous vacuum spacetime of the Bianchi type can be brought under transformation into a general set of nonlinear differential equations, an all-encompassing general equation implicitly contained in each of the cosmological models studied, most of whose analytic solutions the authors have found. The scalar field displays a considerable influence in the cosmological context during the early, strongly relativistic stage of the universe's expansion where the main difference between the cosmologies of Einstein general relativity and Jordan Brans-Dicke theories lies in the possible existence of a sourceless phi field which, since it is not generated by matter, is contrary to Mach's principle. Several solutions presented are reported for the first time.

We build a spherical halo model for galaxies using a general scalar-tensor theory of gravity in its Newtonian limit. The scalar field is described by a time-independent Klein-Gordon equation with a source that is coupled to the standard Poisson equation of Newtonian gravity. Our model, by construction, fits both the observed rotation velocities of stars in spirals and a typical luminosity profile. As a result, the form of the new Newtonian potential, the scalar field, and dark matter distribution in a galaxy are determined. Taking into account the constraints for the fundamental parameters of the theory (lambda,alpha), we analyze the influence of the scalar field in the dark matter distribution, resulting in shallow density profiles in galactic centers., Comment: 14 pages, 16 plots set in 7 figures, typos and references added

We present some exact solutions and a phase space analysis of metric $f(R)$-gravity models of the type $R^{n}$. We divide our discussion in $n\neq2$ and $n=2$ models. The later model is a good approximation, at late times to the $f(R) = \frac{2}{\pi}R \tan^{-1}(R/\beta^2)$ gravity model, being this an example of a non--singular case. For $n \neq 2$ models we have found power law solutions for the scale factor that are attractors and that comply with WMAP 5-years data if $n, Comment: 8 pages, 3 figures

We present $\Lambda$CDM $N$-body cosmological simulations in the framework of a static general scalar-tensor theory of gravity. Due to the influence of the non-minimally coupled scalar field, the gravitational potential is modified by a Yukawa type term, yielding a new structure formation dynamics. We present some preliminary results and, in particular, we compute the density and velocity profiles of the most massive group., Comment: 4 pages, 6 figures, to appear in Journal of Physics: Conference Series: VII Mexican School on Gravitation and Mathematical Physics. 26 November to 1 December 2006, Playa del Carmen, Quintana Roo, Mexico

We use scaled variables to display a set coupled equations valid for isotropic and anisotropic Bianchi type I, V, IX models in scalar-tensor theories, including Dehnen’s induced gravity theory. In particular, for the Brans-Dicke theory the equations decouple and one is able to integrate the system for FRW and Bianchi I and V models. Addition-ally, we analyze the possibility that anisotropic models asymptotically isotropize, and/or possess inflationary properties.

We present a formulation for potential-density pairs to describe axisymmetric galaxies in the Newtonian limit of scalar-tensor theories of gravity. The scalar field is described by a modified Helmholtz equation with a source that is coupled to the standard Poisson equation of Newtonian gravity. The net gravitational force is given by two contributions: the standard Newtonian potential plus a term stemming from massive scalar fields. General solutions have been found for axisymmetric systems and the multipole expansion of the Yukawa potential is given. In particular, we have computed potential-density pairs of galactic disks for an exponential profile and their rotation curves., Comment: 8 pages, no figures, corrected version to the one that will appear in Gen. Relativ. Gravit., where a small typo in eq. (13) is present

We review a system of autonomous differential equations developed in our previous work [1] describing a flat cosmology filled with a barotropic fluid and a scalar field with a modified kinetic term of the form L=F(X)-V(phi). We analyze the critical points and summarize the conditions to obtain scaling solutions. We consider a set of transformations and show that they leave invariant the equations of motion for the systems in which the scaling solution is obtained, allowing to reduce the number of degrees of freedom., Comment: 7 pages, 1 figure

Using scaled variables we are able to integrate an equation valid for isotropic and anisotropic Bianchi type I, V, IX models in Brans-Dicke (BD) theory. We analyze known and new solutions for these models in relation with the possibility that anisotropic models asymptotically isotropize, and/or possess inflationary properties. In particular, a new solution of curve ($k\neq0$) Friedmann-Robertson-Walker (FRW) cosmologies in Brans-Dicke theory is analyzed., 15 pages, 4 postscript figures, to appear in Gen. Rel. Grav., special issue dedicated in honour of Prof. H. Dehnen

We analyze if Bianchi I, V, and IX models in the Induced Gravity (IG) theory can evolve to a Friedmann--Roberson--Walker (FRW) expansion due to the non--minimal coupling of gravity and the scalar field. The analytical results that we found for the Brans-Dicke (BD) theory are now applied to the IG theory which has $\omega \ll 1$ ($\omega$ being the square ratio of the Higgs to Planck mass) in a cosmological era in which the IG--potential is not significant. We find that the isotropization mechanism crucially depends on the value of $\omega$. Its smallness also permits inflationary solutions. For the Bianch V model inflation due to the Higgs potential takes place afterwads, and subsequently the spontaneous symmetry breaking (SSB) ends with an effective FRW evolution. The ordinary tests of successful cosmology are well satisfied., Comment: 24 pages, 5 figures, to be published in Phys. Rev. D15

The cosmic, general analitic solutions of the Brans--Dicke Theory for the flat space of homogeneous and isotropic models containing perfect, barotropic, fluids are seen to belong to a wider class of solutions --which includes cosmological models with the open and the closed spaces of the Friedmann--Robertson--Walker metric, as well as solutions for models with homogeneous but anisotropic spaces corresponding to the Bianchi--Type metric clasification-- when all these solutions are expressed in terms of reduced variables. The existence of such a class lies in the fact that the scalar field, $\phi$, times a function of the mean scale factor or ``volume element'', $a^3 = a_1 a_2 a_3$, which depends on time and on the barotropic index of the equation of state used, can be written as a function of a ``cosmic time'' reduced in terms of another function of the mean scale factor depending itself again on the barotropic index but independent of the metrics here employed. This reduction procedure permites one to analyze if explicitly given anisotropic cosmological solutions ``isotropize'' in the course of their time evolution. For if so can happen, it could be claimed that there exists a subclass of solutions that is stable under anisotropic perturbations., Comment: 15 pages, Latex

We are considering the cosmological consequences of an induced gravity theory coupled to the minimal standard model of particle physics. The non-minimal coupling parameter between gravity and the Higgs field must then be very large, yielding some new cosmological consequences for the early Universe and new constraints on the Higgs mass. As an outcome, new inflation is only possible for very special initial conditions producing first a short contraction era after which an inflationary expansion automatically follows; a chaotic inflationary scenario is successfully achieved. The contrast of density perturbations required to explain the seed of astronomic structures are obtained for very large values of the Higgs mass ($M_{H} >> G_{F}^{-1/2}$), otherwise the perturbations have a small amplitude; in any case, the spectral index of scalar perturbations agrees with the observed one., 20 pages,4 figures using epsf, Latex

We investigate the cosmological consequences of a theory of induced gravity in which the scalar field is identified with the Higgs field of the first symmetry breaking of a mi\-ni\-mal SU(5) GUT. The mass of the X-boson determines a great value for the coupling constant of gravity-particle physics. Because of this fact, a "slow" rollover dynamics for the Higgs field is not possible in a "new" inflation scenario and, moreover, a contraction era for the scale factor in the early universe exists, \-after\- which inflation follows automatically; "chaotic" inflation is performed without problems. Inflation is successfully achieved due to the relationship among the masses of particle physics at that scale: The Higgs-, X-boson- and Planck-masses. As a result the particle physics pa\-ra\-me\-ter $\lambda$ is not fine-tuned as usual in order to predict acceptable values of re-heating temperature and density and gravitational wave perturbations. Moreover, if the coherent Higgs oscillations didn't decay they could explain the missing mass problem of cosmology., Comment: 19 pages, latex, 6 figures available by request