In this thesis we first apply the 1+3 covariant description of general relativity to analyze n-fluid Friedmann-Lemaitre (FL) cosmologies; that is, homogeneous and isotropic cosmologies whose matter-energy content consists of n non-interacting fluids. We are motivated to study FL models of this type as observations suggest the physical universe is closely described by a FL model with a matter content consisting of radiation, dust and a cosmological constant. Secondly, we use the 1+3 covariant description to analyse scalar, vector and tensor perturbations of FL cosmologies containing a perfect fluid and a cosmological constant. In particular, we provide a thorough discussion of the behaviour of perturbations in the physically interesting cases of a dust or radiation background.
A regularization procedure has been recently suggested for regularizing Big Bang singularities in Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetimes. We argue that this procedure is only appliable to one case of Big Bang singularities and does not affect other types of singularities.
Hawking's proposal that the Universe has no temporal boundary and hence no beginning depends on the notion of imaginary time and is usually referred to as the "no-boundary proposal." This paper discusses a simple alternative approach by means of the five-dimensional Friedmann-Lemaitre-Robertson-Walker model.
We investigate toroidal Marginally Outer Trapped Surfaces (MOTS) and Marginally Outer Trapped Tubes (MOTT) in closed Friedmann-Lemaitre-Robertson-Walker (FLRW) geometries. They are constructed by embedding Constant Mean Curvature (CMC) Clifford tori in a FLRW spacetime. This construction is used to assess the quality of certain isoperimetric inequalities, recently proved in axial symmetry. Similarly to spherically symmetric MOTS existing in FLRW spacetimes, the toroidal ones are also unstable.
According to the AdS/CFT correspondence conjecture, the Randall-Sundrum infinite braneworld is equivalent to four dimensional Einstein gravity with ${\cal N}=4$ super Yang-Mills fields at low energies. Here we derive a four dimensional effective equation of motion for tensor-type perturbations in two different pictures, and demonstrate their equivalence.
The study of the matching of stationary and axisymmetric spacetimes with Friedmann-Lemaitre-Robertson-Walker spacetimes preserving the axial symmetry is presented. We show, in particular, that any orthogonally transitive stationary and axisymmetric region in FLRW must be static, irrespective of the matter content. Therefore, previous results on static regions in FLRW cosmologies apply. As a result, the only stationary and axisymmetric vacuum region that can be matched to a (non-static) FLRW spacetime is a spherically symmetric region of Schwarzschild. This constitutes another uniqueness result…
A cosmological time variable is emerged from the Hamiltonian formulation of Friedmann model to measure the evolution of dynamical observables in the theory. A set of observables has been identified for the theory on the null hypersurfaces that its evolution is with respect to the volume clock introduced by the cosmological time variable.
We obtain the correct hamiltonian which describes the dynamics of classes of asymptotic open Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) spacetimes, which includes Tolman geometries. We calculate the surface term that has to be added to the usual hamiltonian of General Relativity in order to obtain an improved hamiltonian with well defined functional derivatives. For asymptotic flat FLRW spaces, this surface term is zero, but for asymptotic negative curvature FLRW spaces it is not null in general. In the particular case of the Tolman geometries, they vanish. The surface term evaluated on a pa…
We reconsider the cosmological model discussed by Sung-Won Kim [Phys. Rev D 53, 6889 (1996)] in the context of Friedmann-Robertson-Walker cosmologies with a traversable wormhole, where it is assumed that the matter content is divided into two parts: the cosmic part that depends on time only and the wormhole part that depends on space only. The cosmic part obeys the barotropic equation of state $p_c=γρ_c$. The complete analysis requires further care and reveals more interesting results than what was previously shown by the author. They can be readily applied to the evolution of a large class of…
Using the standard canonical formalism, the equations of mechanics and kinetics in the Friedmann-Lemaitre-Robertson-Walker (FLRW) space-times in Cartesian coordinates have been obtained. The transformation law of the generalized momentum under the shift of the origin of the coordinate system has been found, and the form invariance of the Hamiltonian function relative to the shift transformation has been proved. The general solution of the collisionless Boltzmann equation has been found. In the case of the homogeneous distribution the solutions of the kinetic equation for several simple, but im…
Elliptic functions are known to appear in many problems, applied and theoretical. However, a lesser known application is in the study of exact solutions to Einstein's gravitational field equations in a Friedmann-Robertson-Lemaitre-Walker (FRLW) cosmology. We will show explicitly how Jacobi and Weierstrass elliptic functions arise in this context, and will additionally show connections with theta functions.
We build a simple cosmological model by means of a parabolic Lemaître-Tolman-Bondi (LTB) metric up to a redshift $z\simeq 0.4$, an hyperbolic Friedmann metric for $z\sim 0.4$ up to the scale where dimming galaxies are observed ($z\sim 1.4$) and a bulk spatially flat metric up to the last scattering surface. Following Wiltshire, by taking into account the different rate of clocks for an observer at the centre of a parabolic LTB spacetime with respect to a one in the hyperbolic Friedmann metric, an "apparent" negative deceleration parameter is perceived by the observer at the centre of LTB, prov…
We show that the Big Bang singularity of the Friedmann-Lemaitre-Robertson-Walker model does not raise major problems to General Relativity. We prove a theorem showing that the Einstein equation can be written in a non-singular form, which allows the extension of the spacetime before the Big Bang. The physical interpretation of the fields used is discussed. These results follow from our research on singular semi-Riemannian geometry and singular General Relativity.
Electrodynamics for self-interacting scalar fields in spatially flat Friedmann-Robertson-Walker space-times is studied. The corresponding one-loop field equation for the expectation value of the complex scalar field in the conformal vacuum is derived. For exponentially expanding universes, the equations for the Bogoliubov coefficients describing the coupling of the scalar field to gravity are solved numerically. They yield a non-local correction to the Coleman-Weinberg effective potential which does not modify the pattern of minima found in static de Sitter space. Such a correction contains a …
We present an autonomous phase-plane describing the evolution of Friedmann-Robertson-Walker models containing a perfect fluid (with barotropic index gamma) in Brans-Dicke gravity (with Brans-Dicke parameter omega). We find self-similar fixed points corresponding to Nariai's power-law solutions for spatially flat models and curvature-scaling solutions for curved models. At infinite values of the phase-plane variables we recover O'Hanlon and Tupper's vacuum solutions for spatially flat models and the Milne universe for negative spatial curvature. We find conditions for the existence and stabilit…
As a rule in General Relativity the spacetime metric fixes the Einstein tensor and through the Field Equations (FE) the energy-momentum tensor. However one cannot write the FE explicitly until a class of observers has been considered. Every class of observers defines a decomposition of the energy-momentum tensor in terms of the dynamical variables energy density ($μ$), the isotropic pressure ($p$), the heat flux $q^a$ and the traceless anisotropic pressure tensor $π_{ab}$. The solution of the FE requires additional assumptions among the dynamical variables known with the generic name equations…
Einstein's equation, in its standard form, breaks down at the Big Bang singularity. A new version, equivalent to Einstein's whenever the latter is defined, but applicable in wider situations, is proposed. The new equation remains smooth at the Big Bang singularity of the Friedmann-Lemaitre-Robertson-Walker model. It is a tensor equation defined in terms of the Ricci part of the Riemann curvature. It is obtained by taking the Kulkarni-Nomizu product between Einstein's equation and the metric tensor.
We illustrate how the group of symmetry transformations, which preserve the form of the n--dimensional flat Friedmann--Robertson--Walker cosmologies satisfying Einstein equations, acts in any dimension. This group relates the energy density and the isotropic pressure of the cosmic fluid to the expansion rate. The freedom associated with the dimension of the space time yields assisted inflation even when the energy density of the fluid is a dimensional invariant and enriches the set of duality transformations leading to phantom cosmologies.
We report a symmetry property of the Einstein-Friedmann equations for spatially flat Friedmann-Lemaître-Robertson-Walker universes filled with a perfect fluid with any constant equation of state. The symmetry transformations form a one-parameter Abelian group.
It is well-known that there are four distinct basic types (two Big Bang types, Lemaitre and Big Crunch type) for solutions of the general Friedmann equation with positive cosmological constant, where radiation and matter do not couple (see e.g. [2, p.7]. In that paper the system of case distinction parameters contains a "critical radiation parameter" $σ_{cr}$. The present note contains the constructive description of the so-called {\em border lines} between Big Bang/Big Crunch type and Big Bang/Lemaitre type for so-called Hubble solutions of the Friedmann equation by two smooth function branch…
An infinite number of perturbed k=0 Friedmann cosmologies filled with dust and radiation is found. As we go up the sequence, the solutions contain an increasing number of integration functions. With the coordinate gauge adopted to co-move with the perturbed matter, the solution of a pair of coupled equations for the trace h of the metric perturbations and for the radiation density perturbations δρ_r is the key to the problem. An estimate is given of the temperature variation of the cosmic microwave background radiation due to the Sachs-Wolfe effect. It is found that the temperature fluctuation…
In this work a series of methods are developed for understanding the Friedmann equation when it is beyond the reach of the Chebyshev theorem. First it will be demonstrated that every solution of the Friedmann equation admits a representation as a roulette such that information on the latter may be used to obtain that for the former. Next the Friedmann equation is integrated for a quadratic equation of state and for the Randall--Sundrum II universe, leading to a harvest of a rich collection of new interesting phenomena. Finally an analytic method is used to isolate the asymptotic behavior of th…
It is well-known that there are four distinct basic types (two BigBang types, Lemaitre and BigCrunch type) for solutions of the general Friedmann equation with positive cosmological constant, where radiation and matter do not couple. In the note it is shown that the "frontier lines" between BigBang/BigCrunch and BigBang/Lemaitre are given by two smooth function branches, expressing the cosmological constant as unique functions of the matter and radiation density, which satisfy a simple asymptotic relation w.r.t. the matter density. The proof is based on the solution of the equation $σ=σ_{cr}$,…
We study the time evolution of small classical perturbations in a gauge invariant way for a complex scalar field in the early zero curvature Friedmann-Lema\^ıtre universe. We, thus, generalize the analysis which has been done so far for a real scalar field. We give also a derivation of the Jeans wavenumber in the Newtonian regime starting from the general relativistic equations, avoiding the so-called Jeans swindle. During the inflationary phase, whose length depends on the value of the bosonic charge, the behavior of the perturbations turns out to be the same as for a real scalar field. In th…
Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $γ$ for the Locally Rotationally Symmetric (LRS) Bianchi I and flat Friedmann-Lemaître-Robertson-Walker (FLRW) metrics are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averaged versions have the same late-time dynamics. Therefore, the simplest time-averaged system determines the future asymptotic behavior. Depending on the values of $γ$, th…
We develop approximation methods in the hybrid quantization of the Gowdy model with linear polarization and a massless scalar field, for the case of three-torus spatial topology. The loop quantization of the homogeneous gravitational sector of the Gowdy model (according to the improved dynamics prescription) and the presence of inhomogeneities lead to a very complicated Hamiltonian constraint. Therefore, the extraction of physical results calls for the introduction of well justified approximations. We first show how to approximate the homogeneous part of the Hamiltonian constraint, correspondi…
We propose physically motivated spacetime uncertainty relations (STUR) for flat Friedmann-Lemaître cosmologies. We show that the physical features of these STUR crucially depend on whether a particle horizon is present or not. In particular, when this is the case we deduce the existence of a maximal value for the Hubble rate (or equivalently for the matter density), thus providing an indication that quantum effects may rule out a pointlike big bang singularity. Finally, we costruct a concrete realisation of the corresponding quantum Friedmann spacetime in terms of operators on a Hilbert space.
We study the detector's response when moving along an ingoing null geodesic. The backgrounds are chosen to be black hole spacetimes ($(1+1)$ dimensional Schwarzschild metric and near horizon effective metric for any stationary black hole in arbitrary dimensions) as well as Friedmann-Lemaitre-Robertson-Walker (FLRW) Universe. For black holes the trajectories are defined in Schwarzschild coordinates and the field modes are corresponding to {\it Boulware vacuum}. Whereas for FLRW case, the detector is moving along the path defined in original {\it cosmic time} and the field modes are related to {…
Lemaitre-Tolman-Bondi inhomogeneous spacetimes can be used as a cosmological model to account for the type Ia supernova data. However, such models also give rise to large velocities of galaxy clusters with respect to the cosmic microwave background. Those velocities can be measured using the kinematic Sunyaev-Zeldovich effect. This paper presents a calculation of galaxy cluster velocities as a function of redshift for such a model.
The pseudo-complex Friedmann Lemaitre Robertson Walker model and the time dependence of the Hubble constant
University of Mentouri, Constantine 1（孔蒂纳一世门图里大学）；Mathematical and Subatomic Physics Laboratory (LPMPS) University of Mentouri, Constantine 1（孔蒂纳一世门图里大学数学与亚原子物理实验室）；Instituto de Ciencias Nucleares, UNAM（墨西哥国立自治大学核科学研究所）；Frankfurt Institute for Advanced Studies, J. W. von Goethe University（法兰克福高等研究院，约翰·沃尔夫冈·冯·歌德大学）；Department of Physics, San Diego State University（圣地亚哥州立大学物理系）；Department of Physics, University of California at SanDiego (UCSD)（加州大学圣地亚哥分校物理系）；International Center for Relativistic AstrophysicsNetwork (ICRANet)（相对论天体物理学国际网络中心）；Instituto de Física, Universidade Federal do Rio Grandedo Sul (UFRGS)（南里奥格兰德联邦大学物理研究所）
In a universe where, according to the standard cosmological models, some 97% of the total mass-energy is still "missing in action" it behooves us to spend at least a little effort critically assessing and exploring radical alternatives. Among possible, (dare we say plausible), nonstandard but superficially viable models, those spacetimes conformal to the standard Friedmann-Lemaitre-Robertson-Walker class of cosmological models play a very special role --- these models have the unique and important property of permitting large non-perturbative geometric deviations from Friedmann-Lemaitre-Robert…
Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $γ$ for Locally Rotationally Symmetric (LRS) Bianchi III metric and open Friedmann-Lemaître-Robertson-Walker (FLRW) metric are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averaged versions have the same late-time dynamics. Therefore, simple time-averaged systems determine the future asymptotic behavior. Depending on values of barotropic in…
We study the coupled Einstein-Yang-Mills-Dilaton (EYMD) equations for a Fried\-mann-Le\-mai\-tre universe with constant curvature $k=1$. Our detailed analysis is restricted to the case where the dilaton potential and the cosmological constant vanish. Also assuming a static gauge field, we present analytical and numerical results on the behavior of solutions of the EYMD equations. For different values of the dilaton coupling constant we analyze the phase portrait for the time evolution of the dilaton field and give the behavior of the scale factor. It turns out that there are no inflationary st…
Compact, flat Friedmann-Lemaitre-Robertson-Walker (FLRW) models have recently regained interest as a good fit to the observed cosmic microwave background temperature fluctuations. However, it is generally thought that a globally, exactly-flat FLRW model is theoretically improbable. Here, in order to obtain a probability space on the set F of compact, comoving, 3-spatial sections of FLRW models, a physically motivated hypothesis is proposed, using the density parameter Omega as a derived rather than fundamental parameter. We assume that the processes that select the 3-manifold also select a glo…
Recent updated results of quasar spectra suggested a 3.9$σ$ significance of spatial variation of the fine-structure constant. Theoretically, it is important to examine whether the fine-structure constant, as a fundamental constant in quantum theory, is possible varying with space and time. In this paper, we explore the possibility that spatial variation of the fine-structure constant could be compatible with Einstein's general relativity. Namely, the spatially dependent fine-structure constant in the Universe could be originated in different values of the speed of light in separate local frame…
The general solution of the gravitational field equations in the flat Friedmann-Robertson-Walker geometry is obtained in the framework of the full Israel-Stewart-Hiscock theory for a bulk viscous stiff cosmological fluid, with bulk viscosity coefficient proportional to the energy density.
This is the second of a series of papers extending the 1+3 covariant and gauge invariant treatment of kinetic theory to an examination of Cosmic Microwave Background temperature anisotropies arising from inhomogeneities in the early universe. The first paper dealt with algebraic issues. Here we derive the mode form of the integrated Boltzmann equations, first, giving a covariant version of the standard derivation using the mode recursion relations, second, demonstrating the link to the multipole divergence equations and finally various analytic ways of solving the resulting equations are discu…
For a 4-dimensional spatially-flat Friedmann-Robertson-Walker universe with a scalar field $ϕ(x)$, potential $V(ϕ)$ and constant equation of state $w=p/ρ$, we show that an expanding solution characterized by $ε=3(1+w)/2$ produces the same scalar perturbations as a contracting solution with $\hatε=1/ε$. The same symmetry applies to both the dominant and subdominant scalar perturbation modes. This result admits a simple physical interpretation and generalizes to $d$ spacetime dimensions if we define $ε\equiv [(2d-5)+(d-1)w]/(d-2)$.
We investigate the conditions for a bounce to occur in Friedmann-Robertson-Walker cosmologies for the class of fourth order gravity theories. The general bounce criterion is determined and constraints on the parameters of three specific models are given in order to obtain bounces solutions. It is found that unlike the case of General Relativity, a bounce appears to be possible in open and flat cosmologies.
We find the group of symmetry transformations generated by interacting fluids in spatially flat Friedmann-Robertson-Walker (FRW) spacetime which links cosmologies with the same scale factor {\it (identity)} or with scale factors $a$ and $a^{-1}$ {\it (duality)}. There exists a duality between contracting and superaccelerated expanding scenarios associated with {\it (phantom)} cosmologies. We investigate the action of this symmetry group on self-interacting minimally(conformally) coupled quintessence and $k$-essence cosmologies.
The cosmological Higgs vacuum stability has been an attractive research subject and it is crucial to accurately follow the development of the Higgs fluctuations. In this work, we thoroughly investigate how the vacuum fluctuations of the Higgs field affect the stability of the electroweak vacuum in Friedmann-Lemaitre-Robertson-Walker (FLRW) background. Adopting adiabatic (WKB) approximation or adiabatic regularization methods, we clearly show that vacuum fluctuations of the Higgs field in the FLRW background depend on the curvature and also masses of the Higgs or other scalar fields. The Higgs …
Most of the observational claims in cosmology are based on the assumption that the universe is isotropic and homogeneous so they essentially test different types of Friedmann models. This also refers to recent observations of supernovae Ia, which, within the framework of Friedmann cosmologies give strong support to negative pressure matter and also weaken the age conflict. In this essay we drop the assumption of homogeneity, though temporarily leaving the assumption of isotropy with respect to one point, and show that supernovae data can be consistent with a model of the universe with inhomoge…
We solve isotropic, homogeneous cosmological models containing a self-interacting scalar field. Calculations are performed in four and two-dimensional spacetimes. We find several exact solutions that have an inflationary regime or has a final Friedmann stage. Also their asymptotically stability is studied.
Several isotropic, homogeneous cosmological models containing a self-interacting minimally coupled scalar field, a perfect fluid source and cosmological constant are solved. New exact, asymptotically stable solutions with an inflationary regime or a final Friedmann stage are found for some simple, interesting potentials. It is shown that the fluid and the curvature may determine how these models evolve for large times.
Closed, spatially homogeneous cosmological models with a perfect fluid and a scalar field with exponential potential are investigated, using dynamical systems methods. First, we consider the closed Friedmann-Robertson-Walker models, discussing the global dynamics in detail. Next, we investigate Kantowski-Sachs models, for which the future and past attractors are determined. The global asymptotic behaviour of both the Friedmann-Robertson-Walker and the Kantowski-Sachs models is that they either expand from an initial singularity, reach a maximum expansion and thereafter recollapse to a final si…
The idea of a variable dark energy has been entertained many times in the literature and from many different points of view. Quintessence is just a popular way to implement this idea in recent times, but so far with little success. Another possibility is to think of the cosmological term, Lambda, as a ``running quantity'' much in the same way as the electromagnetic coupling constant. However, the fact that Lambda is a dimension-four parameter implies that it may obey a peculiar renormalization group equation, which at low energies could be dominated by ``soft decoupling'' contributions of the …
Scalar field cosmologies with a generalized harmonic potential and matter with energy density $ρ_m$, pressure $p_m$, and barotropic equation of state (EoS) $p_m=(γ-1)ρ_m, \; γ\in[0,2]$ in Kantowski-Sachs (KS) and closed Friedmann--Lemaître--Robertson--Walker (FLRW) metrics are investigated. We use methods from non--linear dynamical systems theory and averaging theory considering a time--dependent perturbation function $D$. We define a regular dynamical system over a compact phase space, obtaining global results. That is, for KS metric the global late--time attractors of full and time--averaged…
In this work we consider Randall-Sundrum braneworld type scenarios, in which the spacetime is described by a five-dimensional manifold with matter fields confined in a domain wall or three-brane. We present the results of a systematic analysis, using dynamical systems techniques, of the qualitative behaviour of Friedmann-Lemaitre-Robertson-Walker type models, whose matter is described by a scalar field with an exponential potential. We construct the state spaces for these models and discuss how their structure changes with respect to the general-relativistic case, in particular, what new criti…
We derive a set of equations monitoring the evolution of covariant and gauge-invariant linear scalar perturbations of Friedman-Lemaître-Robertson-Walker models with multiple interacting non-linear scalar fields. We use a dynamical systems' approach in order to perform a stability analysis for some classes of scalar field potentials. In particular, using a recent approximation for the inflationary dynamics of the background solution, we derive conditions under which homogenization occurs for chaotic (quadratic and quartic potentials) and new inflation. We also prove a cosmic no-hair result for …
Scalar fields coupled to gravity via $ξR Φ^2$ in arbitrary Friedmann-Robertson-Walker backgrounds can be represented by an effective flat space field theory. We derive an expression for the scalar energy density where the effective scalar mass becomes an explicit function of $ξ$ and the scale factor. The scalar quartic self-coupling gets shifted and can vanish for a particular choice of $ξ$. Gravitationally induced symmetry breaking and de-stabilization are possible in this theory.
In this work we consider perturbations of homogeneous and hypersurface orthogonal cosmological backgrounds with local rotational symmetry (LRS), using a method based on the 1 + 1 + 2 covariant split of spacetime. The backgrounds, of LRS class II, are characterised by that the vorticity, the twist of the 2-sheets, and the magnetic part of the Weyl tensor all vanish. They include the flat Friedmann universe as a special case. The matter contents of the perturbed spacetimes are given by vorticity-free perfect fluids, but otherwise the perturbations are arbitrary and describe gravitational, shear,…
For general relativistic spacetimes filled with irrotational `dust' a generalized form of Friedmann's equations for an `effective' expansion factor $a_D (t)$ of inhomogeneous cosmologies is derived. Contrary to the standard Friedmann equations, which hold for homogeneous-isotropic cosmologies, the new equations include the `backreaction effect' of inhomogeneities on the average expansion of the model. A universal relation between `backreaction' and average scalar curvature is also given. For cosmologies whose averaged spatial scalar curvature is proportional to $a_D^{-2}$, the expansion law go…
We present the numerical evolution of a family of conformally-flat, infinite, expanding cubic black-hole lattices. We solve for the initial data using an initial-data prescription presented recently, along with a new multigrid solver developed for this purpose. We then apply the standard tools of numerical relativity to calculate the time development of this initial dataset and derive quantities of cosmological relevance, such as the scaling of proper lengths. Similarly to the case of S3 lattices, we find that the length scaling remains close to the analytical solution for Friedmann-Lemaitre-R…
The covariant gauge invariant perturbation theory of scalar cosmological perturbations is developed for a general Scalar-Tensor Friedmann-Lemaitre-Robertson-Walker cosmology in a vacuum. The perturbation equations are then solved exactly in the long wavelength limit for a specific coupling, potential and background. Differences with the minimally coupled case are briefly discussed.
When using Einstein's equations, there exist a number of techniques for embedding non-linear structures in cosmological backgrounds. These include Swiss cheese models, in which spherically symmetric vacua are patched onto Friedmann solutions, and lattice models, in which weak-field regions are joined together directly. In this talk we will consider how these methods work in f(R) theories of gravity. We will show that their existence places constraints on the large-scale expansion of the universe, and that it may not always be possible to consider the Friedmann solutions and weak-field solution…
The present thesis is focused on the study of FLRW cosmology in modified gravities and with scalar fields. The mystery of dark energy has made that the last decade, many efforts in theoretical physics have been focused on the explanation of the current acceleration of the Universe expansion. On the other hand, an early accelerated epoch, known as inflation, is also required in the standard cosmological model in order to fit the observational data. Here, we study the possibility to explain both effects under the same mechanism, by means of scalar fields or modified gravity. In this sense, F(R) …
