Late-time Cosmic Acceleration Research Articles

Cosmic acceleration in the Randall-Sundrum II brane world

In this paper, we implement the dynamical system tools to study the dynamics of a self-interacting scalar field for suitable interactions of dark energy and dark matter in the Randall-Sundrum II brane scenario. Here we investigate three distinct forms of interaction strength namely, $I_{\phi}=\alpha\dot{\rho_{\phi}}$ , $I_{m1}=\delta \dot{\phi} \rho_{m}$ and $I_{m2}=\frac{\sigma\dot{\phi}^{2} \rho_{m}}{H}$ . We consider a homogeneous and isotropic Friedmann-Robertson-Walker brane model. The transformation equations are simplified to an autonomous system of ordinary differential equations by a suitable change of variables and hence a dynamical system analysis is performed for the respective interacting models in RS II brane cosmology. During the dynamical system analysis, we use the linear stability theory to study the stability of hyperbolic points, but these linearization techniques fail for non-hyperbolic points. So we apply the center manifold theory to determine the stability of non-hyperbolic points. For these specific interaction strengths, the 3D and 4D dynamical system analysis infers the existence of late-time attractors. These attractors are found for constant potential and inverse power law potential. The presence of these attractors results in late-time cosmic acceleration.

Late-time cosmic acceleration from compactification

We investigate the implications of energy conditions on cosmological compactification solutions of the higher-dimensional Einstein field equations. It is known that the strong energy condition forbids time-independent compactifications to de Sitter space but allows time-dependent compactifications to other (homogeneous and isotropic) expanding universes that undergo a transient period of acceleration. Here we show that the same assumptions allow compactification to FLRW universes undergoing late-time accelerated expansion; the late-time stress tensor is a perfect fluid but with a lower bound on the pressure/energy-density ratio that excludes de Sitter but allows accelerated power-law expansion. The compact space undergoes a decelerating expansion that leads to decompactification, but on an arbitrarily long timescale.

Cosmic acceleration from coupling of baryonic and dark matter components: Analysis and diagnostics

In this paper, we examine a scenario in which late-time cosmic acceleration might arise due to the coupling between baryonic matter and dark matter without the presence of extra degrees of freedom. In this case, one can obtain late-time acceleration in Jordan frame and not in Einstein frame. We consider two different forms of parametrization of the coupling function, and put constraints on the model parameters by using an integrated dataset of Hubble parameter, Type Ia supernova and baryon acoustic oscillations. The models under consideration are consistent with the observations. In addition, we perform the statefinder and [Formula: see text] diagnostics, and show that the models exhibit a distinctive behavior due to the phantom characteristic in future which is a generic feature of the underlying scenario.

Dark energy in Horndeski theories after GW170817: A review

The gravitational wave (GW) event GW170817 from a binary neutron star merger together with the electromagnetic counterpart showed that the speed of GWs [Formula: see text] is very close to that of light for the redshift [Formula: see text]. This places tight constraints on dark energy models constructed in the framework of modified gravitational theories. We review models of the late-time cosmic acceleration in scalar–tensor theories with second-order equations of motion (dubbed Horndeski theories) by paying particular attention to the evolution of dark energy equation of state and observables relevant to the cosmic growth history. We provide a gauge-ready formulation of scalar perturbations in full Horndeski theories and estimate observables associated with the evolution of large-scale structures, cosmic microwave background and weak lensing by employing a so-called quasi-static approximation for the modes deep inside the sound horizon. In light of the recent observational bound of [Formula: see text], we also classify surviving dark energy models into four classes depending on different structure-formation patterns and discuss how they can be observationally distinguished from each other. In particular, the nonminimally coupled theories in which the scalar field [Formula: see text] has a coupling with the Ricci scalar [Formula: see text] of the form [Formula: see text], including [Formula: see text] gravity, can be tightly constrained not only from the cosmic expansion and growth histories but also from the variation of screened gravitational couplings. The cross-correlation of integrated Sachs–Wolfe signal with galaxy distributions can be a key observable for placing bounds on the relative ratio of cubic Galileon density to total dark energy density. The dawn of GW astronomy will open up a new window to constrain nonminimally coupled theories further by the modified luminosity distance of tensor perturbations.

Spherically symmetric static vacuum solutions in hybrid metric-Palatini gravity

We consider vacuum static spherically symmetric solutions in the hybrid metric-Palatini gravity theory, which is a combination of the metric and Palatini $f(R)$ formalisms unifying local constraints at the Solar System level and the late-time cosmic acceleration. We adopt the scalar-tensor representation of the hybrid metric-Palatini theory, in which the scalar-tensor definition of the potential can be represented as a Clairaut differential equation. Due to their mathematical complexity, it is difficult to find exact solutions of the vacuum field equations, and therefore we adopt a numerical approach in studying the behavior of the metric functions and of the scalar field. After reformulating the field equations in a dimensionless form, and by introducing a suitable independent radial coordinate, the field equations are solved numerically. We detect the formation of a black hole from the presence of a singularity in the metric tensor components. Several models, corresponding to different functional forms of the scalar field potential are considered. The thermodynamic properties of these black hole solutions (horizon temperature, specific heat, entropy and evaporation time due to Hawking luminosity) are also investigated in detail.

Bigravity and Horndeski gravity connected by a disformal coupling

In this paper, we have studied bi-gravity theory in a very specific limit where we focused only on one degree of freedom generated by the massive graviton. We have analyzed the model in the context of cosmology and demonstrated that the model can give rise to late time cosmic acceleration as an attractor of the dynamical system. However, the observational constraints due to tensor perturbations are stringent giving rise to large fine tuning.

Electroweak relaxation of cosmological hierarchy

A simple model for the late-time cosmic acceleration problem is presented in the Starobinsky inflation with a negative bare cosmological constant as well as a nonminimal coupling to the Higgs boson. After electroweak symmetry breaking, the Starobinsky inflaton has been frozen until very recently, becoming a thawing quintessence, and a comparable magnitude to the observed dark energy density can be achieved without fine-tuning. Our proposal essentially reduces the cosmological constant problem into the electroweak hierarchy problem, and its late-time behaviour is also consistent with the recently proposed swampland criteria.

Tracker and scaling solutions in DHOST theories

In quadratic-order degenerate higher-order scalar–tensor (DHOST) theories compatible with gravitational-wave constraints, we derive the most general Lagrangian allowing for tracker solutions characterized by ϕ˙/Hp=constant, where ϕ˙ is the time derivative of a scalar field ϕ, H is the Hubble expansion rate, and p is a constant. While the tracker is present up to the cubic-order Horndeski Lagrangian L=c2X−c3X(p−1)/(2p)□ϕ, where c2,c3 are constants and X is the kinetic energy of ϕ, the DHOST interaction breaks this structure for p≠1. Even in the latter case, however, there exists an approximate tracker solution in the early cosmological epoch with the nearly constant field equation of state wϕ=−1−2pH˙/(3H2). The scaling solution, which corresponds to p=1, is the unique case in which all the terms in the field density ρϕ and the pressure Pϕ obey the scaling relation ρϕ∝Pϕ∝H2. Extending the analysis to the coupled DHOST theories with the field-dependent coupling Q(ϕ) between the scalar field and matter, we show that the scaling solution exists for Q(ϕ)=1/(μ1ϕ+μ2), where μ1 and μ2 are constants. For the constant Q, i.e., μ1=0, we derive fixed points of the dynamical system by using the general Lagrangian with scaling solutions. This result can be applied to the model construction of late-time cosmic acceleration preceded by the scaling ϕ-matter-dominated epoch.

Dark Energy in Light of Multi-Messenger Gravitational-Wave Astronomy

Gravitational waves (GWs) provide a new tool to probe the nature of dark energy (DE) and the fundamental properties of gravity. We review the different ways in which GWs can be used to test gravity and models for late-time cosmic acceleration. Lagrangian-based gravitational theories beyond general relativity (GR) are classified into those breaking fundamental assumptions, containing additional fields and massive graviton(s). In addition to Lagrangian based theories we present the effective theory of DE and the $\mu$-$\Sigma$ parametrization as general descriptions of cosmological gravity. Multi-messenger GW detections can be used to measure the cosmological expansion (standard sirens), providing an independent test of the DE equation of state and measuring the Hubble parameter. Several key tests of gravity involve the cosmological propagation of GWs, including anomalous GW speed, massive graviton excitations, Lorentz violating dispersion relation, modified GW luminosity distance and additional polarizations, which may also induce GW oscillations. We summarize present constraints and their impact on DE models, including those arising from the binary neutron star merger GW170817. Upgrades of LIGO-Virgo detectors to design sensitivity and the next generation facilities such as LISA or Einstein Telescope will significantly improve these constraints in the next two decades.

Late-time acceleration driven by shift-symmetric Galileon in the presence of torsion

A shift-symmetric Galileon model in presence of spacetime torsion has been constructed for the first time. This has been realized by localizing (or, gauging) the Galileon symmetry in flat spacetime in an appropriate manner. We have applied the above model to study the evolution of the universe at a cosmological scale. Interestingly, for a wide class of torsional structures we have shown that the model leads to late time cosmic acceleration. Furthermore, as torsion vanishes, our model reproduces the standard results.

Anisotropic cosmological reconstruction in f(R, T) gravity

Anisotropic cosmological models are constructed in f(R, T) gravity theory to investigate the dynamics of universe concerning the late time cosmic acceleration. Using a more general and simple approach, the effect of the coupling constant and anisotropy on the cosmic dynamics have been investigated. In this study, it is found that cosmic anisotropy substantially affects cosmic dynamics.

Non-Locality and Late-Time Cosmic Acceleration from an Ultraviolet Complete Theory †

A local phenomenological model that reduces to a non-local gravitational theory giving dark energy is proposed. The non-local gravity action is known to fit the data as well as Λ-CDM thereby demanding a more fundamental local treatment. It is seen that the scale-invariant higher-derivative scalar-tensor theory of gravity, which is known to be ultraviolet perturbative renormalizable to all loops and where ghosts become innocuous, generates non-locality at low energies. The local action comprises of two real scalar fields coupled non-minimally with the higher-derivative gravity action. When one of the scalar acquiring the Vacuum Expectation Value (VEV) induces Einstein–Hilbert gravity, generates mass for fields, and gets decoupled from system, it leaves behind a residual theory which in turn leads to a non-local gravity generating dark energy effects.

Cosmology in scalar-vector-tensor theories

We study the cosmology on the Friedmann-Lema\^{\i}tre-Robertson-Walker background in scalar-vector-tensor theories with a broken $U(1)$ gauge symmetry. For parity-invariant interactions arising in scalar-vector-tensor theories with second-order equations of motion, we derive conditions for the absence of ghosts and Laplacian instabilities associated with tensor, vector, and scalar perturbations at linear order. This general result is applied to the computation of the primordial tensor power spectrum generated during inflation as well as to the speed of gravity relevant to the late-time cosmic acceleration. We also construct a concrete inflationary model in which a temporal vector component ${A}_{0}$ contributes to the dynamics of cosmic acceleration besides a scalar field $\ensuremath{\phi}$ through their kinetic mixings. In this model, we show that all the stability conditions of perturbations can be consistently satisfied during inflation and subsequent reheating.

Weak lensing probe of cubic Galileon model

The cubic Galileon model containing the lowest non-trivial order action of the full Galileon action can produce the stable late-time cosmic acceleration. This model can have a significant role in the growth of structures. The signatures of the cubic Galileon model in the structure formation can be probed by the weak lensing statistics. Weak lensing convergence statistics is one of the strongest probes to the structure formation and hence it can probe the dark energy or modified theories of gravity models. In this work, we investigate the detectability of the cubic Galileon model from the ΛCDM model or from the canonical quintessence model through the convergence power spectrum and bi-spectrum.

Falsifying cosmological models based on a non-linear electrodynamics

Recently, the nonlinear electrodynamics (NED) has been gaining attention to generate primordial magnetic fields in the Universe and also to resolve singularity problems. Moreover, recent works have shown the crucial role of the NED on the inflation. This paper provides a new approach based on a new model of NED as a source of gravitation to remove the cosmic singularity at the big bang and explain the cosmic acceleration during the inflation era on the background of stochastic magnetic field. Also, we found a realization of a cyclic Universe, free of initial singularity, due to the proposed NED energy density. In addition, we explore whether a NED field without or with matter can be the origin of the late-time acceleration. For this we obtain explicit equations for H(z) and perform a MCMC analysis to constrain the NED parameters by using 31 observational Hubble data (OHD) obtained from cosmic chronometers covering the redshift range 0< z < 1.97; and with the joint-light-analysis (JLA) SNIa compilation consisting in 740 data points in the range 0.01<z<1.2. All our constraints on the current magnetic field give B_{0}sim 10^{-31}mathrm {cm^{-1}}, which are larger than the upper limit 10^{-33}mathrm {cm^{-1}} by the Planck satellite implying that NED cosmologies could not be suitable to explain the Universe late-time dynamics. However, the current data is able to falsify the scenario at late times. Indeed, one is able to reconstruct the deceleration parameter q(z) using the best fit values of the parameters obtained from OHD and SNIa data sets. If the matter component is not included, the data sets predict an accelerated phase in the early Universe, but a non accelerated Universe is preferred in the current epoch. When a matter component is included in the NED cosmology, the data sets predict a q(z) dynamics similar to that of the standard model. Moreover, both cosmological data favor up to 2sigma confidence levels an accelerating expansion in the current epoch, i.e., the Universe passes of a decelerated phase to an accelerated stage at redshift sim 0.6. Therefore, although the NED cosmology with dust matter predict a value B_{0} higher than the one measured by Planck satellite, it is able to drive a late-time cosmic acceleration which is consistent with our dynamical systems analysis and it is preferred by OHD and SNIa data sets.

Coexistence of early-time inflation and late-time acceleration with scalar fields in theory of F(G,T) gravity

In this study, we discuss coexistence of the early-time inflation and the late-time acceleration of the universe in the context of the theory of [Formula: see text] gravity with scalar field which is minimally coupled with the gravity, where [Formula: see text] is the gauss bonnet invariant and [Formula: see text] is the trace of energy–momentum tensor (EMT). We reconstruct the Friedmann equation (FE) and then search for the real value of a particular model [Formula: see text], where [Formula: see text] and [Formula: see text] are real constants. A Gauss–Bonnet system (GBS) for viable cosmologies arising from the matter-source term [Formula: see text] and the scalar field, is obtained. We find that the case [Formula: see text] together with [Formula: see text] in the system gives the late-time cosmic acceleration while the source term [Formula: see text] acts as a quintessence type of dark energy. On the other hand, the general entropy expression of the universe is obtained by making use of the first law of thermodynamics (FLT) method. After theoretically analyzing the inflation in the entropy frame, we find a new condition [Formula: see text] with [Formula: see text] in the system. Then, from the observational analysis of inflation, the spectral index parameter and the scalar-tensor ratio are calculated under the new condition. In brief, we obtain a viable cosmological system arising from some modifications such as the scalar field and the source term, which can unify the early inflation and the late-time cosmic acceleration besides the deceleration regions of the universe.

Brane with variable tension as a possible solution to the problem of the late cosmic acceleration

Braneworld models have been proposed as a possible solution to the problem of the accelerated expansion of the Universe. The idea is to dispense the dark energy (DE) and drive the late-time cosmic acceleration with a five-dimensional geometry. Here, we investigate a brane model with variable brane tension as a function of redshift called chrono-brane. We propose the polynomial $\lambda=(1+z)^{n}$ function inspired in tracker-scalar-field potentials. To constrain the $n$ exponent we use the latest observational Hubble data from cosmic chronometers, Type Ia Supernovae from the full JLA sample, baryon acoustic oscillations and the posterior distance from the cosmic microwave background of Planck 2015 measurements. A joint analysis of these data estimates $n\simeq6.19$ which generates a DE-like or cosmological-constant-like term, in the Friedmann equation arising from the extra dimensions. This model is consistent with these data and can drive the Universe to an accelerated phase at late times.

Dark energy scenario consistent with GW170817 in theories beyond Horndeski gravity

The Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories up to quartic order are the general scheme of scalar-tensor theories allowing the possibility for realizing the tensor propagation speed $c_t$ equivalent to 1 on the isotropic cosmological background. We propose a dark energy model in which the late-time cosmic acceleration occurs by a simple k-essence Lagrangian analogous to the ghost condensate with cubic and quartic Galileons in the framework of GLPV theories. We show that a wide variety of the variation of the dark energy equation of state $w_{\rm DE}$ including the entry to the region $w_{\rm DE}<-1$ can be realized without violating conditions for the absence of ghosts and Laplacian instabilities. The approach to the tracker equation of state $w_{\rm DE}=-2$ during the matter era, which is disfavored by observational data, can be avoided by the existence of a quadratic k-essence Lagrangian $X^2$. We study the evolution of nonrelativistic matter perturbations for the model $c_t^2=1$ and show that the two quantities $\mu$ and $\Sigma$, which are related to the Newtonian and weak lensing gravitational potentials respectively, are practically equivalent to each other, such that $\mu \simeq \Sigma>1$. For the case in which the deviation of $w_{\rm DE}$ from $-1$ is significant at a later cosmological epoch, the values of $\mu$ and $\Sigma$ tend to be larger at low redshifts. We also find that our dark energy model can be consistent with the bounds on the deviation parameter $\alpha_{\rm H}$ from Horndeski theories arising from the modification of gravitational law inside massive objects.

Super inflation mechanism and dark energy from a cosmological entropy perspective

Various approaches are developed that provide a unification of the early inflationary epoch of the universe and dark energy (cosmic accelerating expansion case). In one respect, we express this unification in a universal thermodynamic framework within the context of F ( T , T G ) role=presentation> F ( T , T G ) F ( T , T G ) F\left( T,T_{G} \right) gravity, where T role=presentation> T T T represents the torsion invariant and T G role=presentation> T G T G T_{G} is the teleparallel equivalent of the Gauss--Bonnet term. For a Friedmann-Robertson-Walker universe model bounded by the dynamical apparent horizon, we explore the generalized second law of gravitational thermodynamics (GSLT). Finally, we discuss the super inflation mechanism, the deceleration case (radiation and dust regions), and the late time cosmic acceleration of the universe into the validity of the GSLT that we obtain.

Observational constraints on the generalized α attractor model

We study the generalized [Formula: see text] attractor model in the context of the late time cosmic acceleration. The model interpolates between the scaling freezing and thawing dark energy models. In the slow roll region, the original potential is modified whereas the modification ceases in the asymptotic region and the effective potential behaves as the quadratic one. In our setting, the field rolls slowly around the present epoch and mimics the scaling behavior in the future. We obtain observational constraints on the model parameters by using an integrated database (SN+Hubble+BAO+CMB).