In the context of the so-called Gauss-Bonnet gravity, where the gravitational action includes function of the Gauss-Bonnet invariant, we study cosmological solutions, especially the well-known $Λ$CDM model. It is shown that the dark energy contribution and even the inflationary epoch can be explained in the frame of this kind of theories with no need of any other kind of component. Other cosmological solutions are constructed and the rich properties that this kind of theories provide are explored.
We provide an $F(R)$ gravity description of a $Λ$CDM bouncing model, without the need for matter fluids or for cosmological constant. As we explicitly demonstrate, the two cosmological eras that constitute the $Λ$CDM bouncing model, can be generated by $F(R)$ gravity which can lead to accelerating cosmologies. The resulting F(R) gravity has Einstein frame inflationary properties that have concordance to the latest Planck observational data. Both the $F(R)$ gravity stability properties are thoroughly investigated and also, the gravitational particle production, a feature necessary for the viabi…
We present a comprehensive and updated comparison with cosmological observations of two non-local modifications of gravity previously introduced by our group, the so called RR and RT models. We implement the background evolution and the cosmological perturbations of the models in a modified Boltzmann code, using CLASS. We then test the non-local models against the {\em Planck} 2015 TT, TE, EE and Cosmic Microwave Background (CMB) lensing data, isotropic and anisotropic Baryonic Acoustic Oscillations (BAO) data, JLA supernovae, $H_0$ measurements and growth rate data, and we perform Bayesian pa…
We study the phenomenology of a class of minimally modified gravity theories called $f(\mathcal{H})$ theories, in which the usual general relativistic Hamiltonian constraint is replaced by a free function of it. After reviewing the construction of the theory and a consistent matter coupling, we analyze the dynamics of cosmology at the levels of both background and perturbations, and present a concrete example of the theory with a $3$-parameter family of the function $f$. Finally, we compare this example model to Planck data as well as some later-time probes, showing that such a realization of …
We propose a novel model in the framework of $f(Q)$ gravity, which is a gravitational modification class arising from the incorporation of non-metricity. The model has General Relativity as a particular limit, it has the same number of free parameters to those of $Λ$CDM, however at a cosmological framework it gives rise to a scenario that does not have $Λ$CDM as a limit. Nevertheless, confrontation with observations at both background and perturbation levels, namely with Supernovae type Ia (SNIa), Baryonic Acoustic Oscillations (BAO), cosmic chronometers (CC), and Redshift Space Distortion (RS…
A probability of distinguishing between $Λ$CDM model and modified gravity is studied by using the future observations for the growth rate of cosmic structure (Euclid redshift survey). Adopting extended DGP model, Kinetic Gravity Braiding model, and Galileon model as modified gravity, we compare predicted cosmic growth rate by models to the mock observational data. The growth rate $fσ_8$ in the original DGP model is suppressed compared with the $Λ$CDM case, for the same value of the current density parameter of matter $Ω_{m,0}$, because of the suppression of effective gravitational constant. In…
We present a scalar perturbation for the $Λ$CDM model, which breaks the isotropic symmetry of the universe. Based on the Union2 data, the least-$χ^2$ fit of the scalar perturbed $Λ$CDM model shows that the universe has a preferred direction $(l,b)=(287^\circ\pm25^\circ,11^\circ\pm22^\circ)$. The magnitude of scalar perturbation is about $-2.3\times10^{-5}$. The scalar perturbation for the $Λ$CDM model implies a peculiar velocity, which is perpendicular to the radial direction. We show that the maximum peculiar velocities at redshift $z=0.15$ and $z=0.015$ equal to $73\pm28 \rm km\cdot s^{-1}$ …
There is a growing interest in utilizing intrinsic alignment (IA) of galaxy shapes as a geometric and dynamical probe of cosmology. In this paper we present the first measurements of IA in a modified gravity model using the gravitational shear-intrinsic ellipticity correlation (GI) and intrinsic ellipticity-ellipticity correlation (II) functions of dark-matter halos from $f(R)$ gravity simulations. By comparing them with the same statistics measured in $Λ$CDM simulations, we find that the IA statistics in different gravity models show distinguishable features, with a trend similar to the case …
The holographic $Λ(t)$CDM model in a non-flat universe is studied in this paper. In this model, to keep the form of the stress-energy of the vacuum required by general covariance, the holographic vacuum is enforced to exchange energy with dark matter. It is demonstrated that for the holographic model the best choice for the IR cutoff of the effective quantum field theory is the event horizon size of the universe. We derive the evolution equations of the holographic $Λ(t)$CDM model in a non-flat universe. We constrain the model by using the current observational data, including the 557 Union2 t…
Among various phenomenological $Λ$ models, a time-dependent model $\dot Λ\sim H^3$ is selected here to investigate the $Λ$-CDM cosmology. Using this model the expressions for the time-dependent equation of state parameter $ω$ and other physical parameters are derived. It is shown that in $H^3$ model accelerated expansion of the Universe takes place at negative energy density, but with a positive pressure. It has also been possible to obtain the change of sign of the deceleration parameter $q$ during cosmic evolution.
Concordance $Λ$CDM universe is the simplest model that is consistent with a large variety of cosmological observations till date. But few recent observations indicate inconsistencies in $Λ$CDM model. In this paper, we consider the combination of recent SnIa+Bao+Cmb+Growth+$H(z)$+$H_{0}$ measurements to revisit the constraints on the dark energy evolution using the widely studied CPL parametrisation for the dark energy equation of state. Although the reconstructed behaviour for the dark energy equation of state confirms the inconsistency of $Λ$CDM at $95\%$ confidence level, the reconstructed $…
In this manuscript, we present a number of fascinating explicit reconstructions for the $f(Q)$ gravity from the background of Friedmann-Laîmatre-Robertson-Walker (FLRW) evolution history. We find the more general functions of non-metricity scalar $Q$ that admit exact $Λ$CDM expansion history. Adding extra degrees of freedom to the matter sector is the only method to get the scale factor to behave in this manner for more generic functions of $Q$. In addition, a cosmological reconstruction for modified $f(Q)$ gravity is constructed in terms of e-folding. It is shown how any FLRW cosmology can ar…
Recent anomalies found in cosmological datasets such as the low multipoles of the Cosmic Microwave Background or the low redshift amplitude and growth of clustering measured by e.g., abundance of galaxy clusters and redshift space distortions in galaxy surveys, have motivated explorations of models beyond standard $Λ$CDM. Of particular interest are models where general relativity (GR) is modified on large cosmological scales. Here we consider deviations from $Λ$CDM+GR within the context of Horndeski gravity, which is the most general theory of gravity with second derivatives in the equations o…
In this work, which follows a series of studies on the higher-dimensional steady state universe idea and prepared for Professor Tekin Dereli's Festschrift, we show the influence of the dynamical internal (unobservable) space on the evolution of the possible anisotropy of the external (observable) space. We obtain mathematically exactly the same Friedmann equation of the standard $Λ$CDM model for the external space, but with some remarkable physical differences. In particular, the higher-dimensional negative cosmological constant plays the role of the four-dimensional positive cosmological cons…
Emerging high redshift cosmological probes, in particular quasars (QSOs), show a preference for larger matter densities, $Ω_{m} \approx 1$, within the flat $Λ$CDM framework. Here, using the Risaliti-Lusso relation for standardizable QSOs, we demonstrate that the QSOs recover the \textit{same} Planck-$Λ$CDM Universe as Type Ia supernovae (SN), $Ω_m \approx 0.3$ at lower redshifts $ 0 < z \lesssim 0.7$, before transitioning to an Einstein-de Sitter Universe ($Ω_m =1$) at higher redshifts $z \gtrsim 1$. We illustrate the same trend, namely increasing $Ω_{m}$ and decreasing $H_0$ with redshift, in…
Recently the Chiral Cosmological Model (CCM) coupled to cold dark matter (CDM) has been investigated as $σ$CDM model to study the observed accelerated expansion of the Universe. Dark sector fields (as Dark Energy content) coupled to cosmic dust were considered as the source of Einstein gravity in Friedmann-Robertson-Walker (FRW) cosmology. Such model had a beginning at the matter-dominated era. The purposes of our present investigation are two folds: to extend <<life>> of the $σ$CDM for earlier times to radiation-dominated era and to take into account variation of the exponential potential via…
Two-parameter perturbation theory (2PPT) is a framework designed to include the relativistic gravitational effects of small-scale nonlinear structures on the large-scale properties of the Universe. In this paper we use the 2PPT framework to calculate and study the bispectrum of matter in a spatially-flat $Λ$CDM cosmology. This is achieved by deploying Newtonian perturbation theory to model the gravitational fields of quasi-nonlinear structures, and then subsequently using them as source terms for the large-scale cosmological perturbations. We find that our approach reproduces some of the expec…
We use observations related to the variation of fundamental constants, in order to impose constraints on the viable and most used $f(T)$ gravity models. In particular, for the fine-structure constant we use direct measurements obtained by different spectrographic methods, while for the effective Newton's constant we use a model-dependent reconstruction, using direct observational Hubble parameter data, in order to investigate its temporal evolution. We consider two $f(T)$ models and we quantify their deviation from $Λ$CDM cosmology through a sole parameter. Our analysis reveals that this param…
Rather than obtaining cosmic acceleration with a scalar field potential (quintessence) or noncanonical kinetic term (k-essence), we can do it purely through a modified gravity braiding of the scalar and metric, i.e. the $G_3$ Horndeski action term. Such "Horndessence" allows an exact $Λ$CDM cosmological expansion without any cosmological constant, and by requiring shift symmetry we can derive the exact form of $G_3$. We find that this route of deriving $G_3(X)$ leads to a functional form far from the usual simple assumptions such as a power law. Horndessence without any kinetic term or potenti…
We study observational constraints on the non-metricity $f(Q)$-gravity which reproduces an exact $Λ$CDM background expansion history while modifying the evolution of linear perturbations. To this purpose we use Cosmic Microwave Background (CMB) radiation, baryonic acoustic oscillations (BAO), redshift-space distortions (RSD), supernovae type Ia (SNIa), galaxy clustering (GC) and weak gravitational lensing (WL) measurements. We set stringent constraints on the parameter of the model controlling the modifications to the gravitational interaction at linear perturbation level. We find the model to…
Starting from an inhomogeneous space-time model of the universe we could recreate a scenario of recent time accelerating universe dominated by Dark Energy type of fluid. The background matter component of such a universe was considered to be made up of a combination of an anisotropic fluid, a barotropic fluid and the presureless cold dark matter. It was found that inhomogeneity exhibits itself as the curvature term in such a universe. We corroborated our model with recent supernova Ia-JLA data together with $H_{0}$ data and BAO data. Cosmographic analysis of the dynamical variables further sho…
We study the second-order scalar perturbations in the conventional $Λ$CDM Universe within the cosmic screening approach. The analytic expressions for both the velocity-independent and velocity-dependent second-order scalar perturbations are derived. We demonstrate how the Yukawa screening effect, which is inherent in the first-order metric corrections, manifests itself in the second-order ones. It is shown that the obtained formulas for the second-order perturbations are reduced to the known post-Newtonian expressions at distances much smaller than the Yukawa screening length. In the era of pr…
Within the effective field theory approach to cosmic acceleration, the background expansion can be specified separately from the gravitational modifications. We explore the impact of modified gravity in a background different from a cosmological constant plus cold dark matter ($Λ$CDM) on the stability and cosmological observables, including covariance between gravity and expansion parameters. In No Slip Gravity the more general background allows more gravitational freedom, including both positive and negative Planck mass running. We examine the effects on cosmic structure growth, as well as sh…
We study late-time cosmic accelerating dynamics from Born-Infeld-$f(R)$ gravity in a simplified conformal approach. We find that a variety of cosmic efects such as Little Rip, $Λ$CDM universe and dark energy cosmology with finite-time future singularities may occur. Unlike the convenient Born-Infeld gravity where in the absence of matter only de Sitter expansion may emerge, apparentlly any FRW cosmology maybe reconstructed from this conformal version of the Born-Infeld-$f(R)$ theory. Despite the fact that the explicit form of $f(R)$ is fixed by the conformal ansatz, the relation between the tw…
A time-dependent phenomenological model of $Λ$, viz. $\dot Λ\sim H^3$ is selected to investigate the $Λ$-CDM cosmology. Time-dependent form of the equation of state parameter $ω$ is derived and it has been possible to obtain the sought for flip of sign of the deceleration parameter q. Present age of the Universe, calculated for some specific values of the parameters agrees very well with the observational data.
Noether's theory offers us a useful tool to research the conserved quantities and symmetries of the modified gravity theories, among which the $f(T)$ theory, a generally modified teleparallel gravity, has been proposed to account for the dark energy phenomena. By the Noether symmetry approach, we investigate the power-law, exponential and polynomial forms of $f(T)$ theories. All forms of $f(T)$ concerned in this work possess the time translational symmetry, which is related with energy condition or Hamilton constraint. In addition, we find out that the performances of the power-law and exponen…
We re-analyze the nonlocal gravity model of Deser and Woodard which was proposed to account for the current phase of cosmic acceleration. We show that the growth of perturbations predicted by this nonlocal gravity model when its background evolution is fixed by some particular non-$Λ$CDM models can be substantially lower than when its background is fixed by $Λ$CDM. This can be seen when we consider the background expansion by a dark energy model with a slightly less negative equation of state with respect to cosmological constant. Our results hints towards a fact that the choice of the backgro…
We propose a connection between global physics and local galactic dynamics via quantum gravity. The salient features of cold dark matter (CDM) and modified Newtonian dynamics (MOND) are combined into a unified scheme by introducing the concept of MONDian dark matter which behaves like CDM at cluster and cosmological scales but emulates MOND at the galactic scale.
We use the local value of the Hubble constant recently measured with 2.4% precision, as well as the latest compilation of cosmic chronometers data, together with standard probes such as Supernovae Type Ia and Baryon Acoustic Oscillation distance measurements, in order to impose constraints on the viable and most used f(T) gravity models, where T is the torsion scalar in teleparallel gravity. In particular, we consider three f(T) models with two parameters, out of which one is independent, and we quantify their deviation from $Λ$CDM cosmology through a sole parameter. Our analysis reveals that …
We study the cosmological predictions of two recently proposed non-local modifications of General Relativity. Both models have the same number of parameters as $Λ$CDM, with a mass parameter $m$ replacing the cosmological constant. We implement the cosmological perturbations of the non-local models into a modification of the CLASS Boltzmann code, and we make a full comparison to CMB, BAO and supernova data. We find that the non-local models fit these datasets as well as $Λ$CDM. For both non-local models parameter estimation using Planck+JLA+BAO data gives a value of $H_0$ higher than in $Λ$CDM,…
We point out that $Λ$CDM cosmology has an ignored assumption. That is, the $Λ$ component of the universe moves synchronously with ordinary matters on Hubble scales. If cosmological constant is vacuum energy, this assumption may be very difficult to be understood. We then propose a new mechanism which can explain the accelerating recession of super-novaes. That is, considering the pressures originating from the random moving (including Hubble recession) of galaxy clusters and galaxies. We provide an new analytical solution of Einstein equation which may describe a universe whose pressures origi…
We analyze Brans-Dicke gravity with a cosmological constant, $Λ$, and cold dark matter (BD-$Λ$CDM for short) in the light of the latest cosmological observations on distant supernovae, Hubble rate measurements at different redshifts, baryonic acoustic oscillations, large scale structure formation data, gravitational weak-lensing and the cosmic microwave background under full Planck 2015 CMB likelihood. Our analysis includes both the background and perturbations equations. We find that BD-$Λ$CDM is observationally favored as compared to the concordance $Λ$CDM model, which is traditionally defin…
We show that a cosmology driven by gravitationally induced particle production of all non-relativistic species existing in the present Universe mimics exactly the observed flat accelerating $Λ$CDM cosmology with just one dynamical free parameter. This kind of scenario includes the creation cold dark matter (CCDM) model [Lima, Jesus & Oliveira, JCAP 011(2010)027] as a particular case and also provides a natural reduction of the dark sector since the vacuum component is not needed to accelerate the Universe. The new cosmic scenario is equivalent to $Λ$CDM both at the background and perturbative …
Recent analyses \cite{Nesseris:2017vor,Kazantzidis:2018rnb} have indicated that an effective Newton's constant $G_{\rm eff}(z)$ decreasing with redshift may relieve the observed tension between the Planck15 best fit $Λ$CDM cosmological background ({\it i.e.} Planck15/$Λ$CDM) and the corresponding $Λ$CDM background favored by growth $fσ_8$ and weak lensing data. We investigate the consistency of such a decreasing $G_{\rm eff}(z)$ with some viable scalar-tensor models and $f(R)$ theories. We stress that $f(R)$ theories generically can not lead to a decreasing $G_{\rm eff}(z)$ for any cosmologica…
We construct a generalization of the standard $Λ$CDM model, wherein we simultaneously replace the spatially flat Robertson-Walker metric with its simplest anisotropic generalization (LRS Bianchi I metric), and couple the cold dark matter to the gravity in accordance with the energy-momentum squared gravity (EMSG) of the form $f(T_{μν}T^{μν})\propto T_{μν}T^{μν}$. These two modifications -- namely, two new stiff fluid-like terms of different nature -- can mutually cancel out, i.e., the shear scalar can be screened completely, and reproduce mathematically exactly the same Friedmann equation of t…
We proposed five $f(Q,T)$ models, which are an extension of symmetric teleparallel gravity, where $Q$ is the non-metricity and $T$ is the trace of the stress-energy tensor. By taking specific values of their parameters, these models have a $Λ$CDM limit. Using cosmic chronometers and supernovae Ia data, we found that our models are consistent with $Λ$CDM at a 95\% confidence level. To see whether one of these models can challenge $Λ$CDM at a background perspective, we computed the Bayesian evidence for them and $Λ$CDM. According to it, the concordance model is preferred over four of them, showi…
We search for possible deviations from the expectations of the concordance $Λ$CDM model in the expansion history of the Universe by analysing the Pantheon Type Ia Supernovae (SnIa) compilation along with its Monte Carlo simulations using redshift binning. We demonstrate that the redshift binned best fit $Λ$CDM matter density parameter $Ω_{0m}$ and the best fit effective absolute magnitude $\cal M$ oscillate about their full dataset best fit values with considerably large amplitudes. Using the full covariance matrix of the data taking into account systematic and statistical errors, we show that…
We consider Horndeski modified gravity models obeying stability, velocity of gravitational waves $c_T$ equals $c$ and quasistatic approximation (QSA) on subhorizon scales. We assume further a $Λ$CDM background expansion and a monotonic evolution on the cosmic background of the $α$ functions as $α_i= α_{i0}~a^s$ where $i=M,B$, $a$ is the scale factor and $α_{i0}$ ($α_{M0}, α_{B0}$), $s$ are arbitrary parameters. We show that the growth and lensing reduced (dimensionless) gravitational couplings $μ\equiv G_{\rm growth}/G$, $Σ\equiv G_{\rm lensing}/G$ exhibit the following generic properties toda…
We confront dark energy models which are currently similar to $Λ$CDM theory with observational data which include the SNe data, matter density perturbations and baryon acoustic oscillations data. DE cosmology under consideration may evolve to Big Rip, type II or type III future singularity, or to Little Rip or Pseudo-Rip universe. It is shown that matter perturbations data define more precisely the possible deviation from $Λ$CDM model than consideration of SNe data only. The combined data analysis proves that DE models under consideration are as consistent as $Λ$CDM model. We demonstrate that …
In this letter we investigate some consequences of considering our 4D observable universe as locally and isometrically embeded into a 5D spacetime, where gravity is described by a Brans-Dicke theory in vacuum. Once we impose the embeding conditions we obtain that gravity on the 4D spacetime is governed by the Einstein field equations modified by an extra term that can play the role of a dynamical cosmological constant. Two examples were studied. In the first we derive a cosmological model of a universe filled only with a cosmological constant. In the second we obtain a cosmological solution de…
In this paper, we make a comparison for the impacts of smooth dynamical dark energy, modified gravity, and interacting dark energy on the cosmological constraints on the total mass of active neutrinos. For definiteness, we consider the $Λ$CDM model, the $w$CDM model, the $f(R)$ model, and two typical interacting vacuum energy models, i.e., the I$Λ$CDM1 model with $Q=βHρ_{\rm c}$ and the I$Λ$CDM2 model with $Q=βHρ_Λ$. In the cosmological fits, we use the Planck 2015 temperature and polarization data, in combination with other low-redshift observations including the baryon acoustic oscillations,…
We discuss how dynamical dark energy universes with exotic singularities may be distinguished from the standard $Λ$CDM model on the basis of their redshift drift signal, for which measurements both in the acceleration phase and in the deep matter era will be provided by forthcoming astrophysical facilities. Two specific classes of exotic singularity models are studied: sudden future singularity models and finite scale factor singularity models. In each class we identify the models which can mimic $Λ$CDM and play the role of dark energy as well as models for which redshift drift signals are sig…
In this work, we extend previous analyses of the structure formation in the $f(\Box^{-1}R)$ model of nonlocal gravity proposed by Deser and Woodard (DW), which reproduces the background expansion of $Λ$CDM with no need of a cosmological constant nor of any dimensional constant beside Newton's one. A previous analysis based on redshift-space distortions (RSD) data concluded that the model was ruled out. In this work we revisit the issue and find that, when recast in a localized model, the DW model is not ruled out and actually gives a better fit to RSD data than $Λ$CDM. At the same time, the mo…
It is shown here that in a flat, cold dark matter (CDM) dominated Universe with positive cosmological constant ($Λ$), modelled in terms of a Newtonian and collisionless fluid, particle trajectories are analytical in time (representable by a convergent Taylor series) until at least a finite time after decoupling. The time variable used for this statement is the cosmic scale factor, i.e., the "$a$-time", and not the cosmic time. For this, a Lagrangian-coordinates formulation of the Euler-Poisson equations is employed, originally used by Cauchy for 3-D incompressible flow. Temporal analyticity fo…
We study here how the presence of non-zero matter density and a cosmological constant could affect the observation of gravitational waves in Pulsar Timing Arrays. Conventionally, the effect of matter and cosmological constant is included by considering the redshift in frequency due to the expansion. However, there is an additional effect due to the change of coordinate systems from the natural ones in the region where waves are produced to the ones used to measure the pulsar timing residuals. This change is unavoidable as the strong gravitational field in a black hole merger distorts clocks an…
The age problem in the $Λ$CDM model is re-examined. We define the elapsed time $T$ of an object is its age plus the age of the Universe when it was born. Therefore in any cosmology, $T$ must be smaller than the age of the Universe. For the old quasar APM 08279+5255 at $z=3.91$, previous studies have determined the best-fit value of $T$, 1 $σ$ lower limit and the lowest limit to $T$ are 2.3, 2.0 and 1.7 Gyr, respectively. Constrained from SNIa$+R+A+d$, SNIa$+R+A+d+H(z)$, and WMAP5+2dF+SNLS+HST+BBN, the $Λ$CDM model can only accommodate $T(z=3.91)=1.7$ Gyr at 1 $σ$ deviation. Constrained from WM…
We present a detailed investigation of the Rastall gravity extension of the standard $Λ$CDM model. We review the model for two simultaneous modifications of different nature in the Friedmann equation due to the Rastall gravity: the new contributions of the material (actual) sources (considered as effective source) and the altered evolution of the material sources. We discuss the role/behavior of these modifications with regard to some low redshift tensions, including the so-called $H_0$ tension, prevailing within the standard $Λ$CDM. We constrain the model at the level of linear perturbations,…
Comparative Analysis of Perturbed $f(R)$ Gravity and Perturbed Rastall Gravity Models in Describing Cosmic Evolution from Early to Late Universe Relative to the $Λ$CDM Model
In this paper we compare outcomes of some extended phantom-like cosmologies with each other and also with $Λ$CDM\, and $Λ$DGP. We focus on the variation of the luminosity distances, the age of the universe and the deceleration parameter versus the redshift in these scenarios. In a dynamical system approach, we show that the accelerating phase of the universe in the $f(R)$-DGP scenario is stable if one consider the \emph{curvature fluid} as a phantom scalar field in the equivalent scalar-tensor theory, otherwise it is a transient and unstable phenomenon. Up to the parameters values adopted in t…
In this study, we investigate the effect of the generalized uncertainty principle on the $Λ$CDM cosmological model. Using quantum corrected Unruh effect and Verlinde's entropic gravity idea, we find Planck-scale corrected Friedmann equations with a cosmological constant. These results modify the $Λ$CDM cosmology.
