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Our paper introduces a new theory called Fractional Einstein-Gauss-Bonnet scalar field cosmology, which has significant implications for Cosmology. We derived a modified Friedmann equation and a modified Klein-Gordon equation using fractional calculus to modify the gravitational action integral. Our research reveals non-trivial solutions associated with exponential potential, exponential couplings to the Gauss-Bonnet term, and logarithmic scalar field, which are dependent on two cosmological parameters, $m$ and $\alpha_{0}=t_{0}H_{0}$ and the fractional derivative order $\mu$. By employing linear stability theory, we reveal the phase space structure and analyze the dynamic effects of the Gauss-Bonnet couplings. The scaling behavior at some equilibrium points reveals that the geometric corrections in the coupling to the Gauss-Bonnet scalar can mimic the behavior of the dark sector in modified gravity. Using data from cosmic chronometers, type Ia supernovae, supermassive black hole shadows, and strong gravitational lensing, we estimated the values of $m$ and $\alpha_{0}$, indicating that the solution is consistent with an accelerated expansion at late times with the values $\alpha_0=1.38\pm 0.05$, $m=1.44\pm 0.05$, and $\mu=1.491$ (consistent with $\Omega_{m,0}=0.311\pm 0.016$ and $h=0.712\pm 0.007$), resulting in an age of the Universe $t_{0}=19.0\pm 0.7$ [Gyr] at 1$\sigma$ CL. Ultimately, we obtained late-time accelerating power-law solutions supported by the most recent cosmological data, and we proposed an alternative explanation for the origin of cosmic acceleration other than $\Lambda$CDM. Our results generalize and significantly improve previous achievements in the literature, highlighting the practical implications of fractional calculus in Cosmology., Comment: 56 pages, 16 compound figures

The Kasner spacetimes are exact solutions that are self-similar and of significant interest because they can describe the dynamic evolution of kinematic variables near the singularity of the Mixmaster universe. The chaotic behavior of the Mixmaster universe is related to the Kasner relations. This study investigates Kasner and Kasner-like solutions in symmetric teleparallel $f\left( Q\right) $-gravity. We consider three families of connections for the spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker. We found that Kasner-like solutions are present in the theory when the nonmetricity scalar $Q$ vanishes. Kasner-like relations are introduced only for the field equations of the connection defined in the coincidence gauge. Finally, we perform a detailed phase-space analysis to understand the dynamics of $f\left( Q\right) $-gravity in the evolution of anisotropies and the effects of different connections on this evolution., Comment: 24 pages, no figures

We study the dynamics of the field equations in a five-dimensional spatially flat Friedmann-Lema\^itre-Robertson-Walker metric in the context of a Gauss-Bonnet-Scalar field theory where the quintessence scalar field is coupled to the Gauss-Bonnet scalar. Contrary to the four-dimensional Gauss-Bonnet theory, where the Gauss-Bonnet term does not contribute to the field equations, in this five-dimensional Einstein-Scalar-Gauss-Bonnet model, the Gauss-Bonnet term contributes to the field equations even when the coupling function is a constant. Additionally, we consider a more general coupling described by a power-law function. For the scalar field potential, we consider the exponential function. For each choice of the coupling function, we define a set of dimensionless variables and write the field equations into a system of ordinary differential equations. We perform a detailed analysis of the dynamics for both systems and classify the stability of the equilibrium points. We determine the presence of scaling and super-collapsing solutions using the cosmological deceleration parameter. This means that our models can explain the Universe's early and late-time acceleration phases. Consequently, this model can be used to study inflation or as a dark energy candidate., Comment: 31 pages, 6 tables, 14 compound figures

Fractional differential calculus is a mathematical tool that has found applications in the study of social and physical behaviors considered ``anomalous''. It is often used when traditional integer derivatives models fail to represent cases where the power law is observed accurately. Fractional calculus must reflect non-local, frequency- and history-dependent properties of power-law phenomena. This tool has various important applications, such as fractional mass conservation, electrochemical analysis, groundwater flow problems, and fractional spatiotemporal diffusion equations. It can also be used in cosmology to explain late-time cosmic acceleration without the need for dark energy. We review some models using fractional differential equations. We look at the Einstein--Hilbert action, which is based on a fractional derivative action, and add a scalar field, $\phi$, to create a non-minimal interaction theory with the coupling, $\xi R \phi^2 $, between gravity and the scalar field, where $\xi$ is the interaction constant. By employing various mathematical approaches, we can offer precise schemes to find analytical and numerical approximations of the solutions. Moreover, we comprehensively study the modified cosmological equations and analyze the solution space using the theory of dynamical systems and asymptotic expansion methods. This enables us to provide a qualitative description of cosmologies with a scalar field based on fractional calculus formalism., Comment: 99 pages, 3 tables, 20 compound figures (This article belongs to the Special Issue Advances in Fractional Modeling and Computation) https://www.mdpi.com/journal/fractalfract/special_issues/4X6L41Z9X2

In Yukawa cosmology, a recent discovery revealed a relationship between baryonic matter and the dark sector. The relation is described by the parameter {\alpha} and the long-range interaction parameter {\lambda} - an intrinsic property of the graviton. Applying the uncertainty relation to the graviton raises a compelling question: Is there a quantum mechanical limit to the measurement precision of the Hubble constant (H0)? We argue that the uncertainty relation for the graviton wavelength {\lambda} can be used to explain a running of H0 with redshift. We show that the uncertainty in time has an inverse correlation with the value of the Hubble constant. That means that the measurement of the Hubble constant is intrinsically linked to length scales (redshift) and is connected to the uncertainty in time. On cosmological scales, we found that the uncertainty in time is related to the look-back time quantity. For measurements with a high redshift value, there is more uncertainty in time, which leads to a smaller value for the Hubble constant. Conversely, there is less uncertainty in time for local measurements with a smaller redshift value, resulting in a higher value for the Hubble constant. Therefore, due to the uncertainty relation, the Hubble tension is believed to arise from fundamental limitations inherent in cosmological measurements. Finally, our findings indicate that the mass of the graviton fluctuates with specific scales, suggesting a possible mass-varying mechanism for the graviton., Comment: 19 pages, 7 compound figures, 3 tables, references added, subsections added, discussion was improved

This study derives a novel family of charged black hole solutions featuring short- and long-range modifications. These ones are achieved through a Yukawa-like gravitational potential modification and a nonsingular electric potential incorporation. The short-range corrections encode quantum gravity effects, while the long-range adjustments simulate gravitational effects akin to those attributed to dark matter. Our investigation reveals that the total mass of the black hole undergoes corrections owing to the apparent presence of dark matter mass and the self-adjusted electric charge mass. Two distinct solutions are discussed: a regular black hole solution characterizing small black holes, where quantum effects play a crucial role, and a second solution portraying large black holes at considerable distances, where the significance of Yukawa corrections comes into play. Notably, these long-range corrections contribute to an increase in the total mass and hold particular interest as they can emulate the role of dark matter. Finally, we explore the phenomenological aspects of the black hole. Specifically, we examine the influence of electric charge and Yukawa parameters on thermodynamic quantities, the quasinormal modes for the charged scalar perturbations as well as for the vector perturbations, analysis of the geodesics of light/massive particles, and the accretion of matter onto the charged black hole solution., Comment: 19 pages in two column, 18 figures and 2 tables

We investigate the impact of conformal transformations on the physical properties of solution trajectories in nonmetricity gravity. Specifically, we explore the phase-space and reconstruct the cosmological history of a spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker universe within scalar-nonmetricity theory in both the Jordan and Einstein frames. A detailed analysis is conducted for three different connections defined in both the coincident and non-coincident gauges. Our findings reveal the existence of a unique one-to-one correspondence for equilibrium points in the two frames. Furthermore, we demonstrate that solutions describing accelerated universes remain invariant under the transformation that relates these conformally equivalent theories., Comment: 35 pages, 5 figures, Latex2e source file

This study uses a nonsingular Yukawa--modified potential to obtain a static and spherically symmetric black hole solution with a cosmological constant. Such Yukawa--like corrections are encoded in two parameters, $\alpha$ and $\lambda$, that modify Newton's law of gravity in large distances, and a deformation parameter $\ell_0$, which plays an essential role in short distances. The most significant effect is encoded in $\alpha$, which modifies the total black hole mass with an extra mass proportional to $\alpha M$, mimicking the dark matter effects at large distances from the black hole. On the other hand, the effect due to $\lambda$ is small for astrophysical values. We scrutinize the \textit{quasinormal} frequencies and shadows associated with a spherically symmetric black hole and the thermodynamical behavior influenced by the Yukawa potential. In particular, the thermodynamics of this black hole displays a rich behavior, including possible phase transitions. We use the WKB method to probe the \textit{quasinormal} modes of massless scalar, electromagnetic, and gravitational field perturbations. In order to check the influence of the parameters on the shadow radius, we consider astrophysical data to determine their values, incorporating information on an optically thin radiating and infalling gas surrounding a black hole to model the black hole shadow image. In particular, we consider Sgr A* black hole as an example and we find that its shadow radius changes by order of $10^{-9}$, meaning that the shadow radius of a black hole with Yukawa potential practically gives rise to the same result encountered in the Schwarzschild black hole. Also, in the eikonal regime, using astrophysical data for Yukawa parameters, we show that the value of the real part of the QNMs frequencies changes by $10^{-18}$., Comment: 24 pages in double column, 13 figures and 5 tables

This research focuses on scalar field cosmologies with a generalized harmonic potential. Our attention is centred on the anisotropic LRS Bianchi I and III metrics, Bianchi V metrics, and their isotropic limits. We provide a comprehensive overview of the first two metrics classes and offer new findings for Bianchi V metrics. We show that the Hubble parameter is a time-dependent perturbation parameter that controls the magnitude of the error between full-system and time-averaged solutions as it decreases, such that those complete and time-averaged systems have the same asymptotic behaviour. Therefore, oscillations entering the system can be controlled and smoothed out, which simplifies the problem at hand., Comment: Research Program Averaging Generalized Scalar Field Cosmologies, part IV. 40 pages, 4 compound figures. Updated references

We comprehensively analyze the dynamics for the gravitational field equations for the Chiral-Quintom theory in a Friedman-Lema\^itre-Robertson-Walker cosmology with an additional matter source. We consider a new set of dimensionless variables and write the field equations in the equivalent form of an algebraic-differential system. Specifically, we consider two families of quintom models where the two scalar fields interact in the kinetic sector. We mathematically focus on the dynamical effect of spatial curvature. Physically, we find two periods of inflation related to the Universe's early and late-time acceleration phases., Comment: 71 pages, 18 figures

We explore the phase-space of a multiscalar-torsion gravitational theory within a cosmological framework characterized by a spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker model. Our investigation focuses on teleparallelism and involves a gravitational model featuring two scalar fields, where one scalar field is coupled to the torsion scalar. We consider coupling in the two scalar fields' kinetic and potential components. We employ exponential functions for the scalar field potentials and analyze the field equations' equilibrium points to reconstruct the cosmological evolution. Remarkably, we discover many equilibrium points in this multiscalar field model, capable of describing various eras of cosmological evolution. Hence, this model can be used to describe the early and late time acceleration phases of the universe and as a unification model for the elements of the dark sector of the universe., Comment: 32 pages, 16 compound figures, revised version, improved discussion

We confront Yukawa modified cosmology, proposed in arXiv:2304.11492 [Jusufi et al. arXiv:2304.11492], with data from Supernovae Type Ia (SNe Ia) and Hubble parameter (OHD) observations. Yukawa cosmology is obtained from a Yukawa-like gravitational potential, with coupling parameter $\alpha$ and wavelength parameter $\lambda$, which gives rise to modified Friedmann equations. We show that the agreement with observations is very efficient, and within $1\sigma$ confidence level we find the best-fit parameters $\lambda=\left(2693_{-1262}^{+1191}\right)\, \rm Mpc$, $\alpha=0.416_{-0.326}^{+1.137}$, and a graviton mass of $m_{g}=\left(2.374_{-0.728}^{+2.095}\right)\times 10^{-42}\, \text{GeV}$. Additionally, we establish a connection between the effective dark matter and dark energy density parameters and the angular radius of the black hole shadow of the SgrA and M87 black holes in the low-redshift limit, consistent with the Event Horizon Telescope findings., Comment: 13 pages, 5 figures. Minor changes

Recently, a new field of study called fractional cosmology has emerged. It uses fractional calculus to modify the standard derivative equations and change the Friedmann equations. The evolution of cosmic species densities is also affected by the $\mu$ fractional parameter and the age of the Universe $t_0$. This new approach to cosmology modifies the Friedmann equations and allows for a late cosmic acceleration without the need for a dark energy component. This could be a breakthrough in solving longstanding problems in cosmology. By analyzing observational Hubble data and Type Ia supernovae, we have been able to place strict constraints on the fractional and cosmological parameters. Our results suggest that the Universe may be older than previously estimated. We also explore whether fractional cosmology can help resolve the $H_0$ tension., Comment: We have gathered information from arXiv:2207.00878 and arXiv:2303.16409 to create a report on the topic of [gr-qc]. The report focuses on the presentation given by Genly Leon at the Tensions in Cosmology Corfu2022 conference, titled "Cosmology under the fractional calculus approach: a possible $H_0$ tension resolution?" (limit of 15 pages)

We argue that the effect of cold dark matter in the cosmological setup can be explained by the coupling between the baryonic matter particles in terms of the long-range force having a graviton mass $m_g$ via the Yukawa gravitational potential. Such a quantum-corrected Yukawa-like gravitational potential is characterized by the coupling parameter $\alpha$, the wavelength parameter $\lambda$, which is related to the graviton mass via $m_g=\hbar/(\lambda c)$, that determines the range of the force and, finally, a Planck length quantity $l_0$ that makes the potential regular at the centre. The corrected Friedmann equations are obtained using Verlinde's entropic force interpretation of gravity based on the holographic scenario and the equipartition law of energy. The parameter $\alpha$ modifies Newton's constant as $G_{\rm eff}\rightarrow G(1+\alpha)$. We argue that dark matter is an apparent effect as no dark matter particle exists in this picture. Furthermore, the dark energy is also related to graviton mass and $\alpha$; in particular, we point out that the cosmological constant can be viewed as a self-interaction effect between gravitons. We further show that there exists a precise correspondence with Verlinde's emergent gravity theory, and due to the long-range force, the theory can be viewed as a non-local gravity theory. To this end, we performed the phase space analyses and estimated $\lambda\simeq 10^3 $[Mpc] and $\alpha \in (0.0385,0.0450)$, respectively. Finally, from these values, for the graviton mass, we get $m_g\simeq 10^{-68}$ kg, and cosmological constant $\Lambda \simeq 10^{-52}\rm m^{-2}$. Further, we argue how this theory reproduces the MOND phenomenology on galactic scales via the acceleration of Milgrom $a_0 \simeq 10^{-10}\rm m/s^2$., Comment: 13 pages, 4 figures, final version

We study the dynamics of the field equations in a four-dimensional isotropic and homogeneous spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker geometry in the context of Einstein-Gauss-Bonnet theory with a matter source and a scalar field coupled to the Gauss-Bonnet scalar. In this theory, the Gauss-Bonnet term contributes to the field equations. The mass of the scalar field depends on the potential function and the Gauss-Bonnet term. For the scalar field potential, we consider the exponential function and the coupling function between the scalar field and the Gauss-Bonnet scalar is considered to be the linear function. Moreover, the scalar field can have a phantom behaviour. We consider a set of dimensionless variables and write the field equations into a system or algebraic-differential equations. For the latter, we investigate the equilibrium points and their stability properties. In order to perform a global analysis of the asymptotic dynamics, we use compactified variables. This gravitational theory can explain the Universe's recent and past acceleration phases. Therefore, it can be used as a toy model for studying inflation or as a dark energy candidate., Comment: 33 pages, 11 compound figures

This paper investigates exact solutions of cosmological interest in fractional cosmology. Given $\mu$, the order of Caputo's fractional derivative, and $w$, the matter equation of state, we present specific exact power-law solutions. We discuss the exact general solution of the Riccati Equation, where the solution for the scale factor is a combination of power laws. Using cosmological data, we estimate the free parameters. An analysis of type Ia supernovae (SNe Ia) data and the observational Hubble parameter data (OHD), also known as cosmic chronometers, and a joint analysis with data from SNe Ia + OHD leads to best-fit values for the free parameters calculated at $1\sigma$, $2\sigma$ and $3\sigma$ confidence levels (CLs). On the other hand, these best-fit values are used to calculate the age of the Universe, the current deceleration parameter (both at $3\sigma$ CL) and the current matter density parameter at $1\sigma$ CL. Finding a Universe roughly twice as old as the one of $\Lambda$CDM is a distinction of fractional cosmology. Focusing our analysis on these results, we can conclude that the region in which $\mu>2$ is not ruled out by observations. This parameter region is relevant because fractional cosmology gives a power-law solution without matter, which is accelerated for $\mu>2$. We present a fractional origin model that leads to an accelerated state without appealing to $\Lambda$ or dark energy., Comment: 56 pages, 10 figures. This article belongs to the Special Issue Fractional Gravity/Cosmology in Classical and Quantum Regimes in Fractal and Fractional

We perform a detailed study of the phase-space of the field equations of an Einstein-Gauss-Bonnet scalar field cosmology for a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker spacetime. For the scalar field potential, we consider the exponential function. In contrast, for the coupling function of the scalar field with the Gauss-Bonnet term, we assume two cases, the exponential function and the power-law function. We write the field equations in dimensionless variables and study the equilibrium points using Poincare variables. For the exponential coupling function, the asymptotic solutions describe de Sitter universes or spacetimes where the Gauss-Bonnet term dominates. We recovered previous results but found new asymptotic solutions not previously studied. For the power-law coupling function, equilibrium points which describe the scaling solution appear. Finally, the power-law coupling provides a rich cosmological phenomenology., Comment: 56 pages, 50 compound figures

We use the recently modified Friedmann equations obtained from string T-duality effects that encode the zero-point length (Phys. Lett. B 836 (2023), 137621) to study the phase space analyses of a bouncing early universe. An important implication of such stringy effects is that they can alleviate the initial singularity since the Raychaudhuri equation is modified. We investigate if the Universe can undergo an accelerated expansion phase for a specific domain of the equation of state parameter. The stringy effects are encoded in the parameter $\Gamma$, which depends not only on the zero-point length but also on the state parameter $\omega$. We construct two dynamical systems depending on whether $-1 < \omega \leq -1/3$ and $\omega \geq -1/3$, and we classify the equilibrium points of each system. Exact solutions and cosmological implications are discussed., Comment: 21 pages, 2 compound figures

Recently, the research community has been exploring fractional calculus to address problems related to cosmology; in this approach, the gravitational action integral is altered, leading to a modified Friedmann equation, then the resulting theory is compared against observational data. In this context, dynamical systems can be used along with an analysis the phase spaces for different values of the fractional order of the derivative and their different matter contents. The equilibrium points are classified, providing a range for the order of the fractional derivative in order to investigate whether the cosmological history can be reconstructed and a late-time accelerating power-law solution obtained for the scale factor. In this paper, we discuss the physical interpretation of the corresponding cosmological solutions with particular emphasis on the influence of the fractional order of the derivative in a theory of gravity that includes a scalar field minimally coupled to gravity. The presented results improve and extend those obtained previously, further demonstrating that fractional calculus can play a relevant role in cosmology., Comment: 58 pages, 8 figures. This article belongs to the Special Issue Fractional Gravity/Cosmology in Classical and Quantum Regimes https://www.mdpi.com/journal/fractalfract/special_issues/fractional_cosmology

The Noether symmetry analysis is applied in a multi-scalar field cosmological model in teleparallel gravity. In particular, we consider two scalar fields with interaction in scalar-torsion theory. The field equations have a minisuperspace description, and the evolution of the physical variables depends on the potential function that drives the scalar fields' dynamics. With the requirement for the field equations to admit non-trivial Noether point symmetries and the use of the first theorem of Noether, we constraint all the functional forms for the potential. Finally, we apply symmetry vectors and the corresponding conservation laws to determine exact and analytic solutions in multiscalar-torsion cosmology., Comment: 20 pages, no figures

In this paper, we investigate a non-interacting scalar field cosmology with an arbitrary potential using the $f$-deviser method that relies on the differentiability properties of the potential. Using this alternative mathematical approach, we present a unified dynamical system analysis at a scalar field's background and perturbation levels with arbitrary potentials. For illustration, we consider a monomial and double exponential potential. These two classes of potentials comprise the asymptotic behaviour of several classes of scalar field potentials, and, therefore, they provide the skeleton for the typical behaviour of arbitrary potentials. Moreover, we analyse the linear cosmological perturbations in the matterless case by considering three scalar perturbations: the evolution of the Bardeen potentials, the comoving curvature perturbation, the so-called Sasaki-Mukhanov variable, or the scalar field perturbation in uniform curvature gauge. Finally, an exhaustive dynamical system analysis for each scalar perturbation is presented, including the evolution of Bardeen potentials in the presence of matter., Comment: 79 pages, 16 compound figures. Major revision. Discussion improved. References added

We investigate the phase space of a scalar field theory obtained by minisuperspace deformation. We consider quintessence or phantom scalar fields in the action which arise from minisuperspace deformation on the Einstein-Hilbert action. We use a modified Poisson Algebra where Poisson brackets are the $\alpha$-deformed ones and are related to the Moyal-Weyl star product. We discuss early and late-time attractors, and we reconstruct the cosmological evolution. We show that the model can have $\Lambda$CDM model as a future attractor if we initially consider a massless scalar field without a cosmological constant term., Comment: 13 pages, 8 compound figures

In the context of the modified teleparallel $f(T, B)$-theory of gravity, we consider a homogeneous and anisotropic background geometry described by the Kantowski-Sachs line element. We derive the field equations and investigate the existence of exact solutions. Furthermore, the evolution of the trajectories for the field equations is studied by deriving the stationary points at the finite and infinite regimes. For the $f(T,B)=T+F\left( B\right) $ theory, we prove that for a specific limit of the function $F\left( B\right) $, the anisotropic Universe has the expanding and isotropic Universe as an attractor with zero spatial curvature. We remark that there are no future attractors where the asymptotic solution describes a Universe with nonzero spatial curvature., Comment: 18 pages, 2 figures

We study the asymptotic dynamics of $f(T, B)$-theory in an anisotropic Bianchi III background geometry. We show that an attractor always exists for the field equations, which depends on a free parameter provided by the specific $f(T, B)$ functional form. The attractor is an accelerated spatially flat FLRW or non-accelerated LRS Bianchi III geometry. Consequently, the $f(T, B)$-theory provides a spatially flat and isotropic accelerated Universe., Comment: 14 pages, 2 figures

We address the important issue of isotropisation of a pre-bounce contracting phase in $f(R)$ gravity, which would be relevant to construct any viable nonsingular bouncing scenario in $f(R)$ gravity. The main motivation behind this work is to investigate whether the $f(R)$ gravity, by itself, can isotropise a contracting universe starting initially with small anisotropy without incorporating a super-stiff or non-ideal fluid, that is impossible in general relativity. Considering Bianchi I cosmology and employing a dynamical system analysis, we see that this is not possible for $R^n$ ($n>1$) and $R+\alpha R^2$ ($\alpha>0$) theory, but possible for $\frac{1}{\alpha}e^{\alpha R}$ ($\alpha>0$) theory. On the other hand, if one does not specify an $f(R)$ theory a priori but demands a cosmology smoothly connecting an ekpyrotic contraction phase to a nonsingular bounce, the ekpyrotic phase \emph{may} not fulfil the condition for isotropisation and physically viability simultaneously., Comment: 35 pages, 4 figures

Fractional cosmology modifies the standard derivative to Caputo's fractional derivative of order $\mu$, generating changes in General Relativity. Friedmann equations are modified, and the evolution of the species densities depends on $\mu$ and the age of the Universe $t_U$. We estimate stringent constraints on $\mu$ using cosmic chronometers, Type Ia supernovae, and joint analysis. We obtain $\mu=2.839^{+0.117}_{-0.193}$ within the $1\sigma$ confidence level providing a non-standard cosmic acceleration at late times; consequently, the Universe would be older than the standard estimations. Additionally, we present a stability analysis for different $\mu$ values. This analysis identifies a late-time attractor corresponding to a power-law decelerated solution for $\mu < 2$. Moreover, a non-relativistic critical point exists for $\mu > 1$ and a sink for $\mu > 2$. This solution is a decelerated power-law if $1 < \mu < 2$ and an accelerated power-law solution if $\mu > 2$, consistent with the mean values obtained from the observational analysis. Therefore, for both flat FLRW and Bianchi I metrics, the modified Friedmann equations provide a late cosmic acceleration under this paradigm without introducing a dark energy component. This approach could be a new path to tackling unsolved cosmological problems., Comment: 15 pages, 8 figures. Moderate revision. Matches the version accepted for publication in MNRAS

We investigate the inflation driven by a nonlinear electromagnetic field based on an NLED lagrangian density ${\cal L}_{\text{nled}} = - {F} f \left( {F} \right)$, where $f \left( {F}\right)$ is a general function depending on ${F}$. We first formulate an $f$-NLED cosmological model with a more general function $f \left( {F}\right)$ and show that all NLED models can be expressed in this framework; then, we investigate in detail two interesting examples of the function $f \left( {F}\right)$. We present our phenomenological model based on a new Lagrangian for NLED. Solutions to the field equations with the physical properties of the cosmological parameters are obtained. We show that the early Universe had no Big-Bang singularity, which accelerated in the past. We also investigate the qualitative implications of NLED by studying the inflationary parameters, like the slow-roll parameters, spectral index $n_s$, and tensor-to-scalar ratio $r$, and compare our results with observational data. Detailed phase-space analysis of our NLED cosmological model is performed with and without matter source. As a first approach, we consider the motion of a particle of unit mass in an effective potential. Our systems correspond to fast-slow systems for physical values of the electromagnetic field and the energy densities at the end of inflation. We analyze a complementary system using Hubble-normalized variables to investigate the cosmological evolution before the matter-dominated Universe., Comment: 27 pages, 13 compound figures

We revise recent results on the classification of the generalized three-dimensional Hamiltonian Ermakov system. We show that a statement published recently is incorrect, while the solution for the classification problem was incomplete. We present the correct classification for the three-dimensional system by using results which related the background space with the dynamics. Finally, we extend our results for the generalized $n$% -dimensional Hamiltonian Ermakov system., Comment: 10 pages, published in Mathematical Methods in the Applied Sciences

Using the singularity analysis, we investigate the integrability properties and existence of analytic solutions in $f\left( R\right)$-cosmology. Specifically, for some power-law $f\left( R\right) $-theories of particular interest, we apply the ARS algorithm to prove if the field equations possess the Painlev\'{e} property. Constraints for the free parameters of the power-law models are derived, and new analytic solutions are derived, expressed in terms of Laurent expansions., Comment: 16 pages, no figures

We shall present a complete (compactified) dynamical systems analysis of the Quintom model comprised of an interacting quintessence scalar field and a phantom. We find a range for the model parameters $\kappa, \lambda$ such that there are expanding Quintom cosmologies that undergo two inflationary periods, and this behaviour is not destabilized by spatial curvature. We also discuss a class of bouncing cosmologies. Finally, the linear cosmological perturbations are studied., Comment: 12 pages, 4 figures

We study the temporal equation of radiating stars by using three powerful methods for the analysis of nonlinear differential equations. Specifically, we investigate the global dynamics for the given master ordinary differential equation to understand the evolution of solutions for various initial conditions as also to investigate the existence of asymptotic solutions. Moreover, with the application of Lie's theory, we can reduce the order of the master differential equation, while an exact similarity solution is determined. Finally, the master equation possesses the Painlev\'{e} property, which means that the analytic solution can be expressed in terms of a Laurent expansion., Comment: 18 pages, 6 compound figures. Fits the published version. arXiv admin note: text overlap with arXiv:2105.03970

We present a unified description of the matter and dark energy epochs, using a class of scalar-torsion theories. We provide a Hamiltonian description, and by applying Noether's theorem and by requiring the field equations to admit linear-in-momentum conservation laws we obtain two specific classes of scalar-field potentials. We extract analytic solutions and we perform a detailed dynamical analysis. We show that the system possesses critical points that correspond to scaling solutions in which the effective, total equation-of-state parameter is close to zero and points in which it is equal to the cosmological constant value $-1$. Therefore, during evolution, the Universe remains for sufficiently long times at the epoch corresponding to dust-matter domination, while at later times it enters the accelerated epoch and it eventually results in the de Sitter phase. Finally, in contrast to other unified scenarios, such as Chaplygin gas-based models as well as Horndeski-based constructions, the present scenario is free from instabilities and pathologies at the perturbative level., Comment: 12 pages, 4 figures

We consider a cosmological model consisting of two scalar fields defined in the hyperbolic plane known as hyperbolic inflation. For the background space, we consider a homogeneous and isotropic spacetime with nonzero curvature. We study the asymptotic behaviour of solutions and we search for attractors in the expanding regime. We prove that two hyperbolic inflationary stages are stable solutions that can solve the flatness problem and describe acceleration for both open and closed models, and additionally we obtain a Milne-like attractor solution for the open model. We also investigate the contracting branch obtaining mirror solutions with the opposite dynamical behaviours., Comment: 13 pages. Major revision. One calculation error was amended

We investigate exact solutions and the asymptotic dynamics for the Friedmann-Lema\^{\i}tre-Robertson-Walker universe with nonzero spatial curvature in the fourth-order modified teleparallel gravitational theory known as $f\left( T, B\right) $ theory. We show that the field equations admit a minisuperspace description, and they can reproduce any exact form of the scale factor. Moreover, we calculate the equilibrium points and analyze their stability. We show that Milne and Milne-like solutions are supported, and the de Sitter universe is provided. To complete our analysis, we use Poincar\'e variables to investigate the dynamics at infinity., Comment: 18 pages. 4 compound figures

We consider a modification of the Brans-Dicke gravitational Action Integral inspired by the existence of a minimum length uncertainty for the scalar field. In particular, the kinetic part of the Brans-Dicke scalar field is modified such that the equation of motion for the scalar field be modified according to the quadratic Generalized Uncertainty Principle (GUP). For the background geometry, we assume the homogeneous and isotropic Friedmann--Lema\^{\i}tre--Robertson--Walker metric. We investigate the dynamics and the cosmological evolution for the dynamical variables of the theory and we compare the results with the unmodified Brans-Dicke theory. It follows that in consideration because of the additional degrees of freedom in the energy-momentum tensor the dynamical variables describe various aspects of the cosmological history. This is one of the first studies on the effects of GUP in a Machian gravitational theory., Comment: 27 pages, 2 figures

We study the scenario of Kanadiakis horizon entropy cosmology which arises from the application of the gravity-thermodynamics conjecture using the Kaniadakis modified entropy. The resulting modified Friedmann equations contain extra terms that constitute an effective dark energy sector. We use data from Cosmic chronometers, Supernova Type Ia, HII galaxies, Strong lensing systems, and Baryon acoustic oscillations observations and we apply a Bayesian Markov Chain Monte Carlo analysis to construct the likelihood contours for the model parameters. We find that the Kaniadakis parameter is constrained around 0, namely, around the value where the standard Bekenstein-Hawking is recovered. Concerning the normalized Hubble parameter, we find $h=0.708^{+0.012}_{-0.011}$, a result that is independently verified by applying the $\mathbf{\mathbb{H}}0(z)$ diagnostic and, thus, we conclude that the scenario at hand can alleviate the $H_0$ tension problem. Regarding the transition redshift, the reconstruction of the cosmographic parameters gives $z_T=0.715^{+0.042}_{-0.041}$. Furthermore, we apply the AICc, BIC and DIC information criteria and we find that in most datasets the scenario is statistical equivalent to $\Lambda$CDM one. Moreover, we examine the Big Bang Nucleosynthesis (BBN) and we show that the scenario satisfies the corresponding requirements. Additionally, we perform a phase-space analysis, and we show that the Universe past attractor is the matter-dominated epoch, while at late times the Universe results in the dark-energy-dominated solution. Finally, we show that Kanadiakis horizon entropy cosmology accepts heteroclinic sequences, but it cannot exhibit bounce and turnaround solutions., Comment: Version accepted in MNRAS

We investigate Kaniadakis-holographic dark energy by confronting it with observations. We perform a Markov Chain Monte Carlo analysis using cosmic chronometers, supernovae type Ia, and Baryon Acoustic Oscillations data. Concerning the Kaniadakis parameter, we find that it is constrained around zero, namely around the value in which Kaniadakis entropy recovers standard Bekenstein-Hawking one. Additionally, for the present matter density parameter $\Omega_m^{(0)}$, we obtain a value slightly smaller compared to $\Lambda$CDM scenario. Furthermore, we reconstruct the evolution of the Hubble, deceleration and jerk parameters extracting the deceleration-acceleration transition redshift as $z_T = 0.86^{+0.21}_{-0.14}$. Finally, performing a detailed local and global dynamical system analysis, we find that the past attractor of the Universe is the matter-dominated solution, while the late-time stable solution is the dark-energy-dominated one., Comment: Version accepted in MNRAS

The Szekeres system with cosmological constant term describes the evolution of the kinematic quantities for Einstein field equations in $\mathbb{R}^4$. In this study, we investigate the behavior of trajectories in the presence of cosmological constant. It has been shown that the Szekeres system is a Hamiltonian dynamical system. It admits at least two conservation laws, $h$ and $I_{0}$ which indicate the integrability of the Hamiltonian system. We solve the Hamilton-Jacobi equation, and we reduce the Szekeres system from $\mathbb{R}^4$ to an equivalent system defined in $\mathbb{R}^2$. Global dynamics are studied where we find that there exists an attractor in the finite regime only for positive valued cosmological constant and $I_0<2.08$. Otherwise, trajectories reach infinity. For $I_ {0}>0$ the origin of trajectories in $\mathbb{R}^2$ is also at infinity. Finally, we investigate the evolution of physical properties by using dimensionless variables different from that of Hubble-normalization conducing to a dynamical system in $\mathbb{R}^5$. We see that the attractor at the finite regime in $\mathbb{R}^5$ is related with the de Sitter universe for a positive cosmological constant., Comment: 45 pages, 20 compound figures, 1 table

In this work, we use an observational approach and dynamical system analysis to study the cosmological model recently proposed by Saridakis (2020), which is based on the modification of the entropy-area black hole relation proposed by Barrow (2020). The Friedmann equations governing the dynamics of the Universe under this entropy modification can be calculated through the gravity-thermodynamics conjecture. We investigate two models, one considering only a matter component and the other including matter and radiation, which have new terms compared to the standard model sourcing the late cosmic acceleration. A Bayesian analysis is performed in which we use five cosmological observations (observational Hubble data, type Ia supernovae, HII galaxies, strong lensing systems, and baryon acoustic oscillations) to constrain the free parameters of both models. From a joint analysis, we obtain constraints that are consistent with the standard cosmological paradigm within $2\sigma$ confidence level. In addition, a complementary dynamical system analysis using local and global variables is developed which allows obtaining a qualitative description of the cosmology. As expected, we found that the dynamical equations have a de Sitter solution at late times., Comment: 32 pages, 8 compound figures, 3 tables

We propose an Einstein-{\ae}ther scalar-tensor cosmological model. In particular in the scalar-tensor Action Integral we introduce the {\ae}ther field with {\ae}ther coefficients to be functions of the scalar field. This cosmological model extends previous studies on Lorentz-violating theories. For a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker background space we write the field equations which are of second-order with dynamical variables the scale factor and the scalar field. The physical evolution of the field equations depends upon three unknown functions which are related to the scalar-tensor coupling function, the scalar field potential and the {\ae}ther coefficient functions. We investigate the existence of analytic solutions for the field equations and the integrability properties according to the existence of linear in the momentum conservation laws. We define a new set of variables in which the dynamical evolution depends only upon the scalar field potential. Furthermore, the asymptotic behaviour and the cosmological history is investigated where we find that the theory provides inflationary eras similar with that of scalar-tensor theory but with Lorentz-violating terms provided by the {\ae}ther field. Finally, in the new variables we found that the field equations are integrable due to the existence of nonlocal conservation laws for arbitrary functional forms of the three free functions., Comment: 22 pages, 1 compound figure

In this paper, we study a cosmological model inspired in the axionic matter with two canonical scalar fields $\phi_1$ and $\phi_2$ interacting through a term added to its potential. Introducing novel dynamical variables, and a dimensionless time variable, the resulting dynamical system is studied. The main difficulties arising in the standard dynamical systems approach, where expansion normalized dynamical variables are usually adopted, are due to the oscillations entering the nonlinear system through the Klein-Gordon (KG) equations. This motivates the analysis of the oscillations using methods from the theory of averaging nonlinear dynamical systems. We prove that time-dependent systems, and their corresponding time-averaged versions, have the same late-time dynamics. Then, we study the time-averaged system using standard techniques of dynamical systems. We present numerical simulations as evidence of such behavior., Comment: 35 pages, 7 compound figures

For the fourth-order teleparallel $f\left(T,B\right) $ theory of gravity, we investigate the cosmological evolution for the universe in the case of a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker background space. We focus on the case for which $f\left(T,B\right) $ is separable, that is, $f\left(T,B\right) _{,TB}=0$ and $f\left(T,B\right) $ is a nonlinear function on the scalars $T$ and $B$. For this fourth-order theory we use a Lagrange multiplier to introduce a scalar field function which attributes the higher-order derivatives. In order to perform the analysis of the dynamics we use dimensionless variables which allow the Hubble function to change sign. The stationary points of the dynamical system are investigated both in the finite and infinite regimes. The physical properties of the asymptotic solutions and their stability characteristics are discussed., Comment: 18 pages, 6 compound figures

In this work, we present for the first time the general solution of the temporal evolution equation arising from the matching of a conformally flat interior to the Vaidya solution. This problem was first articulated by Banerjee et al. (A. Banerjee, S. B. Dutta Choudhury, and Bidyut K. Bhui, Phys. Rev. D, 40 (670) 1989) in which they provided a particular solution to the temporal equation. This simple exact solution has been widely utilized in modeling dissipative collapse with the most notable result being a prediction of the avoidance of the horizon as the collapse proceeds. We study the dynamics of dissipative collapse arising from the general solution obtained via the method of symmetries and of the singularity analysis. We show that the end-state of collapse for our model is significantly different from the widely used linear solution., Comment: 8 pages, 7 figures

We perform a detailed analysis of the asymptotic behavior of a multifield cosmological model with phantom terms. Specifically, we consider the Chiral-Phantom model consisting of two scalar fields with a mixed kinetic term, while one scalar field has negative kinetic energy, that is, it has phantom properties. We show that the Hubble function can change sign, and we study the global evolution of the field equation in the finite and infinity regions with the use of Poincar\'{e} variables. We find that in the Chiral-Phantom model the limit of the quintessence scalar field is recovered while the cosmological evolution differs from the standard hyperbolic theory. Finally, the linear cosmological perturbations are studied., Comment: 24 pages, 11 compound figures. Section 4 about linear cosmological perturbations added