arXiv subjects

V. K. Oikonomou

Publications and source records attributed to V. K. Oikonomou.

At least 127 records · Page 7Linked to original sources

arXiv2020

Canonical Scalar Field Inflation with String and $R^2$-Corrections

Assuming that a scalar field controls the inflationary era, we examine the combined effects of string and $f(R)$ gravity corrections on the inflationary dynamics of canonical scalar field inflation, imposing the constraint that the speed of the primordial gravitational waves is equal to that of light's. Particularly, we study the inflationary dynamics of an Einstein-Gauss-Bonnet gravity in the presence of $αR^2$ corrections, where $α$ is a free coupling parameter. As it was the case in the pure Einstein-Gauss-Bonnet gravity, the realization that the gravitational waves propagate through spacetime with the velocity of light, imposes the constraint that the Gauss-Bonnet coupling function $ξ(ϕ)$ obeys the differential equation $\ddotξ=H\dotξ$, where $H$ is the Hubble rate. Subsequently, a relation for the time derivative of the scalar field is extracted which implies that the scalar functions of the model, which are the Gauss-Bonnet coupling and the scalar potential, are interconnected and simply designating one of them specifies the other immediately. In this framework, it is useful to freely designate $ξ(ϕ)$ and extract the corresponding scalar potential from the equations of motion but the opposite is still feasible. We demonstrate that the model can produce a viable inflationary phenomenology and for a wide range of the free parameters. Also, a mentionable issue is that when the coupling parameter $α$ of the $R^2$ correction term is $α<10^{-3}$ in Planck Units, the $R^2$ term is practically negligible and one obtains the same equations of motion as in the pure Einstein-Gauss-Bonnet theory, however the dynamics still change, since now the time derivative of $\frac{\partial f}{\partial R}$ is nonzero.

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arXiv2020

Non-minimally Coupled Einstein-Gauss-Bonnet Gravity with Massless Gravitons: The Constant-roll Case

In this letter we study the behavior of non-minimally coupled Einstein-Gauss-Bonnet gravity theories with the constant-roll condition. Recalling the results of the striking GW170817 event, we demand that the velocity of the gravitational waves is equated to unity in natural units, meaning that $c_T^2=1$. This is a powerful restriction since it leads to a decrease in the degrees of freedom and subsequently reveals a connection between the scalar functions of the theory which presumably have different origins. In this framework, we shall assume that a scalar potential is present and can be extracted easily from the equations of motion by simply designating the scalar coupling functions. Obviously, a different approach is feasible but such choice will prove to be extremely convenient. Afterwards, we impose certain approximations in order to facilitate our study. Each assumption is capable of producing different phenomenology so a summary of all the possible configurations for Hubble's parameter, its derivative and the scalar potential along with the corresponding assumptions are present at the end of the paper. We show that compatibility under the constant-roll assumption can be achieved for a variety of model functions and different approaches, although one must always be aware of the imposed approximations since the possibility of a model producing viable results while simultaneously violating even a single approximation exists. Finally, in the end, a new formalism which leads to a plethora of convenient coupling functions according to the readers choice is presented. Utilizing such formalism may lead to new cases for coupling functions which have not been used yet, but are in fact able of producing viable phenomenology for the inflationary era.

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arXiv2020

$f(R)$ Gravity Phase Space in the Presence of Thermal Effects

In this paper, we shall consider $f(R)$ gravity and its cosmological implications, when an extra matter term generated by thermal effects is added by hand in the Lagrangian. We formulate the equations of motion of the theory as a dynamical system, that can be treated as an autonomous one only for specific solutions for the Hubble rate, which are of cosmological interest. Particularly, we focus our analysis on subspaces of the total phase space, corresponding to (quasi-)de Sitter accelerating expansion, matter-dominated and radiation-dominated solutions. In all the aforementioned cases, the dynamical system is an autonomous dynamical system. With regard to the thermal term effects, these are expected to significantly affect the evolution near a Big Rip singularity, and we also consider this case in terms of the corresponding dynamical system, in which case the system is non-autonomous, and we attempt to extract analytical and numerical solutions that can assess the specific cases. This course is taken twice: the first for the vacuum theory and the second when two perfect fluids (dust and radiation) are included as matter sources in the field equations. In both cases, we reach similar conclusions. The results of this theory do not differ significantly from the results of the pure $f(R)$ in the de Sitter and quasi-de Sitter phases, as the same fixed points are attained, so for sure the late-time era de Sitter is not affected. However, in the matter-dominated and radiation-dominated phases, the fixed points attained are affected by the presence of the thermal term, so surely the thermal effects would destroy the matter and radiation domination eras.

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arXiv2020

From a Bounce to the Dark Energy Era with $F(R)$ Gravity

In this work we consider a cosmological scenario in which the Universe contracts initially having a bouncing-like behavior, and accordingly after it bounces off, it decelerates following a matter dominated like evolution and at very large positive times it undergoes through an accelerating stage. Our aim is to study such evolution in the context of $F(R)$ gravity theory, and confront quantitatively the model with the recent observations. Using several reconstruction techniques, we analytically obtain the form of $F(R)$ gravity in two extreme stages of the universe, particularly near the bounce and at the late time era respectively. With such analytic results and in addition by employing appropriate boundary conditions, we numerically solve the $F(R)$ gravitational equation to determine the form of the $F(R)$ for a wide range of values of the cosmic time. The numerically solved $F(R)$ gravity realizes an unification of certain cosmological epochs of the universe, in particular, from a non-singular bounce to a matter dominated epoch and from the matter dominated to a late time dark energy epoch. Correspondingly, the Hubble parameter and the effective equation of state parameter of the Universe are found and several qualitative features of the model are discussed. The Hubble radius goes to zero asymptotically in both sides of the bounce, which leads to the generation of the primordial curvature perturbation modes near the bouncing point. Correspondingly, we calculate the scalar and tensor perturbations power spectra near the bouncing point, and accordingly we determine the observable quantities like the spectral index of the scalar curvature perturbations, the tensor-to-scalar ratio, and as a result, we directly confront the present model with the latest Planck observations. Furthermore the $F(R)$ gravity dark energy epoch is confronted with the Sne-Ia+BAO+H(z)+CMB data.

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arXiv2020

GW170817-compatible Constant-roll Einstein-Gauss-Bonnet Inflation and Non-Gaussianities

In this paper we investigate the inflationary phenomenology of an Einstein-Gauss-Bonnet theory compatible with the GW170817 event, by imposing the constant-roll evolution on the scalar field. We develop the constant-roll GW170817-compatible Einstein-Gauss-Bonnet formalism, and we calculate the slow-roll indices and the observational indices of inflation, for several models of interest. As we demonstrate, the phenomenological viability of the models we study is achieved for a wide range of the free parameters. In addition, for the same values of the free parameters that guarantee the inflationary phenomenological viability of the models, we also make predictions for the non-Gaussianities of the models, since the constant-roll evolution is known to enhance non-Gaussianities. As we show the non-Gaussianities are of the same order for the slow-roll and constant-roll case, and in fact in some cases, the amount of the non-Gaussianities is smaller in the constant-roll case.

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arXiv2020

Bottom-up reconstruction of non-singular bounce in F(R) gravity from observational indices

We apply the bottom-up reconstruction technique in the context of bouncing cosmology in F(R) gravity, where the starting point is a suitable ansatz of observable quantity (like spectral index or tensor to scalar ratio) rather than a priori form of Hubble parameter. In inflationary scenario, the slow roll conditions are assumed to hold true, and thus the observational indices have general expressions in terms of the slow-roll parameters, as for example the tensor to scalar ratio in F(R) inflation can be expressed as $r = 48ε_F^2$ with $ε_F = -\frac{1}{H_F^2}\frac{dH_F}{dt_F}$ and $H_F$, $t_F$ are the Hubble parameter, cosmic time respectively. However, in the bouncing cosmology (say in F(R) gravity theory), the slow-roll conditions are not satisfied, in general, and thus the observable quantities do not have any general expressions that will hold true irrespective of the form of F(R). Thus, in order to apply the bottom-up reconstruction procedure in F(R) bouncing model, we use the conformal correspondence between F(R) and scalar-tensor model where the conformal factor in the present context is chosen in a way such that it leads to an inflationary scenario in the scalar-tensor frame. Due to the reason that the scalar and tensor perturbations remain invariant under conformal transformation, the observable viability of the scalar-tensor inflationary model confirms the viability of the conformally connected F(R) bouncing model. Motivated by these arguments, here we construct a viable non-singular bounce in F(R) gravity directly from the observable indices of the corresponding scalar-tensor inflationary model.

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arXiv2020

Rectifying Einstein-Gauss-Bonnet Inflation in View of GW170817

In this work we introduce a new theoretical framework for Einstein-Gauss-Bonnet theories of gravity, which results to particularly elegant, functionally simple and transparent gravitational equations of motion, slow-roll indices and the corresponding observational indices. The main requirement is that the Einstein-Gauss-Bonnet theory has to be compatible with the GW170817 event, so the gravitational wave speed $c_T^2$ is required to be $c_T^2\simeq 1$ in natural units. This assumption was also made in a previous work of ours, but in this work we express all the related quantities as functions of the scalar field. The constraint $c_T^2\simeq 1$ restricts the functional form of the scalar Gauss-Bonnet coupling function $ξ(ϕ)$ and of the scalar potential $V(ϕ)$, which must satisfy a differential equation. However, by also assuming that the slow-roll conditions hold true, the resulting equations of motion and the slow-roll indices acquire particularly simple forms, and also the relation that yields the $e$-foldings number is $N=\int_{ϕ_i}^{ϕ_f}ξ''/ξ'd ϕ$, a fact that enables us to perform particularly simple calculations in order to study the inflationary phenomenological implications of several models. As it proves, the models we presented are compatible with the observational data, and also satisfy all the assumptions made during the process of extracting the gravitational equations of motion. More interestingly, we also investigated the phenomenological implications of an additional condition $ξ'/ξ''\ll 1$, which is motivated by the slow-roll conditions that are imposed on the scalar field evolution and on the Hubble rate, in which case the study is easier. Our approach opens a new window in viable Einstein-Gauss-Bonnet theories of gravity.

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arXiv2020

A Nearly Massless Graviton in Einstein-Gauss-Bonnet Inflation with Linear Coupling Implies Constant-roll for the Scalar Field

The striking GW170817 event indicated that the graviton is nearly massless, since the gamma rays emitted from the two neutron stars merging arrived almost simultaneously with the gravitational waves. Thus, the graviton must also be massless during the inflationary and post-inflationary era, since there is no obvious reason to believe otherwise. In this letter we shall investigate the theoretical implications of the constraint that the graviton is massless to an Einstein-Gauss-Bonnet theory with linear coupling of the scalar field to the four dimensional Gauss-Bonnet invariant. As we show, the constraint of having gravitational wave speed of the primordial gravitational waves equal to one, severely restricts the dynamics of the scalar field, imposing a direct constant-roll evolution on it. Also, as we show, the spectral index of the primordial scalar perturbations for the GW170817-compatible Einstein-Gauss-Bonnet theory with linear coupling is different in comparison to the same theory with non-linear coupling. Thus the phenomenology of the model is expected to be different, and we briefly discuss this issue too. In addition, the constant-roll condition is always related to non-Gaussianities, thus it is interesting that the imposition of a massless graviton in an Einstein-Gauss-Bonnet theory with linear coupling may lead to non-Gaussianities, so we briefly discuss this issue too.

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arXiv2020

Unifying Holographic Inflation with Holographic Dark Energy: a Covariant Approach

In the present paper, we use the holographic approach to describe the early-time acceleration and the late-time acceleration eras of our Universe in a unified manner. Such ``holographic unification'' is found to have a correspondence with various higher curvature cosmological models with or without matter fields. The corresponding holographic cut-offs are determined in terms of the particle horizon and its derivatives, or the future horizon and its derivatives. As a result, the holographic energy density we propose is able to merge various cosmological epochs of the Universe from a holographic point of view. We find the holographic correspondence of several $F(R)$ gravity models, including axion-$F(R)$ gravity models, of several Gauss-Bonnet $F(G)$ models and finally of $F(T)$ models, and in each case we demonstrate that it is possible to describe in a unified way inflation and late-time acceleration in the context of the same holographic model.

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arXiv2020

Non-Minimally Coupled Einstein Gauss Bonnet Inflation Phenomenology in View of GW170817

We study the inflationary phenomenology of a non-minimally coupled Einstein Gauss-Bonnet gravity theory, in the presence of a scalar potential, under the condition that the gravitational wave speed of the primordial gravitational waves is equal to unity, that is $c_T^2=1$, in natural units. The equations of motion, which are derived directly from the gravitational action, form a system of differential equations with respect to Hubble's parameter and the inflaton field which are very complicated and cannot be solved analytically, even in the minimal coupling case. In this paper, we present a variety of different approximations which could be used, along with the constraint $c_T^2=1$, in order to produce an inflationary phenomenology compatible with recent observations. All the different approaches are able to lead to viable results if the model coupling functions obey simple relations, however, different approaches contain different approximations which must be obeyed during the first horizon crossing, in order for the model to be rendered correct. Models which may lead to a non-viable phenomenology are presented as well in order to understand better the inner framework of this theory. Furthermore, since the velocity of the gravitational waves is set equal to $c_T^2=1$, as stated by the striking event of GW170817 recently, the non-minimal coupling function, the Gauss-Bonnet scalar coupling and the scalar potential are related to each other. Here, we shall assume no particular form of the scalar potential and we choose freely the scalar functions coupled to the Ricci scalar and the Gauss-Bonnet invariant. Certain models are also studied in order to assess the phenomenological validity of the theory, but we need to note that all approximations must hold true in order for a particular model to be valid.

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arXiv2020

Unifying Inflation with Early and Late-time Dark Energy in $F(R)$ Gravity

In this work we shall present models of $F(R)$ gravity which realize in a unified way the inflationary era along with a post-inflationary early dark energy era, with the late-time dark energy era. We shall use two approach methods in order to realize the unified cosmological eras, firstly we specify a Hubble rate which may describe the three distinct acceleration eras, and then by using well known $F(R)$ gravity reconstruction techniques, we shall find the differential equation which may yield the $F(R)$ gravity that realizes the cosmologies. In our second approach, we shall present in a qualitative way, several $F(R)$ gravities which unify the inflationary era with the early and late-time dark energy eras, and we discuss several qualitative issues related to the terms that realize the post-inflationary early dark energy era. We quantify our analysis by numerically solving the Friedmann equation, using the redshift as the main variable, and expressing all the physical quantities as functions of the statefinder $y_\mathrm{H}(z)$, which depends on the redshift and the Hubble rate $H(z)$. For the model studied numerically, we present the behavior of some statefinder quantities, like the deceleration parameter, and we calculate the dark energy density parameter and the dark energy equation of state parameter at present time. After demonstrating that the dark energy era is viable, we investigate when the early dark energy term does not affect the late-time era, and this restricts the free parameters of the model.

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arXiv2020

Periodic Strategies II: Generalizations and Extensions

At a mixed Nash equilibrium, the payoff of a player does not depend on her own action, as long as her opponent sticks to his. In a periodic strategy, a concept developed in a previous paper (arXiv:1307.2035v4), in contrast, the own payoff does not depend on the opponent's action. Here, we generalize this to multi-player simultaneous perfect information strategic form games. We show that also in this class of games, there always exists at least one periodic strategy, and we investigate the mathematical properties of such periodic strategies. In addition, we demonstrate that periodic strategies may exist in games with incomplete information; we shall focus on Bayesian games. Moreover we discuss the differences between the periodic strategies formalism and cooperative game theory. In fact, the periodic strategies are obtained in a purely non-cooperative way, and periodic strategies are as cooperative as the Nash equilibria are. Finally, we incorporate the periodic strategies in an epistemic game theory framework, and discuss several features of this approach.

cs.GT↗

arXiv2020

Autonomous Dynamical System of Einstein-Gauss-Bonnet Cosmologies

In this paper, we study the phase space of cosmological models in the context of Einstein-Gauss-Bonnet theory. More specifically, we consider a generalized dynamical system that encapsulates the main features of the theory and for the cases that this is rendered autonomous, we analyze its equilibrium points and stable and unstable manifolds corresponding to several distinct cosmological evolutions. As we demonstrate, the phase space is quite rich and contains invariant structures, which dictate the conditions under which the theory may be valid and viable in describing the evolution Universe during different phases. It is proved that a stable equilibrium point and two invariant manifolds leading to the fixed point, have both physical meaning and restrict the physical aspects of such a rich in structure modified theory of gravity. More important we prove the existence of a heteroclinic orbit which drives the evolution of the system to a stable fixed point. However, while on the fixed point the Friedman constraint corresponding to a flat Universe is satisfied, the points belonging to the heteroclinic orbit do not satisfy the Friedman constraint. We discuss the origin of this intriguing issue in some detail.

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arXiv2020

Inflationary Attractors in $F(R)$ Gravity

In this letter we shall demonstrate that the viable $F(R)$ gravities can be classified mainly into two classes of inflationary attractors, either the $R^2$ attractors or the $α$-attractors. To show this, we shall derive the most general relation between the tensor-to-scalar ratio $r$ and the spectral index of primordial curvature perturbations $n_s$, namely the $r-n_s$ relation, by assuming that the slow-roll condition constrains the values of the slow-roll indices. As we show, the relation between the tensor-to-scalar ratio and the spectral index of the primordial curvature perturbations has the form $r\simeq \frac{48 (1-n_s)^2}{(4-x)^2}$, where the dimensionless parameter $x$ contains higher derivatives of the $F(R)$ gravity function with respect to the Ricci scalar, and it is a function of the $e$-foldings number $N$ and may also be a function of the free parameters of the various $F(R)$ gravity models. For $F(R)$ gravities which have a spectral index compatible with the observational data and also yield $x\ll 1$, these belong to the $R^2$-type of attractors, with $r\sim 3 (1-n_s)^2$, and these are viable theories. Moreover, in the case that $x$ takes larger values in specific ranges and is constant for a given $F(R)$ gravity, the resulting $r-n_s$ relation has the form $r\sim 3 α(1-n_s)^2$, where $α$ is a constant. Thus we conclude that the viable $F(R)$ gravities may be classified into two limiting types of $r-n_s$ relations, one identical to the $R^2$ model at leading order in $x$, and one similar to the $α$-attractors $r-n_s$ relation, for the $F(R)$ gravity models that yield $x$ constant. Finally, we also discuss the case that $x$ is not constant.

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arXiv2020

Rectifying an Inconsistency in $F(R)$ Gravity Inflation

In this letter we shall provide a formal derivation of the inflationary slow-roll indices for $F(R)$ gravity from the power spectrum without the condition $\dotε_1=0$, frequently used in the literature, where $ε_1=-\frac{\dot{H}}{H^2}$ is the first slow-roll index. We shall employ Karamata's theorem for regularly varying functions, and as we show, we shall derive the same expressions for the scalar and tensor spectral index of $F(R)$ gravity, also appearing in the current literature, without the misleading and rather strong condition $\dotε_1=0$. The only conditions that are needed are the slow-roll assumption, and the smallness of the slow-roll indices and of their derivatives during inflation.

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arXiv2020

$f(R)$ Gravity $k$-Essence Late-time Phenomenology

In this work we shall study the late-time behavior of $k$-Essence $f(R)$ gravity without scalar potential, in the presence of matter and radiation perfect fluids. We quantify the late-time study by using the statefinder function $Y_H(z)=\frac{ρ_{DE}}{ρ_m^{(0)}}$, which is a function of the redshift and of the Hubble rate. By appropriately rewriting the Friedmann equation in terms of the redshift and of the function $Y_H(z)$, we numerically solve it using appropriate initial conditions, and we critically examine the effects of the $k$-Essence higher order kinetic terms. As we demonstrate, the effect of the higher order scalar field kinetic terms on the late-time dynamics is radical, since the dark energy oscillations are absent, and in addition, the cosmological physical quantities are compatible with the latest Planck data and also the model is almost indistinguishable from the $Λ$ Cold Dark Matter model. This is in contrast to the standard $f(R)$ gravity case, where the oscillations are present. Furthermore, by choosing a different set of values of two of the free parameters of the model, and specifically the coefficient of the higher order kinetic term and of the exponent of $R^δ$ appearing in the $f(R)$ action, we demonstrate that it is possible to obtain $ρ_{DE}<0$ for redshifts $z\sim 2-3.8$, which complies phenomenologically with, and seems to explain, the observational data for the same redshifts, and also to obtain a viable cosmological evolution at $z\sim 0$, at least when the dark energy equation of state parameter and the dark energy density parameters are considered.

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arXiv2020

Swampland Implications of GW170817-compatible Einstein-Gauss-Bonnet Gravity

We revisit the Einstein-Gauss-Bonnet theory in view of the GW170817 event, which compels that the gravitational wave speed is equal to $c_T^2=1$ in natural units. We use an alternative approach compared to one previous work of ours, which enables us to express all the slow-roll indices and the observational indices as functions of the scalar field. Using our formalism we investigate if the Swampland criteria are satisfied for the Einstein-Gauss-Bonnet theory and as we demonstrate, the Swampland criteria are satisfied for quite general forms of the potential and the Gauss-Bonnet coupling function $ξ(ϕ)$, if the slow-roll conditions are assumed to hold true.

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arXiv2020

Aspects of Axion $F(R)$ Gravity

We provide a compact review on recent developments on axion $F(R)$ gravity. The axion field is a string theory originating theoretical particle that is a perfect candidate for low-mass particle dark matter. In this review we present how a viable inflationary phenomenology and a viable late-time evolution can be described by an axion $F(R)$ gravity theory, in which the $F(R)$ gravity part can drive in a geometric way the inflationary and the late-time era, and the axion field behaves as dark matter, with its energy density $ρ_a$ behaving as a function of the scale factor as $ρ_a\sim a^{-3}$. We also briefly discuss the effect of a non-trivial axion Chern-Simons coupling on the inflationary phenomenology of the $R^2$ model. Finally, we briefly discuss the effects of a non-minimal coupling of the axion field with the curvature on neutron stars, and also the propagation of gravity waves in Chern-Simons axion gravity.

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