arXiv subjects

S. D. Odintsov

Publications and source records attributed to S. D. Odintsov.

At least 91 records · Page 5Linked to original sources

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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arXiv2020

Extended matter bounce scenario in ghost free $f(R,\mathcal{G})$ gravity compatible with GW170817

In the context of a ghost free $f(R,\mathcal{G})$ model, an extended matter bounce scenario is studied where the form of the scale factor is given by $a(t) = (a_0t^2 + 1)^n$. The ghost free character of the model is ensured by the presence of a Lagrange multiplier, as developed in \cite{Nojiri:2018ouv}. The conditions under which, in this model, the speed of gravitational waves becomes equal to the speed of light (equal to one, in natural units), thus becoming compatible with the striking event GW170817, is investigated. It is shown that this happens for a class of Gauss-Bonnet (GB) coupling functions ($h(t)$) which satisfies a constraint equation of the form $\ddot{h} = \dot{h}H$, with $H$ the Hubble parameter. This constraint is then imposed on the ghost free $f(R,\mathcal{G})$ gravity theory to be consistent with the GW170817 event, subsequently, the corresponding non-singular bouncing cosmology with the aforementioned scale factor is extensively studied. The forms of the coupling function and Lagrange multiplier in the "low curvature limit" of the theory are reconstructed, yielding a viable approximation for $n < 1/2$. Correspondingly, by solving the cosmological perturbation equation, the main observable quantities, namely the spectral index, tensor to scalar ratio, and the running index are determined and confronted with the latest Planck 2018 data. Consistency with the data is proven for those parametric regimes that which correspond to $n < 1/2$. This makes the low curvature approximation a viable one for calculating the scalar and tensor power spectra.

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arXiv2020

Propagation of Gravitational Waves in Chern-Simons Axion $F(R)$ Gravity

In this paper we shall study the evolution of cosmological gravitational waves in the context of Chern-Simons axion $F(R)$ gravity. In the case of Chern-Simons axion $F(R)$ gravity there exist spin-0, spin-2 and spin-1 modes. As we demonstrate, from all the gravitational waves modes of the Chern-Simons axion $F(R)$ gravity, only the two tensor modes are affected, while the spin-0 and spin-1 modes are not affected at all. With regard to the two tensor modes, we show that these modes propagate in a non-equivalent way, so the resulting tensor modes are chiral. Notably, with regard to the propagation of the spin-2 graviton modes, the structure of the dispersion relations becomes more complicated in comparison with the Einstein gravity with the Chern-Simons axion, but the resulting qualitative features of the propagating modes are not changed. With regard to the spin-0 and spin-1 modes, the Chern-Simons axion $F(R)$ gravity contains two spin-0 modes and no vector spin-1 mode at all. We also find that for the very high energy mode, both the group velocity and the phase velocity are proportional to the inverse of the square root of the wave number, and therefore the velocities become smaller for larger wave numbers or even vanish in the limit that the wave number goes to infinity.

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arXiv2020

Spherically symmetric black holes with electric and magnetic charge in extended gravity: Physical properties, causal structure, and stability analysis in Einstein's and Jordan's frames

Novel static black hole solutions with electric and magnetic charges are derived for the class of modified gravities: $f({\cal R})={\cal R}+2β\sqrt{\cal R}$, with or without a cosmological constant. The new black holes behave asymptotically as flat or (A)dS space-times with a dynamical value of the Ricci scalar given by $R=\frac{1}{r^2}$ and $R=\frac{8r^2Λ+1}{r^2}$, respectively. They are characterized by three parameters, namely their mass and electric and magnetic charges, and constitute black hole solutions different from those in Einstein's general relativity. Their singularities are studied by obtaining the Kretschmann scalar and Ricci tensor, which shows a dependence on the parameter $β$ that is not permitted to be zero. A conformal transformation is used to display the black holes in Einstein's frame and check if its physical behavior is changed w.r.t. the Jordan one. The thermal stability of the solutions is discussed by using thermodynamical quantities, in particular the entropy, the Hawking temperature, the quasi-local energy, and the Gibbs free energy. Also, the casual structure of the new black holes is studied, and a stability analysis is performed in both frames using the odd perturbations technique and the study of the geodesic deviation. It is concluded that, generically, there is coincidence of the physical properties of the novel black holes in both frames, although this turns not to be the case for the Hawking temperature.

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arXiv2020

Geometric Inflation and Dark Energy with Axion $F(R)$ Gravity

We present a model of $F(R)$ gravity in the presence of a string theory motivated misalignment axion like particle materialized in terms of a canonical scalar field minimally coupled with gravity, and we study the cosmological phenomenology of the model, emphasizing mainly on the late-time era. The main result of the paper is that inflation and the dark energy era may be realized in a geometric way by an $F(R)$ gravity, while the axion is the dark matter constituent of the Universe. The $F(R)$ gravity model consists of an $R^2$ term, which as we show dominates the evolution during the early time, thus producing a viable inflationary phenomenology, and a power law term $\sim R^δ$ with $δ\ll 1 $ and positive, which eventually controls the late-time era. The axion field remains frozen during the inflationary era, which is an effect known for misalignment axions, but as the Universe expands, the axion starts to oscillate, and its energy density scales eventually as we show, as $ρ_a\sim a^{-3}$. After appropriately rewriting the gravitational equations in terms of the redshift $z$, we study in detail the late-time phenomenology of the model, and we compare the results with the $Λ$CDM model and the latest Planck 2018 data. As we show, the model for small redshifts $0<z<5$ is phenomenologically similar to the $Λ$CDM model, however at large redshifts and deeply in the matter domination era, the results are different from those of the $Λ$CDM model due to the dark energy oscillations. For the late-time study we investigate the behavior of several well-known statefinder quantities, like the deceleration parameter, the jerk and $Om(z)$, and we demonstrate that the statefinders which contain lower derivatives of the Hubble rate have similar behavior for both the $Λ$CDM and the axion $F(R)$ gravity model.

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arXiv2019

Viable non-singular cosmic bounce in holonomy improved F(R) gravity endowed with a Lagrange multiplier

Matter and quasi-matter bounce scenarios are studied for an F(R) gravity model with holonomy corrections and a Lagrange multiplier, with a scale factor $a(t) = \left(a_0t^2 + 1 \right)^n$, where the Hubble parameter squared has a linear and a quadratic dependence on the effective energy density. Provided $n < 1/2$, it is shown that the primordial curvature perturbations are generated deeply into the contracting era, at large negative time, which makes the low-curvature limit a good approximation for calculating the perturbation power spectrum. Moreover, it is shown that, for $n$ within this range, the obtained cosmological quantities are fully compatible with the Planck constraints, and that the "low curvature limit" comes as a viable approximation to calculate the power spectra of both scalar and tensor perturbations. Using reconstruction techniques for F(R) gravity with the Lagrange multiplier, the precise form of the effective F(R) gravity is found, from which one determines the power spectra of scalar and tensor perturbations in such bouncing scenario. Correspondingly, the spectral index for curvature perturbations and the tensor to scalar ratio are obtained, and these values are successfully confronted with the latest Planck observations. Further, it is shown that both the weak and the null energy conditions are satisfied, thanks to the holonomy corrections performed in the theory--which are then proven to be necessary for achieving this goal. In fact, when approaching the bouncing era, the holonomy corrections become significant and play a crucial role in order to restore the energy conditions. Summing up, a cosmological bouncing scenario with the scale factor above and fulfilling the energy conditions can be adequately described by the F(R) model with a Lagrange multiplier and holonomy corrections, which prove to be very important.

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arXiv2019

Thermodynamical correspondence of $f(R)$ gravity in Jordan and Einstein frames

We study the thermodynamical aspects of $f(R)$ gravity in the Jordan and the Einstein frame, and we investigate the corresponding equivalence of the thermodynamical quantities in the two frames. We examine static spherically symmetric black hole solutions with constant Ricci scalar curvature $R$, and as we demonstrate, the thermodynamical quantities in the two frames are equivalent. However, for the case of black holes with non-constant scalar curvature $R$, the thermodynamical equivalence of the two frames is no longer valid. In addition, we examine cosmological solutions with non-trivial curvatures and as we demonstrate the thermodynamical quantities in both frames are not equivalent. In conclusion, although $f(R)$ gravity and its corresponding scalar-tensor theory are mathematically equivalent, at least for conformal invariant quantities, the two frames are not thermodynamically equivalent at a quantitative level, in terms of several physical quantities.

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arXiv2019

Constant-roll $k$-Inflation Dynamics

In this work we shall investigate the phenomenological implications of the constant-roll condition on a $k$-Inflation theory of gravity. The latter theories are particularly promising, since these remained robust to the results of GW170817, since these have a gravitational wave speed $c_T=1$ in natural units. We shall mainly focus on the phenomenology of the $k$-Inflation models, with the only assumption being the slow-roll condition imposed on the first and fourth slow-roll parameters, and the constant-roll condition for the evolution of the scalar field. We present in detail the final form of the gravitational equations of motion that control the dynamics of the cosmological system, with the constant-roll condition imposed, and by using a conveniently, from the perspective of analytical manipulations, chosen potential, we express the slow-roll indices and the resulting observational indices of the theory as functions of the $e$-foldings number. The results of our analysis indicate that the constant-roll $k$-Inflation theory can be compatible with the Planck 2018 data, for a wide range of the free parameters. Also we examine in a quantitative way the effects of the constant-roll condition on the parameter $f_{NL}^{equil}$ on which the bispectrum is proportional, in the equilateral momentum approximation, and we demonstrate that the effect of the constant-roll condition is non-trivial. In effect, non-Gaussianities in the theory may be enhanced, a phenomenon which is known to be produced by constant-roll scalar theories of gravity in general.

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arXiv2019

Ghost-free non-local $F(R)$ Gravity Cosmology

In this work we shall study ghost-free non-local $F(R)$ gravity models. Firstly we shall demonstrate how the ghost degrees of freedom may occur in the non-local $F(R)$ gravity models, and accordingly we shall modify appropriately the gravitational action of non-local $F(R)$ gravity models in order to eliminate the ghosts. Also we shall investigate how the (anti-)de Sitter and the Minkowski spacetime cosmological solutions may arise in the theory, and we investigate when these solutions are stable. Moreover, we shall examine the inflationary phenomenology of the Jordan frame ghost-free non-local $F(R)$ gravity. We shall study two $F(R)$ gravity models, the power law $F(R)$ gravity model $\sim R^n$ with $1<n<2$, $n\neq 2$ and the $R^2$ model, assuming that the slow-roll condition holds true for the Hubble rate during the inflationary era $\dot{H}\ll H^2$ and that the general constant-roll condition $\ddotϕ=3βH\dotϕ$ holds true for the evolution of the scalar field, which includes the slow-roll case for $β=0$. As we shall demonstrate, the power-law non-local $F(R)$ gravity case can produce a viable inflationary era, compatible with observations, in the constant-roll case, unlike for the $R^2$ model. It is conceivable that the results are model dependent, as in the ordinary vacuum $F(R)$ gravity.

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arXiv2019

Non-singular Bounce Cosmology from Lagrange Multiplier $F(R)$ Gravity

In this work we study non-singular{ bounce cosmology} in the context of the Lagrange multiplier generalized $F(R)$ gravity theory of gravity. We specify our study by using a specific variant form of the well known matter{ bounce cosmology}, with scale factor $a(t) = \left(a_0t^2 + 1 \right)^n$, and we demonstrate that for $n < 1/2$, the primordial curvature perturbations are generated deeply in the contraction era. Particularly, we show explicitly that the perturbation modes exit the horizon at a large negative time during the contraction era, which in turn makes the ``low-curvature'' regime, the era for which the calculations of observational indices related to the primordial power spectrum can be considered reliable. Using the reconstruction techniques for the Lagrange multiplier $F(R)$ gravity, we construct the form of effective $F(R)$ gravity that can realize such a cosmological evolution, and we determine the power spectrum of the primordial curvature perturbations. Accordingly, we calculate the spectral index of the primordial curvature perturbations and the tensor-to-scalar ratio, and we confront these with the latest observational data. We also address the issue of stability of the primordial metric perturbations, and to this end, we determine the form of $F(R)$ which realizes the non-singular cosmology for the whole range of cosmic time $-\infty < t < \infty$, by solving the Friedmann equations without the ``low-curvature'' approximation. This study is performed numerically though, due to the high complexity of the resulting differential equations. We also investigate the energy conditions in the present context. The phenomenology of the non-singular bounce is also studied in the context of a standard $F(R)$ gravity.

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arXiv2019

Propagation of Gravitational Waves in Chern-Simons Axion Einstein Gravity

In this paper we shall investigate the propagation of gravitational waves in a flat Friedman-Robertson-Walker background, in the context of a string motivated corrected Einstein gravity. Particularly, we shall consider a misalignment axion Einstein gravity in the presence of a string originating Chern-Simons coupling of the axion field to the Chern-Pontryagin density in four dimensions. We shall focus our study on the propagation of the gravitational waves, and we shall investigate whether there exists any difference in the propagation of the polarization states of the gravitational waves. As we demonstrate, the dispersion relations are different in the Right-handed mode and the Left-handed mode. Finally, we compare the propagation of the axion Chern-Simons Einstein theory with that of standard $F(R)$ gravity.

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arXiv2019

Inflationary Phenomenology of Einstein Gauss-Bonnet Gravity Compatible with GW170817

In this work we shall study Einstein Gauss-Bonnet theories and we investigate when these can have their gravitational wave speed equal to the speed of light, which is unity in natural units, thus becoming compatible with the striking event GW170817. We demonstrate how this is possible and we show that if the scalar coupling to the Gauss-Bonnet invariant is constrained to satisfy a differential equation, the gravitational wave speed becomes equal to one. Accordingly, we investigate the inflationary phenomenology of the resulting restricted Einstein Gauss-Bonnet model, by assuming that the slow-roll conditions hold true. As we demonstrate, the compatibility with the observational data coming from the Planck 2018 collaboration, can be achieved, even for a power-law potential. We restricted ourselves to the study of the power-law potential, due to the lack of analyticity, however more realistic potentials can be used, in this case though the calculations are not easy to be performed analytically. We also pointed out that a string-corrected extension of the Einstein Gauss-Bonnet model we studied, containing terms of the form $\sim ξ(ϕ) G^{ab}\partial_aϕ\partial_b ϕ$ can also provide a theory with gravity waves speed $c_T^2=1$ in natural units, if the function $ξ(ϕ)$ is appropriately constrained, however in the absence of the Gauss-Bonnet term $\sim ξ(ϕ) \mathcal{G}$ the gravity waves speed can never be $c_T^2=1$. Finally, we discuss which extensions of the above models can provide interesting cosmologies, since any combination of $f(R,X,ϕ)$ gravities with the above string-corrected Einstein Gauss-Bonnet models can yield $c_T^2=1$, with $X=\frac{1}{2}\partial_μϕ\partial^μϕ$.

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arXiv2019

$F(R)$ Gravity with an Axion-like Particle: Dynamics, Gravity Waves, Late and Early-time Phenomenology

In this work we investigate several theoretical and phenomenological implications of a scalar -$F(R)$ gravity containing a non-minimal coupling to the scalar curvature. This kind of model is a generalization of axion-$F(R)$ gravity models, so we shall examine several implications of the latter theory. Firstly we study in detail the Einstein frame picture of the model, and also we discuss the dynamics of the cosmological system. By appropriately using the equations of motion, we demonstrate that an arbitrary cosmological evolution can be realized. Also we study the gravitational waves of the theory, and we demonstrate that the speed of their propagation is the same as in $F(R)$ gravity, but there is the possibility of enhancement or dissipation of the gravitational waves, an effect quite similar to the propagation of gravity waves in a viscous fluid. Finally, we examine the energy momentum tensor and we investigate which quantities related to it are conserved. We also present the constraints imposed by the radiation domination era on the non-minimal coupling of the axion scalar field to the scalar curvature.

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arXiv2019

Viable Inflationary Models in a Ghost-free Gauss-Bonnet Theory of Gravity

In this work we investigate the inflationary phenomenological implications of a recently developed ghost-free Gauss-Bonnet theory of gravity. The resulting theory can be viewed as a scalar Einstein-Gauss-Bonnet theory of gravity, so by employing the formalism for cosmological perturbations for the latter theory, we calculate the slow-roll indices and the observational indices, and we compare these with the latest observational data. Due to the presence of a freely chosen function in the model, in principle any cosmological evolution can be realized, so we specify the Hubble rate and the freely chosen function and we examine the phenomenology of the model. Specifically we focus on de Sitter, quasi-de Sitter and a cosmological evolution in which the Hubble rate evolves exponentially, with the last two being more realistic choices for describing inflation. As we demonstrate, the ghost-free model can produce inflationary phenomenology compatible with the observational data. We also briefly address the stability of first order scalar and tensor cosmological perturbations, for the exponential Hubble rate, and as we demonstrate, stability is achieved for the same range of values of the free parameters that guarantee the phenomenological viability of the models.

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arXiv2019

Unification of Inflation with Dark Energy in $f(R)$ Gravity and Axion Dark Matter

In this work we introduce an effective model of $f(R)$ gravity containing a non-minimal coupling to the axion scalar field. The axion field is described by the misalignment model, in which the primordial $U(1)$ Peccei-Quinn symmetry is broken during inflation and the $f(R)$ gravity is described by the $R^2$ model, and in addition, the non-minimal coupling has the form $\sim h(ϕ)R^γ$, with $0<γ<0.75$. By appropriately constraining the non-minimal coupling at early times, the axion field remains frozen in its primordial vacuum expectation value, and the $R^2$ gravity dominates the inflationary era. As the Universe expands, when $H$ equals the axion mass $m_a$ and for cosmic times for which $m_a\gg H$, the axion field oscillates. By assuming a slowly varying evolution of the axion field, the axion energy density scales as $ρ_a\sim a^{-3}$, where $a$ is the scale factor, regardless of the background Hubble rate, thus behaving as cold dark matter. At late times, the axion still evolves as $ρ_a\sim a^{-3}$, however the Hubble rate of the expansion and thus the dynamical evolution of the Universe is controlled by terms containing the higher derivatives of $\sim R^γ$, which are related to the non-minimal coupling, and as we demonstrate, the resulting solution of the Friedman equation at late times is an approximate de Sitter evolution. The late-time de Sitter Hubble rate scales as $H\sim Λ^{1/2}$, where $Λ$ is an integration constant of the theory, which has its allowed values very close to the current value of the cosmological constant. Finally, the theory has a prediction for the existence of a pre-inflationary primordial stiff era, in which the energy density of the axion scales as $ρ_a\sim a^{-6}$.

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arXiv2019

Finite-time Singularities in Swampland-related Dark Energy Models

In this work we shall investigate the singularity structure of the phase space corresponding to an exponential quintessence dark energy model recently related to swampland models. The dynamical system corresponding to the cosmological system is an autonomous polynomial dynamical system, and by using a mathematical theorem we shall investigate whether finite-time singularities can occur in the dynamical system variables. As we demonstrate, the solutions of the dynamical system are non-singular for all cosmic times and this result is general, meaning that the initial conditions corresponding to the regular solutions, belong to a general set of initial conditions and not to a limited set of initial conditions. As we explain, a dynamical system singularity is not directly related to a physical finite-time singularity. Then, by assuming that the Hubble rate with functional form $H(t)=f_1(t)+f_2(t)(t-t_s)^α$, is a solution of the dynamical system, we investigate the implications of the absence of finite-time singularities in the dynamical system variables. As we demonstrate, Big Rip and a Type IV singularities can always occur if $α<-1$ and $α>2$ respectively. However, Type II and Type III singularities cannot occur in the cosmological system, if the Hubble rate we quoted is considered a solution of the cosmological system.

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arXiv2019

$f(R)$ Gravity Inflation with String-Corrected Axion Dark Matter

It is quite well known for some time that string inspired axionic terms of the form $ν(ϕ)\tilde{R}R$, known also as Chern-Simons terms, do not affect the scalar perturbations and the background evolution for a flat Friedman-Robertson-Walker Universe. In this paper we study and quantify the implications of the presence of the above term in the context of vacuum $f(R)$. Particularly, we assume that axionic dark matter is present during inflation, and we examine in a quantitative way the effects of axionic Chern-Simons terms on the tensor perturbations. The axion field is quantified in terms of a canonical scalar field, with broken Peccei-Quinn symmetry. The model perfectly describing axions as potential dark matter candidates is based on the so-called misalignment mechanism, in which case the axion is frozen near its non-zero vacuum expectation value during early times in which $H\gg m_a$. In effect, the inflationary era is mainly controlled by the $f(R)$ gravity and the Chern-Simons term. As we demonstrate, the Chern-Simons term may achieve to make a non-viable $f(R)$ gravity theory to be phenomenologically viable, due to the fact that the tensor-to-scalar ratio is significantly reduced, and the same applies to the spectral index of the tensor perturbations $n_T$. Also by studying the Starobinsky model in the presence of the Chern-Simons term, we demonstrate that it is possible to further reduce the amount of primordial gravitational radiation. The issues of having parity violating gravitational waves, also the graceful exit from inflation due to axion oscillations and finally the unification of dark energy-inflation and axion dark matter in the same $f(R)$ gravity-axion dark matter model, are also briefly discussed.

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