Classical and quantum cosmology of $K$-essentially modified $R^2$ and pure $R^p$ gravity

Kan, Nahomi; Shiraishi, Kiyoshi; Yashiki, Mai

doi:10.48550/arxiv.1811.11967

Cited by 2 publications

(4 citation statements)

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“…The exponential type model does not yield a viable phenomenology, at least in the slow-roll case, but as we show in a later section, it provides a viable phenomenology only in the constant-roll case. However, the power-law type of model (30) does yield a viable phenomenology in the slow-roll case, as we now demonstrate. So in the rest of this subsection, we focus on the power-law type of model of Eq.…”

Section: A Models With Potential: Slow-roll Phenomenologysupporting

confidence: 53%

“…which are compatible with the Planck 2018 constraints (28). We need to note that the viability for the exponential model ( 29) comes with more difficulty in comparison to the power-law model (30), but this is a model-dependent feature and has nothing to do with the constant-roll condition. Finally, the wave speed is also between 0 < c 2 A < 1, at least for the values of the free parameters that guarantee the phenomenological viability of the model, so no Jeans instabilities or superluminal propagation of scalar modes occur in this case too.…”

Section: B Models With Potential: Constant-roll Phenomenologymentioning

confidence: 83%

“…So in the rest of this subsection, we focus on the power-law type of model of Eq. ( 30), so for the model (30), the slow-roll indices of Eq. ( 52) become,…”

Section: A Models With Potential: Slow-roll Phenomenologymentioning

confidence: 99%

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Non-minimally Coupled Scalar $k$-Inflation Dynamics

Oikonomou

2021

Preprint

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In this work we shall study k-inflation theories with non-minimal coupling of the scalar field to gravity, in the presence of only a higher order kinetic term of the form ∼ const × X µ , with X = 1 2 ∂µφ∂ µ φ. The study will be focused in the cases where a scalar potential is included or is absent, and the evolution of the scalar field will be assumed to satisfy the slow-roll or the constant-roll condition. In the case of the slow-roll models with scalar potential, we shall calculate the slow-roll indices, and the corresponding observational indices of the theory, and we demonstrate that the resulting theory is compatible with the latest Planck data. The same results are obtained in the constant-roll case, at least in the presence of a scalar potential. In the case that models without potential are considered, the results are less appealing since these are strongly model dependent, and at least for a power-law choice of the non-minimal coupling, the theory is non-viable. Finally, due to the fact that the scalar and tensor power spectra are conformal invariant quantities, we argue that the Einstein frame counterpart of the non-minimal k-inflation models with scalar potential, can be a viable theory, due to the conformal invariance of the observational indices. The Einstein frame theory is more involved and thus more difficult to work with it analytically, so one implication of our work is that we provide evidence for the viability of another class of k-inflation models.

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Section: A Models With Potential: Slow-roll Phenomenologysupporting

confidence: 53%

Section: B Models With Potential: Constant-roll Phenomenologymentioning

confidence: 83%

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Non-minimally Coupled Scalar $k$-Inflation Dynamics

Oikonomou

2021

Preprint

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“…With regard to the bounce cosmology alternative description, these theories became popular after the Loop Quantum Cosmology theory [16-19, 21-24, 62] resulted in the generation of a quantum bounce. One of the theories that can also realize a successful inflationary era, are the so-called k-essence theories [35][36][37][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54], which can also generate other appealing features of cosmological evolution. In this paper we shall be interested in studying a k-essence modified f (R) gravity of a simple form, by adding a higher order scalar field kinetic term, along with the vacuum f (R) gravity.…”

Section: Introductionmentioning

confidence: 99%

k-essence f(R) gravity inflation

2019

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solutions of the slow-roll theory, with regard to the scalar field. After that we employ two different approaches in order to study the phenomenological implications of the k-essence f (R) gravity theory. In the first approach, we choose the functional form of the f (R) gravity, and we investigate how the k-essence term affects the cosmological evolution in terms of the Hubble rate. After that we calculate in detail the slow-roll indices of the inflationary theory at hand, and correspondingly the observational indices. Eventually we investigate the parameter space of the theory and we test the phenomenological validity of the theory. The choice of the functional form of the f (R) gravity is such, so that the vacuum f (R) gravity is not phenomenologically viable, so in effect we investigate whether the k-essence f (R) gravity can be a phenomenologically acceptable theory. In the second approach, we fix the functional form of the Hubble rate as a function of the e-foldings number, and we investigate which k-essence f (R) gravity in the slow-roll approximation can produce such a cosmological evolution. After this we express the slow-roll indices as functions of the e-foldings number in the slow-roll approximation, and we provide their functional form in detail, and by using the resulting f (R) gravity, we test the validity of the theory by examining the parameter space. As we will demonstrate, in this case too, it is possible to produce a viable inflationary evolution in the context of k-essence f (R) gravity. In addition we examine the conditions under which ghosts can occur in the theory, so we discriminate the ghost-free and phantom cases, and the above considerations are given in terms of these two cases.This paper is organized as follows: In section II we investigate when ghost degrees of freedom can occur in a general k-essence f (R) gravity, and we find the no-ghost constraints on a special class of k-essence f (R) gravity models. In section III we present the essential features of the proposed k-essence f (R) gravity theory, we derive the equations of motion and we investigate how the slow-roll conditions affect the resulting solution of the scalar field. After that we choose the functional form of the f (R) gravity and we calculate the slow-roll indices of the resulting theory. Accordingly we calculate the observational indices and we test the validity of the theory by confronting it with the observational data. In section IV we use another approach, by fixing the Hubble rate, and we investigate which k-essence f (R) gravity can produce such a cosmic evolution. We provide detailed formulas for the slow-roll indices as functions of the e-foldings number, and we calculate the observational indices in the slow-roll approximation. Accordingly, the viability of the theory is tested by confronting it with the observational data. Finally, the conclusions follow in the end of the paper.Before we get to the core of this paper, we will discuss in brief the geometric framework which shall be assumed in the rest of thi...

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Classical and quantum cosmology of $K$-essentially modified $R^2$ and pure $R^p$ gravity

Cited by 2 publications

References 57 publications

Non-minimally Coupled Scalar $k$-Inflation Dynamics

Non-minimally Coupled Scalar $k$-Inflation Dynamics

k-essence f(R) gravity inflation

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