On the renormalization group perspective of α-attractors

Narain, Gaurav

doi:10.1088/1475-7516/2017/10/032

Cited by 12 publications

(3 citation statements)

References 66 publications

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“…Also the second part of this paper is devoted on studying reconstructed slow-roll models of Einstein Gauss-Bonnet gravity from the observational indices. This bottom-up approach is frequently used in the literature [34][35][36][37][38][39][40][41][42][43][44] and it provides viable inflationary models. We shall provide analytic formulas for the slow-roll indices and for the spectral index of the primordial curvature perturbations and we will investigate the viability of the resulting models in detail.…”

Section: Introductionmentioning

confidence: 99%

Viable inflation in scalar-Gauss-Bonnet gravity and reconstruction from observational indices

2018

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In this paper the focus is on inflationary dynamics in the context of Einstein Gauss-Bonnet gravitational theories. We investigate the implications of the slow-roll condition on the slow-roll indices and we investigate how the inflationary dynamical evolution is affected by the presence of the Gauss-Bonnet coupling to the scalar field. For exemplification of our analysis we investigate how the dynamics of inflationary cubic, quartic order and also exponential scalar potentials are affected by the non-trivial Gauss-Bonnet coupling to the scalar field. As we demonstrate it is possible to obtain a viable phenomenology compatible with the observational data, although the canonical scalar field theory with cubic and quartic order potentials does not yield phenomenologically acceptable results. In addition, with regard to the exponential potential example, the Einstein Gauss-Bonnet extension of the single canonical scalar field model has an inherent mechanism that can trigger the graceful exit from inflation. Furthermore we introduce a bottom-up reconstruction technique, in the context of which by fixing the tensor-to-scalar ratio and the Hubble rate as a function of the e-foldings number, one is capable of reproducing the Einstein Gauss-Bonnet theory which generates the aforementioned quantities. We illustrate how the method works by using some relatively simple examples.PACS numbers: 04.50. Kd, 95.36.+x, 98.80.Cq,

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Section: Introductionmentioning

confidence: 99%

Viable inflation in scalar-Gauss-Bonnet gravity and reconstruction from observational indices

2018

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“…RF and hence by solving this differential equation it follows that f is approximately proportional to R 2 1 (see Ref. [18] for a similar observation). Therefore, R 2 gravity is quite common in slow-roll inflation.…”

Section: F (R) From N S (N ): Analysis In the Einstein Framementioning

confidence: 79%

Reconstructing $f(R)$ gravity from the spectral index

Chiba

2018

Progress of Theoretical and Experimental Physics

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Recent cosmological observations are in good agreement with the scalar spectral index n s with n s − 1 ≃ −2/N , where N is the number of e-foldings. In the previous work, the reconstruction of the inflaton potential for a given n s was studied, and it was found that for n s − 1 = −2/N , the potential takes the form of either α-attractor model or chaotic inflation model with φ 2 to the leading order in the slow-roll approximation.Here we consider the reconstruction of the f (R) gravity model for a given n s both in the Einstein frame and in the Jordan frame. We find that for n s − 1 = −2/N (or more general n s − 1 = −p/N ), f (R) is given parametrically and is found to asymptote to R 2 for large R. This behavior is generic as long as the scalar potential is of slow-roll type.

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“…The R 2 gravity, famously referred to as Starobinsky model of inflation [1,2], is seen to posses wonderful properties as desired to have an early phase of cosmic inflation and falls in the class of F (R)-theories of gravity [21,22]. Moreover, scalar field inflationary models via reconstruction can be cast into F (R) theories and at high-energies are seen to become R 2 gravity [23]. Motivated by acknowledging the supremacy of R 2 gravity among various inflationary models and the benefit of renormalizabilty it enjoys, we realise the necessity to investigate the effect of higher-derivative gravity in the context of Lorentzian quantum cosmology.…”

Section: Introductionmentioning

confidence: 99%

Lorentzian quantum cosmology with $R^2$ correction

Narain¹,

Zhang²

2019

Preprint

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Quantum mechanical transition amplitudes directly tells the probability of each transition and which one is more favourable. Path-integrals offers a systematic methodology to compute this quantum mechanical process in a consistent manner. Although it is not complicated in simple quantum mechanical system but defining path-integral legitimately becomes highly nontrivial in the context of quantumgravity, where apart from usual issues of renormalizability, regularisation, measure, gauge-fixing, boundary conditions, one still has to define the sensible integration contour for convergence. Picard-Lefschetz (PL) theory offers a unique way to find a contour of integration based on the analysis of saddle points and the steepest descent/ascent flow lines in the complex plane. In this paper we make use of PLtheory to investigate Lorentzian quantum cosmology where the gravity gets modified in the ultraviolet with the R 2 corrections. We approach the problem perturbatively and compute the transition amplitude in the saddle point approximation to first order in higher-derivative coupling. This perturbative approximation is valid in certain regimes but the approximation cannot be used to address issues of very early Universe or no-boundary proposal.

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On the renormalization group perspective of α-attractors

Cited by 12 publications

References 66 publications

Viable inflation in scalar-Gauss-Bonnet gravity and reconstruction from observational indices

Viable inflation in scalar-Gauss-Bonnet gravity and reconstruction from observational indices

Reconstructing $f(R)$ gravity from the spectral index

Lorentzian quantum cosmology with $R^2$ correction

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