Dynamical aspects for scalar fields coupled to cubic contractions of the Riemann tensor

We put forward novel extensions of Starobinsky inflation, involving a class of 'geometric' highercurvature corrections that yield second-order Friedmann-Lemaître equations and second-order-intime linearized equations around cosmological backgrounds. We determine the range of models within this class that admit an extended phase of slow roll inflation as an attractor. By embedding these theories in anti-de Sitter space, we derive holographic 'unitarity' bounds on the two dominant higher-order curvature corrections. Finally we compute the leading corrections to the spectral properties of scalar and tensor primordial perturbations, including the modified consistency relation r = −8nT . Remarkably, the range of models singled out by holography nearly coincides with the current observational bounds on the scalar spectral tilt. Our results indicate that future observations have the potential to discriminate between different higher-curvature corrections considered here.

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“…A possible way out is to include a scalar field [26]. See also [27][28][29][30][31][32] for other follow-ups of the geometric inflation scenario.…”

Section: A Geometric Higher-curvature Termsmentioning

confidence: 99%

Novel higher-curvature variations of R2 inflation

2021

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“…Furthermore, the properties of the inflationary era have been analyzed in some specific theories [40][41][42][43][44][45][46]. The coupling of a scalar field with a cubic term has been investigated by considering a dynamical system analysis [47]. Recently, it has been shown that the cubic gravity theory can be associated to the developments of various types of pathological instabilities [48] which have to be addressed in order to construct a viable theory [49].…”

Section: Introductionmentioning

confidence: 99%

Tachyonic cosmology with cubic contractions of the Riemann tensor

Marciu¹

2022

Preprint

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A new cosmological theory is proposed in the theoretical framework of modified gravity theories which is based on a tachyonic field non-minimally coupled with a specific topological invariant constructed with third order contractions of the Riemann tensor. After proposing the action of the cosmological model, the modified Friedmann relations and the Klein-Gordon equations are obtained, describing the corresponding geometrical corrections to the Einstein-Hilbert action. The physical features of the cosmological system are investigated by adopting the dynamical system analysis in the case of an exponential function for the geometrical coupling term. The investigation revealed that the cosmological system can explain the current accelerated expansion of the Universe and the matter dominated epoch, showing a high compatibility to the recent history of our Universe for various values of the coupling coefficients.

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“…An alternative proposal has been analyzed in [53] for the Einsteinian cubic gravity, a specific theory which also includes a cosmological constant. The inclusion of the cubic invariant into possible theories which are embedding scalar fields has been investigated in [54], considering a specific coupling for the quintessence or phantom models. Furthermore, different studies have considered a holographic approach for the Einsteinian cubic gravity [55,56].…”

Section: Introductionmentioning

confidence: 99%

Dark effects in $$\tilde{f}(R,P)$$ gravity

Marciu

2021

Eur. Phys. J. C

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In the present paper a new cosmological model is proposed by extending the Einstein–Hilbert Lagrangian with a generic functional $$\tilde{f}(R,P)$$ f ~ ( R , P ) , which depends on the scalar curvature R and a term P which encodes a possible influence from specific cubic contractions of the Riemann tensor. After proposing the corresponding action, the associated modified Friedmann relations are deduced, in the case where the generic functional has the following decomposition, $$\tilde{f}(R,P)=f(R)+g(P)$$ f ~ ( R , P ) = f ( R ) + g ( P ) . The present study takes into account the power-law and the exponential decomposition for the specific form of the corresponding generic functional. For the analytical approach the specific method of dynamical system analysis is employed, revealing the fundamental properties of the phase space structure, discussing the dynamical consequences for the cosmological solutions obtained. It is revealed that the cosmological solutions associated to the critical points can explain various dynamical eras, with a high sensitivity to the values of the corresponding parameters, encoding different effects due to the geometrical nature of the specific couplings.

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Dynamical aspects for scalar fields coupled to cubic contractions of the Riemann tensor

Cited by 18 publications

References 50 publications

Novel higher-curvature variations of R2 inflation

Novel higher-curvature variations of R2 inflation

Tachyonic cosmology with cubic contractions of the Riemann tensor

Dark effects in $$\tilde{f}(R,P)$$ gravity

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