A note on second-order perturbations of non-canonical scalar fields

We derive a condition on the Lagrangian density describing a generic, single, non-canonical scalar field, by demanding that the intrinsic, non-adiabatic pressure perturbation associated with the scalar field vanishes identically. Based on the analogy with perfect fluids, we refer to such fields as perfect scalar fields. It is common knowledge that models that depend only on the kinetic energy of the scalar field (often referred to as pure kinetic models) possess no non-adiabatic pressure perturbation. While we are able to construct models that seemingly depend on the scalar field and also do not contain any non-adiabatic pressure perturbation, we find that all such models that we construct allow a redefinition of the field under which they reduce to pure kinetic models. We show that, if a perfect scalar field drives inflation, then, in such situations, the first slow roll parameter will always be a monotonically decreasing function of time. We point out that this behavior implies that these scalar fields can not lead to features in the inflationary, scalar perturbation spectrum.Comment: v1: 11 pages; v2: 11 pages, minor changes, journal versio

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“…[7]; in this context, also see Ref. [17]). So, during inflation, in addition to w < −(1/3), we require that c 2 S > 0.…”

Section: An Interesting Implication For Inflationmentioning

confidence: 88%

A note on perfect scalar fields

Unnikrishnan¹,

Sriramkumar²

2010

Phys. Rev. D

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“…A well-known example of a non-valid case is the class B family of Bianchi models [19]. The class of spatially homogeneous Bianchi cosmologies including, the FLRW space-time and Bianchi IX, are valid cases [19][20][21]. Also, in the case of FLRW space-time, this is valid up to second-order in perturbations [21].…”

Section: Tionmentioning

confidence: 99%

Can we bypass no-go theorem for Ricci-inverse Gravity?

Das¹,

Johnson

Shankaranarayanan

2021

Preprint

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Recently, Amendola et al. proposed a geometrical theory of gravity containing higher-order derivative terms [1]. The authors introduced anticurvature scalar (A), which is the trace of the inverse of the Ricci tensor (A µν = R −1 µν ). In this work, we consider two classes of Ricci-inverse -Class I and Class II -models. Class I models are of the form f (R, A) where f is a function of Ricci and anticurvature scalars. Class II models are of the form F(R, A µν A µν ) where F is a function of Ricci scalar and square of anticurvature tensor. For both these classes of models, we numerically solve the modified Friedmann equations in the redshift range 1500 < z < 0. We show that the late-time evolution of the Universe, i.e., evolution from matter-dominated epoch to accelerated expansion epoch, can not be explained by these two classes of models. Using the reduced action approach, we show why we can not bypass the no-go theorem for Ricci-inverse gravity models.Finally, we discuss the implications of our analysis for the early-Universe cosmology.

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“…In ref. [54], it was shown that when the metric perturbations are frozen then the two approaches do not, in general, lead to the same expressions. In this work we address the issue by including the metric perturbations in the theory.…”

Section: Jcap08(2015)050mentioning

confidence: 99%

“…To confirm or infirm the result of ref. [54], that the two approaches lead to different results we focus on non-canonical scalar field, i.e., setting G(X, ϕ) = 0.…”

Section: Jcap08(2015)050mentioning

confidence: 99%

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`Constraint consistency' at all orders in cosmological perturbation theory

Nandi

Shankaranarayanan

2015

J. Cosmol. Astropart. Phys.

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Abstract. We study the equivalence of two -order-by-order Einstein's equation and Reduced action -approaches to cosmological perturbation theory at all orders for different models of inflation. We point out a crucial consistency check which we refer to as 'Constraint consistency' condition that needs to be satisfied in order for the two approaches to lead to identical single variable equation of motion. The method we propose here is quick and efficient to check the consistency for any model including modified gravity models. Our analysis points out an important feature which is crucial for inflationary model building i.e., all 'constraint' inconsistent models have higher order Ostrogradsky's instabilities but the reverse is not true. In other words, one can have models with constraint Lapse function and Shift vector, though it may have Ostrogradsky's instabilities. We also obtain single variable equation for non-canonical scalar field in the limit of power-law inflation for the second-order perturbed variables.

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A note on second-order perturbations of non-canonical scalar fields

Cited by 5 publications

References 43 publications

A note on perfect scalar fields

A note on perfect scalar fields

Can we bypass no-go theorem for Ricci-inverse Gravity?

`Constraint consistency' at all orders in cosmological perturbation theory

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