Frame-Independent Classification of Single-Field Inflationary Models

Järv, Laur; Kannike, Kristjan; Marzola, Luca; Racioppi, Antonio; Raidal, M.; Rünkla, Mihkel; Saal, Margus; Veermäe, Hardi

doi:10.1103/physrevlett.118.151302

Cited by 83 publications

(109 citation statements)

References 37 publications

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“…Earlier work has looked at the differences between the metric and the Palatini formulation for the same action [140,86,59,60,63,68], whereas we have analysed the effect of terms that arise in the Palatini case and have no equivalent in the metric case. It would be interesting to extend the frame-covariant formalism developed to deal with conformal transformations of the metric [142] and partially translations of the connection [153,156,154,155,[157][158][159] to fully cover the transformations in the space of the scalar field, the metric and the connection, and make more transparent the frame-dependent role of the non-metricity and the connection. This connects to formulating the quantum theory in terms of frame-invariant variables to settle the issue of possible non-commutation of quantisation and frame transformations [88,172,173,91,174,175,56,176,154,155,37,39,42,44,47,177,89,[178][179][180].…”

Section: Discussionmentioning

confidence: 99%

Higgs inflation in the Palatini formulation with kinetic terms for the metric

Räsänen¹

2019

TheOJA

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We consider scalar field inflation in the Palatini formulation of general relativity. The covariant derivative of the metric is then non-zero. From the effective theory point of view it should couple to other fields. We write down the most general couplings between it and a scalar field that are quadratic in derivatives. We consider both the case when the torsion is determined by the field equations and the case when it is assumed to be zero a priori. We find the metric derivative terms can significantly modify inflationary predictions. We specialise to Higgs inflation and terms of only up to dimension 4. Transforming to the Einstein frame, we show that by tuning the coefficients of the new terms, we can generate various effective inflationary potentials, including quadratic, hilltop-type, α-attractor and inflection point. Some of these can give inflation in agreement with observations, including with a large tensor-to-scalar ratio, even if the non-minimal coupling is zero.syksy.rasanen@iki.fi 1 False vacuum inflation is a possibility, but requires physics beyond the SM for graceful exit [27][28][29][30][31][32][33]. 2 The Palatini formulation is somewhat of a misnomer, as it was developed by Einstein [112,113]. It is also called the first order formulation, as only first derivatives appear in the gravitational action, unlike in the metric formulation (also referred to as the Hilbert formulation). Metric-affine is perhaps a more descriptive term, but it is often used to refer to the case when the general connection is used in both the gravitational and the matter action, with the name Palatini restricted to the case when the general connection is reserved for the gravitational sector, and the Levi-Civita connection is used in the matter sector [114][115][116]. arXiv:1811.09514v2 [gr-qc]

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Section: Discussionmentioning

confidence: 99%

Higgs inflation in the Palatini formulation with kinetic terms for the metric

Räsänen¹

2019

TheOJA

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“…Despite many different possible parametrizations, all physical observables are in fact independent of the parametrization, and can be expressed in terms of quantities invariant under conformal transformations and scalar field redefinitions [10,11].…”

Section: Scalar-(curvature)tensor Gravitymentioning

confidence: 99%

Effective Gravitational “Constant” in Scalar-(Curvature)Tensor and Scalar-Torsion Gravities

Järv

2017

Universe

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Abstract:In theories where a scalar field couples nonminimally to gravity, the effective gravitational "constant" becomes dependent on the value of the scalar field. This note first gives a brief review on how the cosmological evolution provides a dynamical stabilization for the gravitational "constant" as the system relaxes towards general relativity in matter dominated and potential dominated regimes for scalar-(curvature)tensor and scalar-torsion gravities. Second part summarizes the radius dependence of the gravitational "constant" around a point mass in the parametrized post-Newtonian formalism for scalar-tensor and multiscalar-tensor gravity.

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“…This is known as the frame problem, a long-standing debate whose origin can be traced to alternative theories of gravity [43,44]. It is now commonly accepted that Lagrangians related by frame transformations are different expressions of the same model, insofar as they produce the same observables, at least at the tree level [45][46][47][48][49][50][51][52][53][54][55][56]. Therefore, even if ostensibly it takes three functions f (φ), k(φ) and V (φ) to specify a Lagrangian, a physically distinct single-field model can be fully specified by the canonical potential U (ϕ).…”

Section: Scalar-tensor Theories As Manifoldsmentioning

confidence: 99%

Beyond the poles in attractor models of inflation

Karamitsos

2019

J. Cosmol. Astropart. Phys.

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We offer a geometric interpretation of attractor theories with singular kinetic terms as a union of multiple canonical models. We demonstrate that different domains (separated by poles) can drastically differ in their phenomenology. We illustrate this with the help of a "master model" that leads to distinct predictions depending on which side of the pole the field evolves before examining the more realistic example of α-attractor models. Such models lead to quintessential inflation within the poles when featuring an exponential potential. However, beyond the poles, we discover a novel behaviour: the scalar field responsible for the early-time acceleration of the Universe may reach the boundary of the field-space manifold, indicating that the theory is incomplete and that a boundary condition must be imposed in order to determine its late-time behaviour. If the evolution of the field is arrested before this happens, however, we discover that quintessence can be achieved without a potential offset. Turning to multifield models with singular kinetic terms, we see that poles generalise straightforwardly to singular curves, which act as "model walls" between distinct pole-free inflationary models. As an example, we study a simple two-field α-attractor-inspired model, whose evolution of isocurvature perturbations is sensitive to where the non-canonical field begins its trajectory. We finally discuss initial conditions in attractor theories, where the existence of multiple disconnected canonical models implies that we must make a fundamental choice: in which domain we impose a distribution for the inflaton in order to then determine the likelihood of inflation.

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Frame-Independent Classification of Single-Field Inflationary Models

Cited by 83 publications

References 37 publications

Higgs inflation in the Palatini formulation with kinetic terms for the metric

Higgs inflation in the Palatini formulation with kinetic terms for the metric

Effective Gravitational “Constant” in Scalar-(Curvature)Tensor and Scalar-Torsion Gravities

Beyond the poles in attractor models of inflation

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