Palatini Formulation Of General Relativity Research Articles

Critical points in Palatini Higgs inflation with small non-minimal coupling

We investigate inflation driven by the Higgs boson in the Palatini formulation of General Relativity. Our analysis primarily focuses on a small non-minimal coupling of the Higgs field to gravity in the range 0 < ξ ≲ 1. We incorporate the renormalization group running of the relevant parameters as computed within the Standard Model and allow for small corrections. In addition to ξ, our model features two tunable parameters: the low-energy value of the top Yukawa coupling and an effective jump of the Higgs self-interaction. Our results indicate that critical points leading to a large enhancement of the power spectrum can be produced. However, the observed amplitude of perturbations in the CMB cannot be matched within this setting. On the one hand, this makes it difficult to generate a sizable abundance of primordial black holes. On the other hand, our findings can be viewed as very positive since they provide further evidence that Palatini Higgs inflation has favourable high-energy properties due to robustness against quantum corrections.

Gravitational dark matter production in Palatini preheating

We study preheating in plateau inflation in the Palatini formulation of general relativity, in a special case that resembles Higgs inflation. It was previously shown that the oscillating inflaton field returns to the plateau repeatedly in this model, and this leads to tachyonic production of inflaton particles. We show that a minimally coupled spectator scalar field can be produced even more efficiently by a similar mechanism. The mechanism is purely gravitational, and the scalar field mass can be of order 1013 GeV, larger than the Hubble scale by many orders of magnitude, making this a candidate for superheavy dark matter.

Zero-parameter extension of general relativity with a varying cosmological constant

We provide a new extension of general relativity (GR) which has the remarkable property of being more constrained than GR plus a cosmological constant, having one less free parameter. This is implemented by allowing the cosmological constant to have a consistent space-time variation, through coding its dynamics in the torsion tensor. We demonstrate this mechanism by adding a `quasi-topological' term to the Einstein action, which naturally realizes a dynamical torsion with an automatic satisfaction of the Bianchi identities. Moreover, variation of the action with respect to this dynamical $\Lambda$ fixes it in terms of other variables, thus providing a scenario with less freedom than general relativity with a cosmological constant. Once matter is introduced, at least in the homogeneous and isotropic reduction, $\Lambda$ is uniquely determined by the field content of the model. We make an explicit construction using the Palatini formulation of GR and describe the striking properties of this new theory. We also highlight some possible extensions to the theory. A companion paper [1] explores the Friedmann--Robertson--Walker reduction for cosmology, and future work will study Solar System tests of the theory.

Inflation with R2 term in the Palatini formulation

We study scalar field inflation in F(R) gravity in the Palatini formulation of general relativity. Unlike in the metric formulation, in the Palatini formulation F(R) gravity does not introduce new degrees of freedom. However, it changes the relations between existing degrees of freedom, including the inflaton and spacetime curvature. Considering the case F(R)=R+α R2, we find that the R2 term decreases the height of the effective inflaton potential. By adjusting the value of α, this mechanism can be used to suppress the tensor-to-scalar ratio r without limit in any scalar field model of inflation without affecting the spectrum of scalar perturbations.

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

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, $\alpha$-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.

Planck scale black hole dark matter from Higgs inflation

We study the production of primordial black hole (PBH) dark matter in the case when the Standard Model Higgs coupled non-minimally to gravity is the inflaton. PBHs can be produced if the Higgs potential has a near-critical point due to quantum corrections. In this case the slow-roll approximation may be broken, so we calculate the power spectrum numerically. We consider both the metric and the Palatini formulation of general relativity. Combining observational constraints on PBHs and on the CMB spectrum we find that PBHs can constitute all of the dark matter only if they evaporate early and leave behind Planck mass relics. This requires the potential to have a shallow local minimum, not just a critical point. The initial PBH mass is then below 106 g, and predictions for the CMB observables are the same as in tree-level Higgs inflation, ns=0.96 and r=5×10−3 (metric) or r=4× 10−8 ṡ 2 × 10−7 (Palatini).

Higgs inflation at the hilltop

We study inflation with the non-minimally coupled Standard Model Higgs in the case when quantum corrections generate a hilltop in the potential. We consider both the metric and the Palatini formulation of general relativity. We investigate hilltop inflation in different parts of the Higgs potential and calculate predictions for CMB observables. We run the renormalization group equations up from the electroweak scale and down from the hilltop, adding a jump in-between to account for unknown corrections in the intermediate regime. Within our approximation, no viable hilltop inflation is possible for small field values, where the non-minimal coupling has no role, nor for intermediate field values. For large field values, hilltop inflation works. We find the spectral index to be ns⩽0.96 in both the metric and the Palatini formulation, the upper bound coinciding with the tree-level result. The tensor-to-scalar ratio is r⩽1.2×10−3 in the metric case and r⩽2.2×10−9 in the Palatini case. Successful inflation is possible even when the renormalization group running is continuous with no jumps. In the metric formulation, r is smaller than in Higgs inflation on the tree-level plateau or at the critical point, making it possible to distinguish hilltop inflation from these scenarios with next-generation CMB experiments.

Geometric foundations of Cartan gauge gravity

We use the theory of Cartan connections to analyze the geometrical structures underpinning the gauge-theoretical descriptions of the gravitational interaction. According to the theory of Cartan connections, the spin connection ω and the soldering form θ that define the fundamental variables of the Palatini formulation of general relativity can be understood as different components of a single field, namely a Cartan connection A = ω + θ. In order to stress both the similarities and the differences between the notions of Ehresmann connection and Cartan connection, we explain in detail how a Cartan geometry (PH→ M, A) can be obtained from a G-principal bundle PG→ M endowed with an Ehresmann connection (being the Lorentz group H a subgroup of G) by means of a bundle reduction mechanism. We claim that this reduction must be understood as a partial gauge fixing of the local gauge symmetries of PG, i.e. as a gauge fixing that leaves "unbroken" the local Lorentz invariance. We then argue that the "broken" part of the symmetry — that is the internal local translational invariance — is implicitly preserved by the invariance under the external diffeomorphisms of M.

De Sitter gravity from lattice gauge theory

We investigate a lattice model for Euclidean quantum gravity based on discretization of the Palatini formulation of General Relativity. Using Monte Carlo simulation we show that while a naive approach fails to lead to a vacuum state consistent with the emergence of classical spacetime, this problem may be evaded if the lattice action is supplemented by an appropriate counter term. In this new model we find regions of the parameter space which admit a ground state which can be interpreted as (Euclidean) de Sitter space.