Tracing the high energy theory of gravity: an introduction to Palatini inflation

Abstract

We present an introduction to cosmic inflation in the context of Palatini gravity, which is an interesting alternative to the usual metric theory of gravity. In the latter case only the metric g µν determines the geometry of space-time, whereas in the former case both the metric and the space-time connection Γ λ µν are a priori independent variables -a choice which can lead to a theory of gravity different from the metric one. In scenarios where the field(s) responsible for cosmic inflation are coupled non-minimally to gravity or the gravitational sector is otherwise extended, assumptions of the underlying gravitational degrees of freedom can have a big impact on the observational consequences of inflation. We demonstrate this explicitly by reviewing several interesting and well-motivated scenarios including Higgs inflation, R 2 inflation, and ξ-attractor models. We also discuss some prospects for future research and argue why r = 10 −3 is a particularly important goal for future missions that search for signatures of primordial gravitational waves.

Scale symmetry, the Higgs and the Cosmos

“…For 4cN * 1, the spectral tilt approaches minus infinity while its running and the tensor-to-scalar ratio tend to zero, in good agreement with the single pole behavior at c = 0 [53]. On the other hand, the emerging quadratic pole at c → 0 makes the expressions converge to the well-known Higgs inflation results [28,29]…”

“…and the associated flattening of the potential around them [27]. For ξ χ = 0 (c = 0), the pole Θ = 0 becomes quadratic and one recovers the well-known exponential stretching of Higgs inflation models [28,29]…”

Initial conditions for plateau inflation: a case study

“…This is an example of what is often called a Palatini or metric-affine theory; see Ref [3]. for original work and Ref [18]. for an introduction to the topic, as well as Refs.…”

Scalaron–Higgs inflation reloaded: Higgs-dependent scalaron mass and primordial black hole dark matter

“…The unification of these two models results in the two-field scalaron-Higgs model [15][16][17][18] (in the Palatini formalulation of the model [19][20][21][22][23] the scalaron is not a dynamical degree of freedom). Various aspects of this model have been studied, including the dependence of the inflationary dynamics on the initial conditions [18,24,25], the properties of its RG improvement [18,[26][27][28][29][30][31][32], the stabilization of the SM vacuum [18,33], the (p)reheating scenario [34][35][36][37], and a multifield amplification mechanism that leads to features in the inflationary power spectrum [18].…”