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Register a new userTracing the high energy theory of gravity: an introduction to Palatini inflation
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Tommi Tenkanen
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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 $g_{mu u}$ determines the geometry of space-time, whereas in the former case both the metric and the space-time connection $Gamma^lambda_{mu u}$ 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 $xi$-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.
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It has recently been suggested that the Standard Model Higgs boson could act as the inflaton while minimally coupled to gravity - given that the gravity sector is extended with an $alpha R^2$ term and the underlying theory of gravity is of Palatini, rather than metric, type. In this paper, we revisit the idea and correct some shortcomings in earlier studies. We find that in this setup the Higgs can indeed act as the inflaton and that the tree-level predictions of the model for the spectral index and the tensor-to-scalar ratio are $n_ssimeq 0.941$, $rsimeq 0.3/(1+10^{-8}alpha)$, respectively, for a typical number of e-folds, $N=50$, between horizon exit of the pivot scale $k=0.05, {rm Mpc}^{-1}$ and the end of inflation. Even though the tensor-to-scalar ratio is suppressed compared to the usual minimally coupled case and can be made compatible with data for large enough $alpha$, the result for $n_s$ is in severe tension with the Planck results. We briefly discuss extensions of the model.
In the framework of classical scale invariance, we consider quadratic gravity in the Palatini formalism and investigate the inflationary predictions of the theory. Our model corresponds to a two-field scalar-tensor theory, that involves the Higgs field and an extra scalar field stemming from a gauge $U(1)_X$ extension of the Standard Model, which contains an extra gauge boson and three right-handed neutrinos. Both scalar fields couple nonminimally to gravity and induce the Planck scale dynamically, once they develop vacuum expectation values. By means of the Gildener-Weinberg approach, we describe the inflationary dynamics in terms of a single scalar degree of freedom along the flat direction of the tree-level potential. The one-loop effective potential in the Einstein frame exhibits plateaus on both sides of the minimum and thus the model can accommodate both small and large field inflation. The inflationary predictions of the model are found to comply with the latest bounds set by the Planck collaboration for a wide range of parameters and the effect of the quadratic in curvature terms is to reduce the value of the tensor-to-scalar ratio.
We study preheating in the Palatini formalism with a quadratic inflaton potential and an added $alpha R^2$ term. In such models, the oscillating inflaton field repeatedly returns to the plateau of the Einstein frame potential, on which the tachyonic instability fragments the inflaton condensate within less than an e-fold. We find that tachyonic preheating takes place when $alpha gtrsim 10^{13}$ and that the energy density of the fragmented field grows with the rate $Gamma/H approx 0.011 times alpha^{0.31}$. The model extends the family of plateau models with similar preheating behaviour. Although it contains non-canonical quartic kinetic terms in the Einstein frame, we show that, in the first approximation, these can be neglected during both preheating and inflation.
We develop an approach to compute observables beyond the linear regime of dark matter perturbations for general dark energy and modified gravity models. We do so by combining the Effective Field Theory of Dark Energy and Effective Field Theory of Large-Scale Structure approaches. In particular, we parametrize the linear and nonlinear effects of dark energy on dark matter clustering in terms of the Lagrangian terms introduced in a companion paper, focusing on Horndeski theories and assuming the quasi-static approximation. The Euler equation for dark matter is sourced, via the Newtonian potential, by new nonlinear vertices due to modified gravity and, as in the pure dark matter case, by the effects of short-scale physics in the form of the divergence of an effective stress tensor. The effective fluid introduces a counterterm in the solution to the matter continuity and Euler equations, which allows a controlled expansion of clustering statistics on mildly nonlinear scales. We use this setup to compute the one-loop dark-matter power spectrum.
We consider an alternative to inflation for the generation of superhorizon perturbations in the universe in which the speed of sound is faster than the speed of light. We label such cosmologies, first proposed by Armendariz-Picon, {it tachyacoustic}, and explicitly construct examples of non-canonical Lagrangians which have superluminal sound speed, but which are causally self-consistent. Such models possess two horizons, a Hubble horizon and an acoustic horizon, which have independent dynamics. Even in a decelerating (non-inflationary) background, a nearly scale-invariant spectrum of perturbations can be generated by quantum perturbations redshifted outside of a shrinking acoustic horizon. The acoustic horizon can be large or even infinite at early times, solving the cosmological horizon problem without inflation. These models do not, however, dynamically solve the cosmological flatness problem, which must be imposed as a boundary condition. Gravitational wave modes, which are produced by quantum fluctuations exiting the Hubble horizon, are not produced.
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