We put forward novel extensions of Starobinsky inflation, involving a class of 'geometric' higher-curvature corrections that yield second-order Friedmann-Lemaître equations and second-order-in-time linearized equations around cosmological backgrounds. We determine the range of models within this class that admit an extended phase of slow roll inflation as an attractor. By embedding these theories in anti-de Sitter space, we derive holographic 'unitarity' bounds on the two dominant higher-order curvature corrections. Finally we compute the leading corrections to the spectral properties of scalar and tensor primordial perturbations, including the modified consistency relation $r=-8n_{T}$. Remarkably, the range of models singled out by holography nearly coincides with the current observational bounds on the scalar spectral tilt. Our results indicate that future observations have the potential to discriminate between different higher-curvature corrections considered here.
Recent years have seen the introduction of various multi-field inflationary scenarios in which the curvature and geodesics of the scalar manifold play a crucial role. We outline a simple description that unifies these different proposals and discuss their stability criteria. We demonstrate how the underlying dynamics is governed by an effective potential, whose critical points and bifurcations determine the late-time behaviour of the system, thus unifying hyperinflation, angular, orbital and side-tracked inflation. Interestingly, we show that hyperinflation is a special case of side-tracked in…
We derive lower bounds for the Higgs-curvature coupling from vacuum stability during inflation in three inflationary models: quadratic and quartic chaotic inflation, and Starobinsky-like power-law inflation. In contrast to most previous studies we take the time-dependence of the Hubble rate into account both in the geometry of our past light-cone and in the Higgs effective potential, which is approximated with three-loop renormalisation group improvement supplemented with one-loop curvature corrections. We find that in all three models, the lower bound is $ξ\gtrsim 0.051\ldots 0.066$ depending…
In this paper we investigate the cosmological dynamics of geometric inflation by means of the tools of the dynamical systems theory. We focus in the study of two explicit models where it is possible to sum the infinite series of higher curvature corrections that arises in the formalism. These would be very interesting possibilities since, if regard gravity as a quantum effective theory, a key feature is that higher powers of the curvature invariants are involved at higher loops. Hence, naively, consideration of the whole infinite tower of curvature invariants amounts to consideration of all of…
Inflationary era of our Universe can be characterized as semi-classical because it can be described in the context of four-dimensional Einsteins's gravity involving quantum corrections. These string motivated corrections originate from quantum theories of gravity such as superstring theories and include higher gravitational terms as, Gauss-Bonnet and Chern-Simons terms. In this paper we investigated inflationary phenomenology coming from a scalar field, with quadratic curvature terms in the view of GW170817. Firstly, we derived the equations of motion, directly from the gravitational action. A…
Entropy production in inflation from spectator loops
宇宙微波背景（CMB）光子和宇宙大尺度结构的扰动主要来源于暴胀过程中产生的曲率扰动。本文提出了一个双场暴胀模型，其中暴胀子与一个旁观者场双二次耦合。我们表明，观众诱导的曲率扰动和相关的高斯范诺依曼熵的动量在通货膨胀期间，使初始条件在通货膨胀结束时是从标准的显着不同的快速增长。因此，必须重新考虑描述光子、暗物质和重子流体在辐射和物质时代演化的动力学方程，并考虑曲率微扰及其正则动量是两个{ \it a priory}独立的随机场。我们还简要地分析了可能的印记的CMB温度波动，从更一般的暴胀的情况下，其中包含轻观众场耦合到暴胀。
Within General Relativity, a minimally coupled scalar field governed by a quadratic potential is able to produce an accelerated expansion of the universe provided its value and excursion are larger than the Planck scale. This is an archetypical example of the so called large field inflation models. We show that by including higher curvature corrections to the gravitational action in the form of the Geometric Inflation models, it is possible to obtain accelerated expansion with a free scalar field whose values are well below the Planck scale, thereby turning a traditional large field model into…
The current experimentally measured parameters of the Standard Model (SM) suggest that our Universe lies in a metastable electroweak vacuum, where the Higgs field is prone to vacuum decay to a lower state with catastrophic consequences. Our measurements dictate that such an event has not taken place yet, despite the many different mechanisms that could have triggered it in our past light-cone. The focus of our work has been to calculate the probability of the false vacuum to decay during the period of inflation and use it to constrain the last unknown renormalisable SM parameter $ξ$, which cou…
Based on entropy considerations and the arrow of time Penrose argued that the universe must have started in a special initial singularity with vanishing Weyl curvature. This is often interpreted to be at odds with inflation. Here we argue just the opposite, that Penrose's persuasions are in fact consistent with inflation. Using the example of power law inflation, we show that inflation begins with a past null singularity, where Weyl tensor vanishes when the metric is initially exactly conformally flat. This initial state precisely obeys Penrose's conditions. The initial null singularity breaks…
Preheating with non-minimally coupled scalar fields in higher-curvature inflation models
在高曲率暴胀模型（$R+α_n R^n$）中，我们研究了标量场$χ$与时空曲率$R$（$ξR χ^2$）非极小耦合的参量预热。在$R^2$ -膨胀模型的情况下，对于相当小的$ξ$值，即$|ξ|< several. Although the maximal fluctuation $ \sqrt{< χ^2 >}_{max} \approx 2 \times 10^{17} $ GeV for $ \approx-4 $ is almost the same as the chaotic inflation model with a non-minimally coupled $ × $ field, the growth rate of the fluctuation becomes much larger and efficient preheating is realized. We also investigate preheating for $ R^4 $ model and find that the maximal fluctuation is $ \sqrt{< χ^2 >}_{max} \approx 8 \times 10^{16} $ GeV for $ \approx-35 $，有效预热变得可能。
