arXiv subjects
Publications and source records attributed to Alexandros Karam.
We present two scale invariant models of inflation in which the addition of quadratic in curvature terms in the usual Einstein-Hilbert action, in the context of Palatini formulation of gravity, manages to reduce the value of the tensor-to-scalar ratio. In both models the Planck scale is dynamically generated via the vacuum expectation value of the scalar fields.
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.
Attractor inflation is a particularly robust framework for developing inflationary models that are insensitive to the details of the potential. Such models are most often considered in the metric formulation of gravity. However, non-minimal models may not necessarily maintain their attractor nature in the Palatini formalism where the connection is independent of the metric. In this work, we employ the $β$-function formalism to classify the strong coupling limit of inflationary models in both the metric and the Palatini approaches. Furthermore, we determine the range of values for the non-minimal coupling that lead to theories being observationally indistinguishable in metric and Palatini within current accuracy. Finally, we reconstruct the Jordan frame potential for $ξ$-attractors by imposing an explicit form for the $β$-function, demonstrating the effect that the choice of metric or Palatini has on the inflationary observables of the theory.
We study non-minimal Coleman-Weinberg inflation in the Palatini formulation of gravity in the presence of an $R^2$ term. The Planck scale is dynamically generated by the vacuum expectation value of the inflaton via its non-minimal coupling to the curvature scalar $R$. We show that the addition of the $R^2$ term in Palatini gravity makes non-minimal Coleman-Weinberg inflation again compatible with observational data.
The predictions of standard Higgs inflation in the framework of the metric formalism yield a tensor-to-scalar ratio $r \sim 10^{-3}$ which lies well within the expected accuracy of near-future experiments $ \sim 10^{-4}$. When the Palatini formalism is employed, the predicted values of $r$ get highly-suppressed $r\sim 10^{-12}$ and consequently a possible non-detection of primordial tensor fluctuations will rule out only the metric variant of the model. On the other hand, the extremely small values predicted for $r$ by the Palatini approach constitute contact with observations a hopeless task for the foreseeable future. In this work, we propose a way to remedy this issue by extending the action with the inclusion of a generalized non-minimal derivative coupling term between the inflaton and the Einstein tensor of the form $m^{-2}(ϕ) G_{μν}\nabla^μϕ\nabla^νϕ$. We find that with such a modification, the Palatini predictions can become comparable with the ones obtained in the metric formalism, thus providing ample room for the model to be in contact with observations in the near future.
With a scalar field non-minimally coupled to curvature, the underlying geometry and variational principle of gravity - metric or Palatini - becomes important and makes a difference, as the field dynamics and observational predictions generally depend on this choice. In the present paper we describe a classification principle which encompasses both metric and Palatini models of inflation, employing the fact that inflationary observables can be neatly expressed in terms of certain quantities which remain invariant under conformal transformations and scalar field redefinitions. This allows us to elucidate the specific conditions when a model yields equivalent phenomenology in the metric and Palatini formalisms, and also to outline a method how to systematically construct different models in both formulations that produce the same observables.
We demonstrate that light spectator fields can source sizeable CMB anisotropies through modulated reheating even in the absence of direct couplings to the inflaton. The effect arises when the phase space of the inflaton decay is modulated by the spectator which generates masses for the decay products. We call the mechanism \textit{indirect modulation} and show that it can source perturbations even four orders of magnitude larger than the observed. Importantly, the indirect mechanism is present in the Standard Model extended with right-handed neutrinos. For a minimally coupled Higgs boson this leads to a novel lower bound on the quartic coupling and constrains the neutrino Yukawas below unity.
We present two cases where the addition of the $R^2$ term to an inflationary model leads to single-field inflation instead of two-field inflation as is usually the case. In both cases we find that the effect of the $R^2$ term is to reduce the value of the tensor-to-scalar ratio $r$.
By means of the Green's function method, we computed the spectral indices up to third order in the slow-roll approximation for a general scalar-tensor theory in both the Einstein and Jordan frames. Using quantities which are invariant under the conformal rescaling of the metric and transform as scalar functions under the reparametrization of the scalar field, we showed that the frames are equivalent up to this order due to the underlying assumptions. Nevertheless, care must be taken when defining the number of $e$-folds.
We extend the Coleman--Weinberg inflationary model where a scalar field $ϕ$ is non-minimally coupled to gravity with the addition of the $R^2$ term. We express the theory in terms of two scalar fields and going to the Einstein frame we employ the Gildener--Weinberg formalism, compute the one-loop effective potential and essentially reduce the problem to the case of single-field inflation. It turns out that there is only one free parameter, namely, the mixing angle between the scalars. For a wide range of this angle, we compute the inflationary observables which are in agreement with the latest experimental bounds. The effect of the $R^2$ term is that it lowers the value of the tensor-to-scalar ratio $r$.
The recent interest in modified theories of gravity, involving some type of non-minimal coupling to the Ricci scalar, and the calculation of cosmological observables in the Einstein or the Jordan frame, motivate the formulation of these theories in terms of quantities that are invariant under frame transformations. Furthermore, in view of the description of gravity and its geometry motivated by string theory, such a formulation could be extended to include theories of extra spatial dimensions. In the present article, we generalize the construction of frame-invariant quantities, concerning a general, $D$-dimensional scalar-tensor theory. Then, we limit our scope to the 5D braneworld scenario, where we study thick brane solutions that are localized on the 3-brane and extend the invariant formulation to the case of multiple scalar fields (non-)minimally coupled to gravity.
In constant-roll inflation, the scalar field that drives the accelerated expansion of the Universe is rolling down its potential at a constant rate. Within this framework, we highlight the relations between the Hubble slow-roll parameters and the potential ones, studying in detail the case of a single-field Coleman-Weinberg model characterised by a non-minimal coupling of the inflaton to gravity. With respect to the exact constant-roll predictions, we find that assuming an approximate slow-roll behaviour yields a difference of $Δr = 0.001$ in the tensor-to-scalar ratio prediction. Such a discrepancy is in principle testable by future satellite missions. As for the scalar spectral index $n_s$, we find that the existing 2-$σ$ bound constrains the value of the non-minimal coupling to $ξ_ϕ\sim 0.29-0.31$ in the model under consideration.
In the context of scalar-tensor theories of gravity we compute the third-order corrected spectral indices in the slow-roll approximation. The calculation is carried out by employing the Green's function method for scalar and tensor perturbations in both the Einstein and Jordan frames. Then, using the interrelations between the Hubble slow-roll parameters in the two frames we find that the frames are equivalent up to third order. Since the Hubble slow-roll parameters are related to the potential slow-roll parameters, we express the observables in terms of the latter which are manifestly invariant. Nevertheless, the same inflaton excursion leads to different predictions in the two frames since the definition of the number of e-folds differs. To illustrate this effect we consider a nonminimal inflationary model and find that the difference in the predictions grows with the nonminimal coupling and it can actually be larger than the difference between the first and third order results for the observables. Finally, we demonstrate the effect of various end-of-inflation conditions on the observables. These effects will become important for the analyses of inflationary models in view of the improved sensitivity of future experiments.
In this work we study a classically scale-invariant extension of the Standard Model in which the dark matter and electroweak scales are generated through the Coleman-Weinberg mechanism. The extra $SU(3)_X$ gauge factor gets completely broken by the vacuum expectation values of two scalar triplets. Out of the eight resulting massive vector bosons the three lightest are stable due to an intrinsic $Z_2\times Z_2'$ discrete symmetry and can constitute dark matter candidates. We analyze the phenomenological viability of the predicted multi-Higgs sector imposing theoretical and experimental constraints. We perform a comprehensive analysis of the dark matter predictions of the model solving numerically the set of coupled Boltzmann equations involving all relevant dark matter processes and explore the direct detection prospects of the dark matter candidates.
We present a classically scale-invariant model where the dark matter, neutrino and electroweak mass scales are dynamically generated from dimensionless couplings. The Standard Model gauge sector is extended by a dark $SU(2)_X$ gauge symmetry that is completely broken through a complex scalar doublet via the Coleman-Weinberg mechanism. The three resulting dark vector bosons of equal mass are stable and can play the role of dark matter. We also incorporate right-handed neutrinos which are coupled to a real singlet scalar that communicates with the other scalars through portal interactions. The multi-Higgs sector is analyzed by imposing theoretical and experimental constraints. We compute the dark matter relic abundance and study the possibility of the direct detection of the dark matter candidate from XENON 1T.
We consider a classically scale invariant version of the Standard Model, extended by an extra dark $SU(2)_X$ gauge group. Apart from the dark gauge bosons and a dark scalar doublet which is coupled to the Standard Model Higgs through a portal coupling, we incorporate right-handed neutrinos and an additional real singlet scalar field. After symmetry breaking à la Coleman-Weinberg, we examine the multi-Higgs sector and impose theoretical and experimental constraints. In addition, by computing the dark matter relic abundance and the spin-independent scattering cross section off a nucleon we determine the viable dark matter mass range in accordance with present limits. The model can be tested in the near future by collider experiments and direct detection searches such as XENON 1T.