Towards geometric inflation: The cubic case

2018

We present an up to cubic curvature correction to General Relativity with the following features: (i) its vacuum spectrum solely consists of a graviton and is ghost-free, (ii) it possesses well-behaved black hole solutions which coincide with those of Einsteinian cubic gravity, (iii) its cosmology is well-posed as an initial value problem and, most importantly, (iv) it has the potential to provide a late-time cosmology arbitrarily close to ΛCDM while, at the same time, giving an inflationary period in the early universe with a graceful exit.

Physics Letters B

We argue that the presence of an inflationary epoch is a natural, almost unavoidable, consequence of the existence of a sensible effective action involving an infinite tower of higher-curvature corrections to the Einstein-Hilbert action. No additional fields besides the metric are required. We show that a family of such corrections giving rise to a well-posed cosmological evolution exists and automatically replaces the radiation-dominated early-universe Big Bang by a singularity-free period of exponential growth of the scale factor, which is gracefully connected with standard late-time ΛCDM cosmology. The class of higher-curvature theories giving rise to sensible cosmological evolution share additional remarkable properties such as the existence of Schwarzschild-like non-hairy black holes, or the fact that, just like for Einstein gravity, the only degrees of freedom propagated on the vacuum are those of the standard graviton.

Physical Review D

We investigate the cosmological dynamics of an up to cubic curvature correction to general relativity (GR) known as cosmological Einsteinian cubic gravity, whose vacuum spectrum consists of the graviton exclusively. Its cosmology is well posed as an initial value problem. We are able to uncover the global asymptotic structure of the phase space of this theory. It is revealed that an inflationary, matter-dominated big bang is the global past attractor, which means that inflation is the starting point of any physically meaningful cosmic history. Given that higher-order curvature corrections to GR are assumed to influence the cosmological dynamics at early times-the high energy/large curvature limit-late-time inflation is possible only if one considers a nonvanishing cosmological constant term.

Physical Review D, 2014

We study inflation induced by (power-low) scalar curvature corrections to General Relativity. The class of inflationary scalar potentials V (σ) ∼ exp[n σ], n general parameter, is investigated in the Einsein frame and the corresponding actions in the Jordan frame are derived. We found the conditions for which these potentials are able to reproduce viable inflation according with the last cosmological data and lead to large scalar curvature corrections which emerge only at a mass scale larger than the Planck mass. Cosmological constant may appear or be set equal to zero in the Jordan frame action without changing the behaviour of the model during inflation. Moreover, polynomial corrections to General Relativity are analyzed in detail. When de Sitter space-time emerges as an exact solution of the models, it is necessary to use perturbative equations in the Jordan framework to study their dynamics during the inflation. In this case, we demonstrate that the Ricci scalar decreases after a correct amount of inflation, making the models consistent with the observable evolution of the universe.

Journal of Cosmology and Astroparticle Physics, 2005

We investigate the possibility that the Universe may inflate due to moduli fields, corresponding to flat directions of supersymmetry, lifted by supergravity corrections. Using a hybrid-type potential we obtain a two-stage inflationary model. Depending on the curvature of the potential the first stage corresponds to a period of fast-roll inflation or a period of 'locked' inflation, induced by an oscillating inflaton. This is followed by a second stage of fast-roll inflation. We demonstrate that these two consecutive inflationary phases result in enough total e-foldings to encompass the cosmological scales. Using natural values for the parameters (masses of order TeV and vacuum energy of the intermediate scale corresponding to gravity mediated supersymmetry breaking) we conclude that the η-problem of inflation is easily overcome. The greatest obstacle to our scenario is the possibility of copious production of cosmologically disastrous primordial black holes due to the phase transition switching from the first into the second stage of inflation. We study this problem in detail and show analytically that there is ample parameter space where these black holes do not form at all. To generate structure in the Universe we assume the presence of a curvaton field. Finally we also discuss the moduli problem and how it affects our considerations.

Journal of Cosmology and Astroparticle Physics, 2020

We revisit the recently proposed mechanism of Geometric Inflation. On general grounds, we show that obtaining the right amount of inflation demands an exceedingly large initial energy density. We introduce a scalar field and study the combined action of both mechanisms. Besides fixing the aforementioned issue, a cascading process occurs whose last step seems undistinguishable from ordinary large field inflation. Strikingly, the scalar field remains approximately constant while Geometric Inflation rules the dynamics. This ultimately leads to the possibility of reducing the initial value of the scalar field and its excursion. We discuss the main features of this hybrid scenario.

Modern Physics Letters A, 2018

We consider the cosmological inflation with scalar–tensor gravity and compare it with standard inflation based on General Relativity. The difference is determined by the value of the parameter [Formula: see text]. This approach is associated with using the special ansatz which links a function that defines a type of gravity with a scale factor of the universe.

In this talk, I want to emphasize that NC spacetime is much more radical and mysterious than we thought. So far we have understood the NC spacetime too easily. I will give you an overall picture why NC spacetime necessarily implies emergent spacetime. The emergent spacetime opens a new prospect that may cripple all the rationales to introduce the multiverse hypothesis. (“Emergent Spacetime: Reality or Illusion?”, arXiv:1504.00464). The emergent spacetime picture admits a background-independent formulation of cosmic inflation. Every mathematical details have been addressed in my paper. (“Emergent Spacetime and Cosmic Inflation,” arXiv:1503.00712).

Symmetry

The latest released data from Planck in 2018 put up tighter constraints on inflationary parameters. In the present article, the in-built symmetry of the non-minimally coupled scalar-tensor theory of gravity is used to fix the coupling parameter, the functional Brans–Dicke parameter, and the potential of the theory. It is found that all the three different power-law potentials and one exponential pass these constraints comfortably, and also gracefully exit from inflation.

Physical Review D, 1991

The evolution of an isotropic cosmological model in the R+R 2 −theory of gravity with a coherent massive scalar field is studied analytically and numerically. For certain initial conditions the model goes through a superinflationary stage (Ḣ > 0) followed by usual subinflation (Ḣ < 0). Double inflation consisting of two inflationary stages divided by a period of power-law expansion a(t) ∝ t 2/3 is possible if the scalar particle mass is small compared to the mass of the scalaron (scalar graviton). The spectrum of adiabatic perturbations generated from vacuum quantum fluctuations is investigated. It is quasi-flat (though not necessary varying monotonically with scale) in case of single inflation; for double inflation it has a characteristic step.