Geometric inflation

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 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 entails a geometric mechanism triggering an inflationary period in the early universe (driven by radiation) with a graceful exit to a late-time cosmology arbitrarily close to ΛCDM.

Physics Letters B, 2022

We present a cosmological model arising from a gravitational theory with an infinite tower of higher-order curvature invariants that can reproduce the entire evolution of the Universe: from inflation to late-time acceleration, without invoking an inflaton nor a cosmological constant. The theory is Einsteinian-like. The field equations for a Friedmann-Lemaître-Robertson-Walker metric are of second-order and can reproduce a late-time evolution that is consistent with the acceleration provided by the cosmological constant at low redshift. Our results force us to reinterpret the nature of dark energy, becoming a mechanism that is inherited solely from the geometry of spacetime.

2013

The inflationary phase of the Universe is explored by proposing a toy model related to the scalar field, termed as {\it inflaton}. The potential part of the energy density in the said era is assumed to have a constant vacuum energy density part and a variable part containing the inflaton. The prime idea of the proposed model constructed in the framework of the closed Universe is based on a fact that the inflaton is the root cause of the orientation of the space. According to this model the expansion of the Universe in the inflationary epoch is not approximately rather exactly exponential in nature and thus it can solve some of the fundamental puzzles, viz. flatness as well as horizon problems. It is also predicted that the constant energy density part in the potential may be associated to the dark energy, which is eventually different from the vacuum energy, at least in the inflationary phase of the Universe. However, the model keeps room for the end of inflationary era.

Physics Letters B, 2022

We present a cosmological model arising from a gravitational theory with an infinite tower of higher-order curvature invariants that can reproduce the entire evolution of the Universe: from inflation to late-time acceleration, without invoking an inflaton nor a cosmological constant. The theory is Einsteinian-like. The field equations for a Friedmann-Lemaître-Robertson-Walker metric are of second-order and can reproduce a late-time evolution that is consistent with the acceleration provided by the cosmological constant at low redshift. Our results force us to reinterpret the nature of dark energy, becoming a mechanism that is inherited solely from the geometry of spacetime.

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).

We propose a background-independent formulation of cosmic inflation. The inflation in this picture corresponds to a dynamical process to generate space and time while the conventional inflation is simply an (exponential) expansion of a preexisting spacetime owing to the vacuum energy carried by an inflaton field. We observe that the cosmic inflation is triggered by the condensate of Planck energy into vacuum responsible for the dynamical emergence of spacetime and must be a single event according to the exclusion principle of noncommutative spacetime caused by the Planck energy condensate in vacuum. The emergent spacetime picture admits a background-independent formulation so that the inflation can be described by a conformal Hamiltonian system characterized by an exponential phase space expansion without introducing any inflaton field as well as an {\it ad hoc} inflation potential. This implies that the emergent spacetime may incapacitate all the rationales to introduce the multiverse hypothesis. In Part I we will focus on the physical foundation of cosmic inflation from the emergent spacetime picture to highlight the main idea. Its mathematical exposition will be addressed in Part II with a generalization of the emergent spacetime picture to matrix string theory.

2002

We show that in the case of positively-curved Friedmann-Lemaître universes (k = +1), an inflationary period in the early universe will for most initial conditions not solve the horizon problem, no matter how long inflation lasts. It will only do so for cases where inflation starts in an almost static state, corresponding to an extremely high value of ΩΛ, ΩΛ ≫ 1, at the beginning of inflation. For smaller values, it is not possible to solve the horizon problem because the relevant integral asymptotes to a finite value (as happens also in the de Sitter universe in a k = +1 frame). Thus, for these cases, the causal problems associated with the near-isotropy of the Cosmic Background Radiation have to be solved already in the Planck era. Furthermore both compact space sections and event horizons will exist in these universes even if the present cosmological constant dies away in the far future, raising potential problems for M-theory as a theory of gravity.

We argue that the emergent spacetime picture admits a background-independent formulation of cosmic inflation. The inflation in this picture corresponds to the dynamical emergence of spacetime while the conventional inflation is simply an (exponential) expansion of a preexisting spacetime owing to the vacuum energy carried by an inflaton field. We show that the cosmic inflation arises as a time-dependent solution of the matrix quantum mechanics describing the dynamical process of Planck energy condensate in vacuum without introducing any inflaton field as well as an ad hoc inflation potential. Thus the emergent spacetime picture realizes a background-independent description of the inflationary universe which has a sufficiently elegant and explanatory power to defend the integrity of physics against the multiverse hypothesis. 1. Why Is Emergent Spacetime Necessary for Cosmic Inflation? Like black holes, the big bang in the very early universe involves extreme conditions that neither relativity nor quantum theory can explain on its own. If we trace back the history of our universe, we will meet an initial singularity in which matter reached almost infinite density and then, according to the theory of general relativ-ity, the space was contracted to a point and the time flow nearly stopped. Thus the big bang suffers the initial singularity in which space and time cease to exist. This implies that the big bang must be a cosmological event generating space and time as well as matters. The initial singularity cannot be avoided in the inflationary cosmology either because there has to be a definite beginning to an inflationary universe. 1 This means that the inflation is incomplete to describe the very beginning of our universe and some new physics is needed to probe the past boundary of the inflating regions. One possibility is that there must have been some sort of quantum creation event as a beginning of the universe. The inflation scenario so far has been formulated in the context of effective field theory coupled to general relativity. Hence, in this scenario, the existence of space and time is a priori assumed from the beginning and the scenario only describes what happens in a given spacetime. In other words, the inflationary scenario does not describe any generation (or creation) of spacetime but simply characterizes an expansion of a preexisting spacetime. It never addresses the (dynamical) origin of spacetime. Moreover, in most inflationary models, once inflation happens, it never stops and produces not just one universe, but an infinite number of universes. Therefore the conventional inflation inevitably leads to the multiverse which is not falsifiable since the multiverse cannot be tested experimentally. 2

Journal of Cosmology and Astroparticle Physics, 2012

Inflation creates large-scale cosmological density perturbations that are characterized by an isotropic, homogeneous, and Gaussian random distribution about a locally flat background. Even in a flat universe, the spatial curvature measured within one Hubble volume receives contributions from long wavelength perturbations, and will not in general be zero. These same perturbations determine the Cosmic Microwave Background (CMB) temperature fluctuations, which are O(10 −5 ). Consequently, the low-l multipole moments in the CMB temperature map predict the value of the measured spatial curvature Ω k . On this basis we argue that a measurement of |Ω k | > 10 −4 would rule out slow-roll eternal inflation in our past with high confidence, while a measurement of Ω k < −10 −4 (which is positive curvature, a locally closed universe) rules out false-vacuum eternal inflation as well, at the same confidence level. In other words, negative curvature (a locally open universe) is consistent with false-vacuum eternal inflation but not with slow-roll eternal inflation, and positive curvature falsifies both. Near-future experiments will dramatically extend the sensitivity of Ω k measurements and constitute a sharp test of these predictions.