Pre-inflationary Phase Research Articles

Model independent prediction of the spectral index of primordial quantum fluctuations

One of the most important achievements of inflationary cosmology is to predict a departure from scale invariance of the power spectrum for cosmological scalar perturbations. This tilt is understood as a consequence of a quasi de Sitter classical equation of state describing the inflationary dark energy dominated era. Here, following previous work, we find a departure of scale invariance for the quantum Fisher information associated to de Sitter vacuum for scalar quantum spectator modes. This gives rise to a purely quantum cosmological tilt with a well defined dependence on energy scale. This quantum tilt is imprinted, in a scale dependent energy uncertainty for the spectator modes. The effective quasi de Sitter description of this model independent energy uncertainty uniquely sets the effective quasi de Sitter parameters (i.e., the small deviation from the cosmological constant equation of state) at all energy scales. In particular, in the slow-roll regime characterized by an almost constant ϵ, the quantum Fisher — model independent — prediction for the spectral index is n s = 0.9672. Moreover, the energy scale dependence of the quantum cosmological tilt implies the existence of a cosmological phase transition at energies higher than the CMB scale and of the order of 1 Mpc-1 where the tilt goes from red into blue. This strongly suggest the existence of a pre-inflationary phase where the effective scalaron contributes to the spectral index as normal relativistic matter and where the corresponding growth of the power spectrum can result in dark matter in the form of small mass primordial black holes. The source and features of the quantum cosmological tilt leading to these predictions are determined by the entanglement features of the de Sitter α- vacuum states.

Quantum gravitational onset of Starobinsky inflation in a closed universe

Recent cosmic microwave background observations favor low-energy-scale inflationary models in a closed universe. However, the onset of inflation in such models for a closed universe is known to be severely problematic. In particular, such a universe recollapses within a few Planck seconds and encounters a big crunch singularity when initial conditions are given in the Planck regime. We show that this problem of the onset of inflation in low-energy-scale inflationary models can be successfully overcome in a quantum-gravitational framework where the big bang/big crunch singularities are resolved and a nonsingular cyclic evolution exists prior to inflation. As an example, we consider a model in loop quantum cosmology and demonstrate that the successful onset of low-energy-scale inflation in a closed universe is possible for the Starobinsky inflationary model starting from a variety of initial conditions where it is impossible in the classical theory. For comparison, we also investigate the onset of inflation in the ${\ensuremath{\phi}}^{2}$ inflationary model under highly unfavorable conditions and find similar results. Our numerical investigation including the phase-space analysis shows that the preinflationary phase with quantum gravity effects is composed of nonidentical cycles of bounces and recollapses resulting in a hysteresis-like phenomenon, which plays an important role in creating suitable conditions for inflation to occur after some number of nonsingular cycles. Our analysis shows that the tension in the classical theory amounting to the unsuitability of closed Friedmann-Lema\^{\i}tre-Robertson-Walker universes with respect to the onset of low-energy-scale inflation can be successfully resolved in loop quantum cosmology.

Gravitational particle production in loop quantum cosmology

We investigate the gravitational particle production in the bounce phase of Loop Quantum Cosmology (LQC). We perform both analytical and numerical analysis of the particle production process in a LQC scenario with Bunch-Davies vacuum initial condition in the contracting phase. We obtain that if we extend the validity of the dressed metric approach beyond the limit of small backreaction in which it is well justified, this process would lead to a radiation dominated phase in the pre-inflationary phase of LQC. Our results indicate that the test field approximation, which is required in the truncation scheme used in the dressed metric approach, might not be a valid assumption in a LQC scenario with such initial conditions.

Logolinear series expansions with applications to primordial cosmology

We develop a method for computing series expansions for solutions to ordinary differential equations when the asymptotic form contains both linear and logarithmic terms. Such situations are common in primordial cosmology when considering series expansions out of a singularity in the equations arising from a pre-inflationary phase of the universe. We develop mathematical techniques for generating these series expansions, and apply them to polynomial and Starobinsky inflationary potentials with kinetic initial conditions. Code for analytic and numerical computation of logolinear series is provided on GitHub.

The interacting multiverse and its effect on the cosmic microwave background

We study a toy model of a multiverse consisting of canonically quantized universes that interact with each other on a quantum level based on a field-theoretical formulation of the Wheeler-DeWitt equation. This interaction leads to the appearance of a pre-inflationary phase in the evolution of the individual universes. We analyze scalar perturbations within the model and calculate the influence of the pre-inflationary phase onto the power spectrum of these perturbations. The result is that there is a suppression of power on large scales, which can describe well the Planck 2018 data for the cosmic microwave background anisotropies and could thus indicate a possible solution to the observed quadrupole discrepancy.

Pre-inflation from the multiverse: can it solve the quadrupole problem in the cosmic microwave background?

We analyze a quantized toy model of a universe undergoing eternal inflation using a quantum-field-theoretical formulation of the Wheeler–DeWitt equation. This so-called third quantization method leads to the picture that the eternally inflating universe is converted to a multiverse in which sub-universes are created and exhibit a distinctive phase in their evolution before reaching an asymptotic de Sitter phase. From the perspective of one of these sub-universes, we can thus analyze the pre-inflationary phase that arises naturally. Assuming that our observable universe is represented by one of those sub-universes, we calculate how this pre-inflationary phase influences the power spectrum of the cosmic microwave background (CMB) anisotropies and analyze whether it can explain the observed discrepancy of the power spectrum on large scales, i.e. the quadrupole issue in the CMB. While the answer to this question is negative in the specific model analyzed here, we point out a possible resolution of this issue.

Universal features of quantum bounce in loop quantum cosmology

In this Letter, we study analytically the evolutions of the flat Friedmann–Lemaitre–Robertson–Walker (FLRW) universe and its linear perturbations in the framework of the dressed metric approach in loop quantum cosmology (LQC). Assuming that the evolution of the background is dominated by the kinetic energy of the inflaton at the quantum bounce, we find that both evolutions of the background and its perturbations are independent of the inflationary potentials during the pre-inflationary phase. During this period the effective potentials of the perturbations can be well approximated by a Pöschl–Teller (PT) potential, from which we find analytically the mode functions and then calculate the corresponding Bogoliubov coefficients at the onset of the slow-roll inflation, valid for any inflationary model with a single scalar field. Imposing the Bunch–Davies (BD) vacuum in the contracting phase prior to the bounce when the modes are all inside the Hubble horizon, we show that particles are generically created due to the pre-inflation dynamics. Matching them to those obtained in the slow-roll inflationary phase, we investigate the effects of the pre-inflation dynamics on the scalar and tensor power spectra and find features that can be tested by current and forthcoming observations. In particular, to be consistent with the Planck 2015 data, we find that the universe must have expanded at least 141 e-folds since the bounce.

Probing pre-inflationary anisotropy with directional variations in the gravitational wave background

We perform a detailed analysis on a primordial gravitational-wave background amplified during a Kasner-like pre-inflationary phase allowing for general triaxial anisotropies. It is found that the predicted angular distribution map of gravitational-wave intensity on large scales exhibits topologically distinctive patterns according to the degree of the pre-inflationary anisotropy, thereby serving as a potential probe for the pre-inflationary early universe with future all-sky observations of gravitational waves. We also derive an observational limit on the amplitude of such anisotropic gravitational waves from the B -mode polarisation of the cosmic microwave background.

Vacuum decay in an interacting multiverse

We examine a new multiverse scenario in which the component universes interact. We focus our attention to the process of "true" vacuum nucleation in the false vacuum within one single element of the multiverse. It is shown that the interactions lead to a collective behaviour that might lead, under specific conditions, to a pre-inflationary phase and ensued distinguishable imprints in the comic microwave background radiation.

Entanglement time in the primordial universe

We investigate the behavior of the entanglement entropy of space in the primordial phase of the universe before the beginning of the cosmic inflation. We argue that in this phase the entanglement entropy of a region of space grows from a zero-law to an area-law. This behavior provides a quantum version of the classical Belinsky–Khalatnikov–Lifshitz (BKL) conjecture that spatially separated points decouple in the approach to a cosmological singularity. We show that the relational growth of the entanglement entropy with the scale factor provides a new statistical notion of arrow of time in quantum gravity. The growth of entanglement in the pre-inflationary phase provides a mechanism for the production of the quantum correlations present at the beginning of inflation and imprinted in the CMB sky.

Primordial quantum nonequilibrium and large-scale cosmic anomalies

We study incomplete relaxation to quantum equilibrium at long wavelengths, during a pre-inflationary phase, as a possible explanation for the reported large-scale anomalies in the cosmic microwave background (CMB). Our scenario makes use of the de Broglie-Bohm pilot-wave formulation of quantum theory, in which the Born probability rule has a dynamical origin. The large-scale power deficit could arise from incomplete relaxation for the amplitudes of the primordial perturbations. We show, by numerical simulations for a spectator scalar field, that if the pre-inflationary era is radiation dominated then the deficit in the emerging power spectrum will have a characteristic shape (an inverse-tangent dependence on wavenumber k, with oscillations). It is found that our scenario is able to produce a power deficit in the observed region and of the observed (approximate) magnitude for an appropriate choice of cosmological parameters. We also discuss the large-scale anisotropy, which might arise from incomplete relaxation for the phases of the primordial perturbations. We present numerical simulations for phase relaxation, and we show how to define characteristic scales for amplitude and phase nonequilibrium. The extent to which the data might support our scenario is left as a question for future work. Our results suggest that we have a potentially viable model that might explain two apparently independent cosmic anomalies by means of a single mechanism.

Signatures of the very early Universe: Inflation, spatial curvature, and large scale anomalies

A short inflationary phase may not erase all traces of the primordial universe. Associated observables include both spatial curvature and "anomalies" in the microwave background or large scale structure. The present curvature $\Omega_{K,0}$ reflects the initial curvature, $\Omega_{K,\mathrm{start}}$, and the angular size of anomalies depends on $k_\mathrm{start}$, the comoving horizon size at the onset of inflation. We estimate posteriors for $\Omega_{K,\mathrm{start}}$ and $k_\mathrm{start}$ using current data and simulations, and show that if either quantity is measured to have a non-zero value, both are likely to be observable. Mappings from $\Omega_{K,\mathrm{start}}$ and $k_\mathrm{start}$ to present-day observables depend strongly on the primordial equation of state; $\Omega_{K,0}$ spans ten orders of magnitude for a given $\Omega_{K,\mathrm{start}}$ while a simple and general relationship connects $\Omega_{K,0}$ and $k_\mathrm{start}$. We show that current bounds on $\Omega_{K,0}$ imply that if $k_\mathrm{start}$ is measurable, the curvature was already small when inflation began. Finally, since the energy density changes slowly during inflation, primordial gravitational wave constraints require that a short inflationary phase is preceded by a nontrivial pre-inflationary phase with critical implications for the expected value of $\Omega_{K,\mathrm{start}}$.

BEFORE THE BANG

While inflation has been an extremely successful cosmological paradigm, almost certainly something have had to have happened before it began. Can the pre-inflationary phase be of any theoretical or phenomenological significance? Could Quantum Gravity have played any interesting role in this story? These are some of the questions we want to explore in this essay written for the Gravity Research Foundation 2013 "Awards for Essays on Gravitation" competition.

Initial conditions and sampling for multifield inflation

We investigate the initial conditions problem for multifield inflation. In these scenarios the pre-inflationary dynamics can be chaotic, increasing the sensitivity of the onset of inflation to the initial data even in the homogeneous limit. To analyze physically equivalent scenarios we compare initial conditions at fixed energy. This ensures that each trajectory is counted once and only once, since the energy density decreases monotonically. We present a full analysis of hybrid inflation that reveals a greater degree of long range order in the set of ``successful'' initial conditions than was previously apparent. In addition, we explore the effective smoothing scale for the fractal set of successful initial conditions induced by the finite duration of the pre-inflationary phase. The role of the prior information used to specify the initial data is discussed in terms of Bayesian sampling.

Semiclassical isotropization of the Universe during a de Sitter phase

Semi-classical states for the Wheeler-DeWitt equation of a Bianchi type I model in the presence of a scalar field are analyzed. It is outlined how this scheme can effectively describe more general situations, where the curvature of the Bianchi type IX model and a proper potential term for the scalar field are present. The introduction of a cosmological constant term accounts for the quasi-isotropization mechanism which bridges the proposed framework with a late isotropic phase. This result makes the semi-classical Bianchi I model a plausible scenario for the Universe pre-inflationary phase.

Non-linear resonance in bouncing braneworld universes and initial conditions forinflation

We examine the phase space dynamics of closed Friedmann–Robertson–Walker universeswith a massive inflaton field, where the Friedmann equations contain additional termsarising from high energy corrections to cosmological scenarios. The model is basedupon a Randall–Sundrum type of action, with an extra timelike dimension, andthe corrections implement non-singular bounces in the early evolution of theuniverse. In narrow windows of the parameter space of the models non-linearresonance phenomena of Kolmogorov–Arnold–Moser tori are shown to occur, leadingto the destruction of tori that trap the inflaton. As a consequence the escapeinto inflation takes place. These resonance windows are labeled with an integern≥2,where n is related to the ratio of the frequencies in the scale factor to those in the scalar field degrees offreedom. We examine the constraints imposed by non-linear resonance in the physicaldomain of parameters of the model so that inflation may be realized. The larger the ordern of the resonance, the stronger the gravitational interaction in the braneworld universeinflated from initial conditions connected with the resonance considered. We also discussthe structural stability of the resonance pattern, the complex dynamics arising inthis pre-inflationary phase and some of its possible imprints in the physics ofinflation.

Oscillating and Inflating Universe in SO(3)-Gravitation Theory

Abstract The predictions of SO (3) Gravitation Theory are studied for a homogeneous, isotropic universe. Various types of oscillations are obtained for the pre-inflationary phase, where the geometry experiences violent fluctuations. These are ultimately terminating at either re-collaps or regular inflation.

Chaotic inflation as an attractor in initial-condition space.

We study the evolution of scalar field inhomogeneities in the preinflationary phase of an inflationary universe. We decompose the scalar field configuration in Fourier modes and consider initial conditions in which more than one mode is excited. We find that the long-wavelength modes are stable against perturbations due to short-wavelength excitations and that chaotic inflation results even if at the initial time the short waves contain most of the energy density.

Effects of gravitational perturbations on the evolution of scalar fields in the early universe

We study the evolution of inhomogeneous classical scalar field configurations which are not in thermal equilibrium in a radiation dominated pre-inflationary phase in the early universe. We take into account gravitational perturbations about the Friedmann- Robertson-Walker metric. Making use of gauge invariant variable, we show that provided the initial gravitational perturbations are not too large, they do not prevent the dynamical relaxation of the scalar field configuration to an almost homogeneous configuration which leads to inflation.

Thermal fluctuations in new inflation.

The effects of thermal fluctuations on the evolution of a weakly coupled scalar field in the preinflationary phase of a model of new inflation are studied. Limits on the coupling constants are derived below which the effects of thermal fluctuations are negligible. The stochastic approach to inflation is extended to cover a situation in which spatial gradient terms and acceleration terms in the equation of motion of the scalar field dominate.