Search Results (63)

The continual production of long wavelength gravitons during primordial inflation endows graviton loop corrections with secular growth factors. During a prolonged period of inflation, these factors eventually overwhelm the small loop-counting parameter of $G{H}^2$, causing perturbation theory to break down. A technique was recently developed for summing the leading secular effects at each order in non-linear sigma models, which possess the same kind of derivative interactions as gravity. This technique combines a variant of Starobinsky’s stochastic formalism with a variant of the renormalization group. Generalizing the technique to quantum gravity is a two-step process, the first of which is the determination of the gauge fixing condition that will allow this summation to be realized; this is the subject of this paper. Moreover, we briefly discuss the second step, which shall obtain the Langevin equation, in which secular changes in gravitational phenomena are driven by stochastic fluctuations of the graviton field. Full article

In this work, we elaborate further on a (3+1)-dimensional cosmological Running-Vacuum-type-Model (RVM) of inflation based on string-inspired Chern-Simons(CS) gravity, involving axions coupled to gravitational-CS(gCS) anomalous terms. Inflation in such models is caused by primordial-gravitational-waves(GW)-induced condensation of the gCS terms, which leads to a linear-axion potential. We demonstrate that this inflationary phase may be metastable, due to the existence of imaginary parts of the gCS condensate. These are quantum effects, proportional to commutators of GW perturbations, hence vanishing in the classical theory. Their existence is quantum-ordering-scheme dependent. We argue in favor of a physical importance of such imaginary parts, which we compute to second order in the GW (tensor) perturbations in the framework of a gauge-fixed effective Lagrangian, within a (mean field) weak-quantum-gravity-path-integral approach. We thus provide estimates of the inflation lifetime. On matching our results with the inflationary phenomenology, we fix the quantum-ordering ambiguities, and obtain an order-of-magnitude constraint on the String-Mass-Scale-to-Planck-Mass ratio, consistent with previous estimates by the authors in the framework of a dynamical-system approach to linear-axion RVM inflation. Finally, we examine the role of periodic modulations in the axion potential induced by non-perturbative effects on the slow-roll inflationary parameters, and find compatibility with the cosmological data. Full article

We calculated the two-loop corrections in the primordial power spectrum in models of single-field inflation incorporating an intermediate USR phase employed for PBH formation. Among the overall eleven one-particle irreducible Feynman diagrams, we calculated the corrections from the “double scoop” two-loop diagram involving two vertices of quartic Hamiltonians. We demonstrate herein the fractional two-loop correction in power spectrum scales, like the square of the fractional one-loop correction. We confirm our previous findings that the loop corrections become arbitrarily large in the setup where the transition from the intermediate USR to the final slow-roll phase is very sharp. This suggests that in order for the analysis to be under perturbative control against loop corrections, one requires a mild transition with a long enough relaxation period towards the final attractor phase. Full article

Primordial black holes (PBH), if survive to the present time, can be a fraction, or even the dominant form of dark matter of the Universe. If PBH evaporate before the present time, rare forms of dark matter like superweakly interacting or supermassive particles can be produced in the course of their evaporation. Stable remnants of PBH evaporation can also play the role of dark matter candidates. In the context of the modern standard cosmology, based on inflationary models with baryosynthesis and dark matter, which find their physical grounds beyond the Standard models of elementary particles (BSM), primordial black holes acquire the important role of sensitive probes for BSM models and their parameters. It makes PBHs a profound messenger of physics of Dark Universe. Full article

We study the impact of the expansion of the universe on a broad class of objects, including black holes, neutron stars, white dwarfs, and others. Using metrics that incorporate primordial inhomogeneities, the effects of a hypothetical “center of the universe” on inflation are calculated. Dynamic coordinates for black holes that account for expansions or contractions with arbitrary rates are provided. We consider the possibility that the universe may be bound to evolve into an ultimate state of “total dilution”, wherein stable particles are so widely separated that physical communication among them will be impossible for eternity. This is also a scenario of “cosmic virtuality”, as no wave-function collapse would occur again. We provide classical models evolving this way, based on the Majumdar–Papapetrou geometries. More realistic configurations, instead, indicate that gravitational forces locally counteract expansion, except in the universe’s early stages. We comment on whether quantum phenomena may dictate that total dilution is indeed the cosmos’ ultimate destiny. Full article

In inflationary cosmology, the form of the potential is still an open problem. In this work, second-order effects of the inflationary potential are evaluated and related to the known formula for the primordial perturbations at a wide range of scales. We found effects that may help to unravel the unknown inflationary potential form and impose new constraints on the parameters that define this potential. In particular, we demonstrate that even slight deviations in the inflationary potential can lead to significant differences in the calculated spectra if inflation persists sufficiently long and the normal modes of perturbations are affected by these variations. Full article

We investigate the implications of different quantization approaches in Loop Quantum Cosmology for the primordial power spectrum of tensor modes. Specifically, we consider the hybrid and dressed metric approaches to derive the effective mass that governs the evolution of the tensor modes. Our study comprehensively examines the two resulting effective masses and how to estimate them in order to obtain approximated analytic solutions to the tensor perturbation equations. Since Loop Quantum Cosmology incorporates preinflationary effects in the dynamics of the perturbations, we do not have at our disposal a standard choice of privileged vacuum, like the Bunch–Davies state in quasi-de Sitter inflation. We then select the vacuum state by a recently proposed criterion which removes unwanted oscillations in the power spectrum and guarantees an asymptotic diagonalization of the Hamiltonian in the ultraviolet. This vacuum is usually called the NO-AHD (from the initials of Non-Oscillating with Asymptotic Hamiltonian Diagonalization) vacuum. Consequently, we compute the power spectrum by using our analytic approximations and by introducing a suitable numerical procedure, adopting in both cases an NO-AHD vacuum. With this information, we compare the different spectra obtained from the hybrid and the dressed metric approaches, as well as from the analytic and numerical procedures. In particular, this proves the remarkable accuracy of our approximations. Full article

A modified gravity model of Starobinsky inflation and primordial black hole production is proposed in good (within $1\sigma$) agreement with current measurements of the cosmic microwave background radiation. The model is an extension of the singularity-free Appleby–Battye–Starobinsky model by the $R^4$ term with different values of the parameters whose fine-tuning leads to the efficient production of primordial black holes on smaller scales with the asteroid-size masses between ${10}^{16}$ g and ${10}^{20}$ g. Those primordial black holes may be part (or the whole) of the current dark matter, while the proposed model can be confirmed or falsified by the detection or absence of the induced gravitational waves with the frequencies in the ${10}^{-2}$ Hz range. The relative size of quantum (loop) corrections to the power spectrum of scalar perturbations in the model is found to be of the order of ${10}^{-3}$ or less, so that the model is not ruled out by the quantum corrections. Full article

We provide a short review of the recent developments in entropic cosmology based on two thermodynamic laws of the apparent horizon, namely the first and the second laws of thermodynamics. The first law essentially provides the change in entropy of the apparent horizon during the cosmic evolution of the universe; in particular, it is expressed by $TdS=-d\left(\rho V\right)+WdV$ (where W is the work density and other quantities have their usual meanings). In this way, the first law actually links various theories of gravity with the entropy of the apparent horizon. This leads to a natural question—“What is the form of the horizon entropy corresponding to a general modified theory of gravity?”. The second law of horizon thermodynamics states that the change in total entropy (the sum of horizon entropy + matter fields’ entropy) with respect to cosmic time must be positive, where the matter fields behave like an open system characterised by a non-zero chemical potential. The second law of horizon thermodynamics importantly provides model-independent constraints on entropic parameters. Finally, we discuss the standpoint of entropic cosmology on inflation (or bounce), reheating and primordial gravitational waves from the perspective of a generalised entropy function. Full article

A new formalism is introduced that makes it possible to elucidate the physical and geometric content of quantum space–time. It is based on the Minimum Group Representation Principle (MGRP). Within this framework, new results for entanglement and geometrical/topological phases are found and implemented in cosmological and black hole space–times. Our main results here are as follows: (i) We find the Berry phases for inflation and for the cosmological perturbations and express them in terms of the observables, such as the spectral scalar and tensor indices, $n_S$ and $n_T$, and the tensor-to-scalar ratio r. The Berry phase for de Sitter inflation is imaginary with the sign describing the exponential acceleration. (ii) The pure entangled states in the minimum group (metaplectic) $Mp\left(n\right)$ representation for quantum de Sitter space–time and black holes are found. (iii) For entanglement, the relation between the Schmidt type representation and the physical states of the $Mp\left(n\right)$ group is found: This is a new non-diagonal coherent state representation complementary to the known Sudarshan diagonal one. (iv) Mean value generators of $Mp\left(2\right)$ are related to the adiabatic invariant and topological charge of the space–time, (matrix element of the transition $-\infty <t<\infty$). (v) The basic even and odd n-sectors of the Hilbert space are intrinsic to the quantum space–time and its discrete levels (in particular, continuum for $n\to \infty$), they do not require any extrinsic generation process such as the standard Schrodinger cat states, and are entangled. (vi) The gravity or cosmological domains on one side and another of the Planck scale are entangled. Examples: The quantum primordial trans-Planckian de Sitter vacuum and the classical late de Sitter vacuum today; the central quantum gravity region and the external classical gravity region of black holes. The classical and quantum dual gravity regions of the space–time are entangled. (vii) The general classical-quantum gravity duality is associated with the Metaplectic $Mp\left(n\right)$ group symmetry which provides the complete full covering of the phase space and of the quantum space–time mapped from it. Full article

The stochastic signal observed by collaborations such as NANOGrav, PPTA, EPTA +InPTA, and CPTA may originate from gravitational waves induced by primordial curvature perturbations during inflation. This study investigates small-scale properties of inflation and reheating, assuming a log-normal form for the power spectrum of the primordial curvature and a reheating phase equation of state $w=1/9$. Inflation and reheating scenarios are thoroughly examined using Bayesian methods applied to the NANOGrav 15-year dataset. The analysis establishes constraints on the reheating temperature, suggesting $T_{\mathrm{rh}}\gtrsim 0.1\mathrm{Gev}$, consistent with Big Bang nucleosynthesis constraints. Additionally, the NANOGrav 15-year dataset requires the amplitude (A∼0.1) and width ($\mathsf{\Delta }\lesssim 0.001$) of the primordial curvature power spectrum to be within specific ranges. A notable turning point in the energy density of scalar-induced gravitational waves occurs due to a change in the equation of state w. This turning point signifies a transition from the reheating epoch to radiation domination. Further observations of scalar-induced gravitational waves could provide insights into the precise timing of this transition, enhancing our understanding of early Universe dynamics. Full article

In this study, we present an analysis of the fine-tuning required in various inflationary models in order to explain the production of Primordial Black Holes (PBHs). We specifically examine the degree of fine-tuning necessary in two prominent single-field inflationary models: those with an inflection point and those with step-like features in the potential. Our findings indicate that models with step-like features generally require less fine-tuning compared to those with an inflection point, making them more viable for consistent PBH production. An interesting outcome of these models is that, in addition to improved fine-tuning, they may also predict low-frequency signals that can be detected by pulsar timing array (PTA) collaborations. Additionally, we extend our analysis to multifield inflationary models to assess whether the integration of additional fields can further alleviate the fine-tuning demands. The study also explores the role of a spectator field and its impact on the fine-tuning process. Our results indicate that although mechanisms involving a spectator field can circumvent the issue of fine-tuning parameters for PBH production, both multifield models and models with step-like features present promising alternatives. While fine-tuning involves multiple considerations, our primary objective is to evaluate various inflationary models to identify the one that most naturally explains the formation of PBHs. Hence, this study introduces a novel approach by categorizing existing PBH mechanisms, paving the way for subsequent research to prioritize models that minimize the need for extensive fine-tuning. Full article

The origin and evolution of supermassive black holes (SMBHs) in our universe have sparked controversy. In this study, we explore the hypothesis that some of these black holes may have seeded from the direct collapse of dark energy domains with density significantly higher than the surrounding regions. The mechanism of the origin of such domains relies on the inflationary evolution of a scalar field acting in D dimensions, which is associated with the cosmological constant in our four-dimensional spacetime manifold. Inner space quantum fluctuations of the field during inflation are responsible for the spatial variations of the dark energy density in our space. This finding holds particular significance, especially considering recent evidence from pulsar timing array observations, which supports the existence of a stochastic gravitational wave background consisting of SMBH mergers. Full article

DECIGO is a future Japanese project for the detection of gravitational waves in space. To conduct various scientific missions, including the verification of cosmic inflation through the detection of primordial gravitational waves as the main objective, DECIGO is designed to have high sensitivity in the frequency band from $0.1$ to 10 Hz, with arms of length 1000 km. Furthermore, the use of the Fabry-Perotcavity in these arms has been established for the DECIGO project. In this paper, we scrutinize the significance of the Fabry-Perot cavity for promoting this project, with a focus on the possibility of observing gravitational waves from cosmic inflation and binary compact star systems as indicators. The results show that using the Fabry-Perot cavity is extremely beneficial for detecting them, and it is anticipated to enable the opening of a new window in gravitational wave astronomy. Full article

We study the evolution of quantum fluctuations of gravity around an inflationary solution in renormalizable quantum gravity, in which the initial scalar-fluctuation dominance is shown by the background-free nature expressed by a special conformal invariance. Inflation ignites at the Planck scale and continues until spacetime phase transition occurs at a dynamical scale of about ${10}^{17}$ GeV. We show that during inflation, the initially large scale-invariant fluctuations reduce in amplitude to the appropriate magnitude suggested by tiny CMB anisotropies. The goal of this research is to derive the spectra of scalar fluctuations at the phase transition point, that is, the primordial spectra. A system of nonlinear evolution equations for the fluctuations is derived from the quantum gravity effective action. The running coupling constant is then expressed by a time-dependent average following the spirit of the mean field approximation. In this paper, we determine and examine various nonlinear terms, not treated in previous studies such as the exponential factor of the conformal mode. These contributions occur during the early stage of inflation when the amplitude is still large. Moreover, in order to verify their effects concretely, we numerically solve the evolution equation by making a simplification to extract the most contributing parts of the terms in comoving momentum space. The result indicates that they serve to maintain the initial scale invariance over a wide range beyond the comoving Planck scale. This is a challenge toward the derivation of the precise primordial spectra, and we expect in the future that it will lead to the resolution of the tensions that have arisen in cosmology. Full article