Non-singular Bounce Research Articles

Regularized-renormalized-resummed loop corrected power spectrum of non-singular bounce with Primordial Black Hole formation

AbstractWe present a complete and consistent exposition of the regularization, renormalization, and resummation procedures in the setup of having a contraction and then non-singular bounce followed by inflation with a sharp transition from slow-roll (SR) to ultra-slow roll (USR) phase for generating primordial black holes (PBHs). We consider following an effective field theory (EFT) approach and study the quantum loop corrections to the power spectrum from each phase. We demonstrate the complete removal of quadratic UV divergences after renormalization and softened logarithmic IR divergences after resummation and illustrate the scheme-independent nature of our renormalization approach. We further show that the addition of a contracting and bouncing phase allows us to successfully generate PBHs of solar-mass order, $$M_\textrm{PBH}\sim \mathcal{O}(M_{\odot })$$ M PBH ∼ O ( M ⊙ ) , by achieving the minimum e-folds during inflation to be $$\Delta N_{\textrm{Total}}\sim \mathcal{O}(60)$$ Δ N Total ∼ O ( 60 ) and in this process successfully evading the strict no-go theorem. We notice that varying the effective sound speed between $$0.88\leqslant c_{s}\leqslant 1$$ 0.88 ⩽ c s ⩽ 1 , allows the peak spectrum amplitude to lie within $$10^{-3}\leqslant A \leqslant 10^{-2}$$ 10 - 3 ⩽ A ⩽ 10 - 2 , indicating that causality and unitarity remain protected in the theory. We analyse PBHs in the extremely small, $$M_{\textrm{PBH}}\sim \mathcal{O}(10^{-33}-10^{-27})M_{\odot }$$ M PBH ∼ O ( 10 - 33 - 10 - 27 ) M ⊙ , and the large, $$M_{\textrm{PBH}}\sim \mathcal{O}(10^{-6}-10^{-1})M_{\odot }$$ M PBH ∼ O ( 10 - 6 - 10 - 1 ) M ⊙ , mass limits and confront the PBH abundance results with the latest microlensing constraints. We also study the cosmological beta functions across all phases and find their interpretation consistent in the context of bouncing and inflationary scenarios while satisfying the pivot scale normalization requirement. Further, we estimate the spectral distortion effects and shed light on controlling PBH overproduction.

Anisotropic nonsingular quantum bounce as a seesaw and amplification mechanism for magnetic fields

Anisotropic nonsingular quantum bounce as a seesaw and amplification mechanism for magnetic fields

A comprehensive analysis of cosmic evolution in f(Q,T) theory

This paper examines the bouncing cosmology in f(Q,T) theory, where Q represents non-metricity and T denotes the trace of energy-momentum tensor. The aim of this research is to study the phenomenon of a cosmic bounce, where contraction, bounce point and expansion occur at t < 0, t = 0 and t > 0, respectively. In this perspective, we consider Bianchi Type-I spacetime with perfect matter configuration to study the mysterious universe. Further, we analyze the behavior of cosmological parameters such as scale factor, Hubble parameter, deceleration parameter and equation of state parameter using three distinct functional forms of f(Q,T) theory. A comprehensive examination of energy conditions is analyzed to study the matter bounce in this modified framework. Our findings indicate that the acceleration takes place in the vicinity of the bouncing point and ensures the presence of a nonsingular bounce in this theory.

Unruh-DeWitt particle detectors in bouncing cosmologies

We study semi-classical particle production in non-singular bouncing cosmologies by employing the Unruh-DeWitt model of a particle detector propagating in this class of spacetimes. The scale factor for the bouncing cosmology is derived analytically and is inspired by the modified Friedmann equation employed in the loop quantum cosmology literature. We examine how the detector response varies with the free parameters in this model such as the equation of state during the contraction phase and the critical energy density during the bounce phase. We also investigate whether such a signature in the particle detector survives at late times.

Cosmological constraints on the background dynamics of a two-field nonsingular bounce model

In this study, we consider a nonsingular two-field bounce scenario with non-minimal kinetic coupling between two scalar fields. We derive constraints on the model parameters from the finiteness of the physical quantities at the classical level and from the relation between the late-time accelerated expansion and particle production up to the bounce phase. We then determine the allowed parameter space for the model.

Modified Friedmann equations from Maxwell-Weyl gauge theory

This study investigates the possibility of a homogeneous and isotropic cosmological solution within the context of the Maxwell-Weyl gauge theory of gravity. To achieve this, we utilize the Einstein-Yang-Mills theory as an analogy and represent the Maxwell gauge field in terms of two time-dependent scalar fields. We derive the modified Friedmann equations, integrating the contributions from the Maxwell gauge fields and an effective cosmological constant that depends on the Dirac scalar field. Our analysis reveals how these modifications influence various cosmological scenarios, including power-law evolution, de Sitter-like expansion, inflationary phases, non-singular bounce cosmologies, and cyclic cosmologies.

Requiem to “proof of inflation” or sourced fluctuations in a non-singular bounce

Popular wisdom suggests that measuring the tensor to scalar ratio r on CMB scales is a “proof of inflation” since one generic prediction is a scale-invariant tensor spectrum while alternatives predict r that is many orders of magnitude below the sensitivity of future experiments. A bouncing Universe with sourced fluctuations allows for nearly scale-invariant spectra of both scalar and tensor perturbations challenging this point of view. Past works have analyzed the model until the bounce, under the assumption that the bounce will not change the final predictions. In this work, we discard this assumption. We explicitly follow the evolution of the Universe and fluctuations across the bounce until reheating. The evolution is stable, and the existence of the sourced fluctuations does not destroy the bounce. The bounce enhances the scalar spectrum while leaving the tensor spectrum unchanged. The enhancement depends on the duration of the bounce — a shorter bounce implies a larger enhancement. The model matches current observations and predicts any viable tensor-to-scalar ratio r ≲ 10-2, which may be observed in upcoming CMB experiments. Hence, a measurement of r will no longer be a “proof of inflation”, and a Sourced Bounce is a viable paradigm with distinct predictions.

Global phase space analysis for a class of single scalar field bouncing solutions in general relativity

We carry out a compact phase space analysis of a non-canonical scalar field theory whose Lagrangian is of the form F(X)-V(ϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(X)-V(\\phi )$$\\end{document} within general relativity. In particular, we focus on a kinetic term of the form F(X)=βXm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(X)=\\beta X^m$$\\end{document} (m≠1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m\ e 1/2$$\\end{document}) with power-law potential V0ϕn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V_0 \\phi ^n$$\\end{document} and exponential potential V0e-λϕ/MPl\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V_0 e^{-\\lambda \\phi /M_{Pl}}$$\\end{document} of the scalar field. The Cuscuton case m=1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m=1/2$$\\end{document} where the scalar field is non-dynamical is left out of consideration. The main aim of this work is to investigate the genericity of nonsingular bounce in these models and to investigate the cosmic future of the bouncing cosmologies when they are generic. A global dynamical system formulation that is particularly suitable for investigating nonsingular bouncing cosmologies is used to carry out the analysis. We show that when F(X)=βXm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(X)=\\beta X^m$$\\end{document} (β<0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta <0$$\\end{document}), nonsingular bounce is generic for a power law potential V(ϕ)=V0ϕn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V(\\phi ) = V_0 \\phi ^n$$\\end{document} only within the parameter range 12<m<1,n<2mm-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left\\{ \\frac{1}{2}<m<1,\\,n<\\frac{2\\,m}{m-1}\\right\\} $$\\end{document} and for an exponential potential V(ϕ)=V0e-λϕ/MPl\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V(\\phi ) = V_0 e^{-\\lambda \\phi /M_{Pl}}$$\\end{document} only within the parameter range 12<m≤1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left\\{ \\frac{1}{2}<m\\le 1\\right\\} $$\\end{document}. Except in these cases, nonsingular bounce in these models is not generic due to the non-existence of global past or future attractors. Our analysis serves to show the importance of a global phase space analysis to address important questions about nonsingular bouncing solutions, an idea that may and must be adopted for such solutions even in other theories.

Probing bounce dynamics via Higher-Order Gauss-Bonnet modifications

In this paper, we focus on the Gauss-Bonnet gravity theory, which includes higher curvature corrections to the Einstein-Hilbert action. We investigate the possibility of obtaining a bouncing cosmology in this modified theory of gravity, where the Universe contracts until a minimum scale factor and then expands again. We examines four Higher-Order Gauss-Bonnet Gravity theory models within the FLRW formalism, emphasizing the Universe’s bouncing behavior to resolve Big-Bang cosmology’s singularity problem. We establish cosmological constraints over cosmic time, investigate bounce conditions, reconstruct Higher-Order Gauss-Bonnet Gravity for a hyperbolic expansion law, and extend this reconstruction using the red-shift parameter to derive cosmological parameters signifying accelerated Universe expansion. The stability of these models is subsequently evaluated through an arbitrary speed of sound function for late-time stability assessment. Our results suggest that the Gauss-Bonnet gravity theory can provide a viable mechanism for a non-singular bounce in the early universe.

From the string vacuum to FLRW or de Sitter via α' corrections

We first make more precise a recent “Hamiltonian” reformulation of the Hohm-Zwiebach approach to the tree-level, O(d,d)-invariant string cosmology equations at all orders in the α' expansion, and recall how it allows to give a simple characterization of a large class of cosmological scenarios connecting, through a non-singular bounce, two duality-related perturbative solutions at early and late times. We then discuss the effects of adding to the action a non-perturbative, O(d,d)-breaking, dilaton potential V(ϕ). The resulting cosmological solutions, assumed to approach at early times the perturbative string vacuum (with vanishing curvature and string coupling), can stabilize the dilaton at late times and simultaneously approach either a matter-dominated FLRW cosmology or a de-Sitter-like inflationary phase, depending on initial conditions and on the properties of V(ϕ) at moderate-coupling. We also identify a general mechanism for generating isotropic late-time attractors from a large basin of anisotropic initial conditions.

Traversable Lorentzian wormhole on the Shtanov-Sahni braneworld with matter obeying the energy conditions

In this paper we have explored the possibility of constructing a traversable wormhole on the Shtanov-Sahni braneworld with a timelike extra dimension. We find that the Weyl curvature singularity at the throat of the wormhole can be removed with physical matter satisfying the NEC ρ + p ≥ 0, even in the absence of any effective Λ-term or any type of charge source on the brane. (The NEC is however violated by the effective matter description on the brane arising due to effects of higher dimensional gravity.) Besides satisfying NEC the matter constituting the wormhole also satisfies the Strong Energy Condition (SEC), ρ + 3p ≥ 0, leading to the interesting possibility that normal matter on the brane may be harnessed into a wormhole. Incidentally, these conditions also need to be satisfied to realize a non-singular bounce and cyclic cosmology on the brane [1] where both past and future singularities can be averted. Thus, such a cyclic universe on the brane, constituted of normal matter can naturally contain wormholes. The wormhole shape function on the brane with a time-like extra dimension represents the tubular structure of the wormhole spreading out at large radial distances much better than in wormholes constructed in a braneworld with a spacelike extra dimension and have considerably lower mass resulting in minimization of the amount of matter required to construct a wormhole. Wormholes in the Shtanov-Sahni (SS) braneworld also have sufficiently low tidal forces, facilitating traversability. Additionally they are found to be stable and exhibit a repulsive geometry. We are left with the intriguing possibility that both types of curvature singularity can be resolved with the SS model, which we discuss at the end of the concluding section.

Cosmological Bounces Induced by a Fermion Condensate.

We show that it is possible for fermion condensation of the Nambu-Jona-Lasinio type to induce a nonsingular bounce that smoothly connects a phase of slow contraction to a phase of expansion. A chiral condensate-a nonzero vacuum expectation value of the spinor bilinear ⟨Ψ[over ¯]Ψ⟩-can form spontaneously after a slow contraction phase smooths and flattens the universe and the Ricci curvature exceeds a critical value. In this approach, a high density of spin-aligned free fermions is not required, which avoids the problem of generating a large anisotropy and initiating chaotic mixmaster behavior during the bounce phase.

Transitioning from a bounce to R 2 inflation

Non-singular bouncing cosmologies are well-motivated models for the early universe. Recent observational data are consistent with positive spatial curvature and allow for a natural collapsing and bouncing phase in the very early universe. Additionally, bouncing cosmologies have the potential to rectify conceptual shortcomings identified in the theory of inflation, such as the singularity problem. In this paper we present a classical bouncing model in the context of modified gravity, including an R 2-term in the action. We show that after the bounce, the universe enters naturally a period of inflation, driven by the R 2-term. We analyse the stability of the model and find that the scalaron assists the stability of the model.

A bouncing cosmology from VECROs

We argue that, in the same way that in a black hole space-time VECROs will form in order to cancel the gravitational effects of a collapsing mass shell and prevent the formation of a singularity, in a contracting universe a gas of VECROs will form to hold up the contraction, prevent a Big Crunch singularity, and lead to a nonsingular cosmological bounce.

Late-time acceleration from ekpyrotic bounce in f(Q,T) gravity

In this paper, we investigate the late-time accelerated universe evolution in a flat, homogeneous and isotropic model in the context of [Formula: see text] gravity, where [Formula: see text] and [Formula: see text] are non-metricity scalar and trace of energy–momentum tensor, respectively. The scale factor, by construction, yields ekpyrotic contraction era followed by a non-singular bounce. The expanding era of the universe yields late-time dark energy era preceded by matter-dominating decelerating era. The model unifies an ekpyrotic, non-singular bounce with the present dark energy-dominated epoch. The model parameters in the functional form of [Formula: see text] gravity affect the dynamical evolution of the equation of state (EoS) parameter. The theoretical value of EoS parameter is found to be [Formula: see text] for [Formula: see text], respectively, and it lies in range of the estimated value of EoS parameter from the Planck+SNe+BAO observational data. Different aspects of this bouncing model including behavior of geometrical and physical quantities along with energy conditions have been discussed in detail.

Searching for bounce signature in the early universe from current and future large-scale structure surveys

ABSTRACT The bounce scenario has been an interesting research topic in cosmology, due to its ability to resolve both the singularity problem and the trans-Planckian issue, which are left from the standard inflationary theory. In previous works, we considered an inflationary cosmology with a preceding non-singular bounce and found that this model could suppress the primordial power spectrum at large scales and leave the signature on the angular power spectra of cosmic microwave background (CMB). In this work, we extend this analysis to the large-scale structure (LSS) measurements. Firstly, we consider the angular power spectrum of current LSS data sets, such as the 2MPZ, SDSS-DR12, and DES Y3 galaxy surveys at low redshifts and the NVSS radio survey at high redshifts, and do not obtain good constraint on the model parameters, due to the precision limitation at large scales. When we include the Planck CMB measurements, the constraints become a little bit better: the amplitude Ar = 0.8 ± 0.2 and the slope ${\rm log_{10}}(k_B)=-2.6^{+0.3}_{-1.0}$ at 68 per cent confidence level. In order to evaluate the constraining ability of future LSS surveys, we forecast the clustering measurements, such as the galaxy angular power spectrum and the galaxy lensing shear power spectrum, based on the China Space Station Telescope photometric survey. We find that the standard deviations of model parameters will be significantly shrunk, ΔAr = 0.1 and Δlog10(kB) = 0.1, due to the high precision measurements. Finally, we consider the bounce feature and the primordial non-Gaussianity from inflation theory simultaneously and find that in the bounce inflationary model the limit on fNL will be weaker than that obtained in the standard inflationary model, due to the strong degeneracy among parameters.

Non-singular bouncing model in energy momentum squared gravity

This work is concerned to study the bouncing nature of the Universe for an isotropic configuration of fluid and Friedmann-Lemaître-Robertson-Walker metric scheme. This work is carried out under the novel gravitation by assuming a specific model i.e. = with α and λ are constants, serving as free parameters. The terms and served as an Gauss-Bonnet invariant and square of the energy-momentum trace term as an inclusion in the gravitational action respectively, and is proportional to . A specific functional form of the Hubble parameter is taken to provide the evolution of cosmographic parameters. A well known equation of state parameter, is used to represent the dynamical behavior of energy density, matter pressure and energy conditions. A detailed graphical analysis is also provided to review the bounce. Furthermore, all free parameters are set in a way, to make the supposed Hubble parameter act as the bouncing solution and ensure the viability of energy conditions. Conclusively, all necessary conditions for a bouncing model are checked.

Novel relationship between shear and energy density at the bounce in nonsingular Bianchi I spacetimes

In classical Bianchi I spacetimes, underlying conditions for what dictates the singularity structure---whether it is anisotropic shear or energy density, can be easily determined from the generalized Friedmann equation. However, in nonsingular bouncing anisotropic models these insights are difficult to obtain in the quantum gravity regime where the singularity is resolved at a nonvanishing mean volume which can be large compared to the Planck volume, depending on the initial conditions. Such nonsingular models may also lack a generalized Friedmann equation making the task even more difficult. We address this problem in an effective spacetime description of loop quantum cosmology (LQC) where energy density and anisotropic shear are universally bounded due to quantum geometry effects, but a generalized Friedmann equation has been difficult to derive due to the underlying complexity. Performing extensive numerical simulations of effective Hamiltonian dynamics, we bring to light a surprising, seemingly universal relationship between energy density and anisotropic shear at the bounce in LQC. For a variety of initial conditions for a massless scalar field, an inflationary potential, and two types of ekpyrotic potentials we find that the values of energy density and the anisotropic shear at the quantum bounce follow a novel parabolic relationship which reveals some surprising results about the anisotropic nature of the bounce, such as that the maximum value of the anisotropic shear at the bounce is reached when the energy density reaches approximately half of its maximum allowed value. The relationship we find can prove very useful for developing our understanding of the degree of anisotropy of the bounce, isotropization of the postbounce universe, and discovering the modified generalized Friedmann equation in Bianchi I models with quantum gravity corrections.

Nonlocal de Sitter gravity and its exact cosmological solutions

This paper is devoted to a simple nonlocal de Sitter gravity model and its exact vacuum cosmological solutions. In the Einstein-Hilbert action with Λ term, we introduce nonlocality by the following way: R-2Lambda =sqrt{R-2Lambda}kern1em sqrt{R-2Lambda}to sqrt{R-2Lambda}kern1em Fleft(square right)kern1em sqrt{R-2Lambda} , where Fleft(square right)=1+{sum}_{n=1}^{+infty}left({f}_n{square}^n+{f}_{-n}{square}^{-n}right) is an analytic function of the d’Alembert-Beltrami operator □ and its inverse □−1. By this way, R and Λ enter with the same form into nonlocal version as they are in the local one, and nonlocal operator F(□) is dimensionless. The corresponding equations of motion for gravitational field gμν are presented. The first step in finding some exact cosmological solutions is solving the equation square sqrt{R-2Lambda}=qsqrt{R-2Lambda} , where q = ζΛ (ζ ∈ R) is an eigenvalue and sqrt{R-2Lambda} is an eigenfunction of the operator □. We presented and discussed several exact cosmological solutions for homogeneous and isotropic universe. One of these solutions mimics effects that are usually assigned to dark matter and dark energy. Some other solutions are examples of the nonsingular bounce ones in flat, closed and open universe. There are also singular and cyclic solutions. All these cosmological solutions are a result of nonlocality and do not exist in the local de Sitter case.

Universe before Big Bang

The ghost condensation of the early universe in a pre-big bang phase has been presented in this paper through duration of a non-singular bounce. The undergoing universe contracts and passes smoothly in an expanding universe via a post-big bang phase. Initially developing and then taming any ghost like instabilities, the Null Energy Condition (NEC) is explicitly violated through the curvature mechanism of an adiabatic perturbed metric. The vacuum state of the ongoing phase is stabilized via a Lagrangian that in essence stabilizes the vacuum state under the higher order derivatives. The violation of the NEC regards a catastrophic vacuum instability, which re-emerges with a correction valid at small energies and momenta, below the UV-cut-off scale that, could potentially be problematic if one tries to construct a UV-completed theory of this Ekpyrotic model. The scale-invariant curvature perturbation, that arises and is sourced out of the scale-invariant entropy perturbations sourced by 2-Ekpyrotic scalar fields, that, in contrast, becomes constant on the super-horizon limits, due to the non-singular nature of the background geometry. Apart, from the ghost condensates, this theory addresses the new Ekpyrotic theory which in order becomes a distinguishable alternative to inflation theory for the birth of the universe. As per the recent WMAP data, the Ekpyrotic model has a spectral red tilt that shows the bounced scalar potential falling through a negative phase shift during the matter-fluid fluctuations in the hot big bang phase.