Spectrum Of Primordial Gravitational Waves Research Articles

Imprints of Barrow–Tsallis cosmology in primordial gravitational waves

Both the Barrow and Tsallis δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta $$\\end{document} entropies are one-parameter generalizations of the black-hole entropy, with the same microcanonical functional form. The ensuing deformation is quantified by a dimensionless parameter Δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta $$\\end{document}, which in the case of Barrow entropy represents the anomalous dimension caused by quantum fluctuations over the horizon surface, while in Tsallis’ case, it describes the deviation of the holographic scaling from extensivity. Here, we utilize the gravity-thermodynamics conjecture with the Barrow–Tsallis entropy to investigate the implications of the related modified Friedmann equations on the spectrum of primordial gravitational waves. We show that, with the experimental sensitivity of the next generation of gravitational wave detectors, such as the Big Bang Observer, it will be possible to discriminate deviations from the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model up to Δ≲O(10-3)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta \\lesssim \\mathcal {O}(10^{-3})$$\\end{document}. In this limit, Barrow–Tsallis entropy reduces to a logarithmic correction to holographic scaling, which is nearly universally predicted by both entanglement entropy calculations in the UV regime and by several candidate theories of quantum gravity. Hence, our considerations and results are expected to have general validity in the quantum gravity framework.

Cosmology from string T-duality and zero-point length

Inspired by string T-duality and taking into account the zero-point length correction, l0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l_0$$\\end{document}, to the gravitational potential, we construct modified Friedmann equations by applying the first law of thermodynamics on the apparent horizon of the Friedmann–Robertson–Walker (FRW) Universe. The cosmological viability of this extended scenario is investigated by studying influences on the evolution of the early Universe and performing cosmographic analysis. Furthermore, we explore the inflationary paradigm under the slow-roll condition. By testing the model against observational data, the zero-point length is constrained around the Planck scale, in compliance with the original assumption from string T-duality. We also study the growth of density perturbations in the linear regime. It is shown that the zero-point length stands out as an alternative characterization for the broken-power-law spectrum, providing a better fit for the experimental measurements than the simple power-law potential. Finally, we focus on implications for the primordial gravitational wave (PGW) spectrum. Should the zero-point length be running over energy scales, as is the case for all parameters and coupling constants in quantum gravity under renormalization group considerations, deviations from general relativity (GR) might be potentially tested through upcoming PGW observatories.

Solution for cosmological observables in the Starobinsky model of inflation

This paper focuses on the Starobinsky model of inflation in the Einstein frame. We derive solutions for various cosmological observables, such as the scalar spectral index ns\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_s$$\\end{document}, the tensor-to-scalar ratio r and their runnings, as well as the number of e-folds of inflation, reheating, and radiation, with minimal assumptions. The impact of reheating on inflation is explored by constraining the equation of state parameter ωre\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega _{re}$$\\end{document} at the end of reheating. An equation linking inflation with reheating is established, which is solved for the spectral index ns\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_s$$\\end{document}. Using consistency relations of the model, we determine the other observables while the number of e-folds during inflation Nk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_k$$\\end{document}, and the number of e-folds during reheating Nre\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_{re}$$\\end{document} are determined by their respective formulas involving ns\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_s$$\\end{document}. We find remarkable agreement between the Starobinsky model and current measurements of the power spectrum of primordial curvature perturbations and the present bounds on the spectrum of primordial gravitational waves.

Observable gravitational waves from hyperkination in Palatini gravity and beyond

We consider cosmology with an inflaton scalar field with an additional quartic kinetic term. Such a theory can be motivated by Palatini R+R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R+R^2$$\\end{document} modified gravity. Assuming a runaway inflaton potential, we take the Universe to become dominated by the kinetic energy density of the scalar field after inflation. Initially, the leading kinetic term is quartic and we call the corresponding period hyperkination. Subsequently, the usual quadratic kinetic term takes over and we have regular kination, until reheating. We study, both analytically and numerically, the spectrum of primordial gravitational waves generated during inflation and re-entering the horizon during the subsequent eras. We demonstrate that the spectrum is flat for modes re-entering during radiation domination and hyperkination and linear in frequency for modes re-entering during kination: kinetic domination boosts the spectrum, but hyperkination truncates its peak. As a result, the effects of the kinetic period can be extended to observable frequencies without generating excessive gravitational waves, which could otherwise destabilise the process of Big Bang Nucleosynthesis. We show that there is ample parameter space for the primordial gravitational waves to be observable in the near future. If observed, the amplitude and ‘knee’ of the spectrum will provide valuable insights into the background theory.

Primordial stochastic gravitational wave backgrounds from a sharp feature in three-field inflation. Part I. The radiation era

The detection of a primordial stochastic gravitational wave background has the potential to reveal unprecedented insights into the early universe, and possibly into the dynamics of inflation. Generically, UV-complete inflationary models predict an abundance of light scalars, so any inflationary stochastic background may well be formed in a model with several interacting degrees of freedom. The stochastic backgrounds possible from two-field inflation have been well-studied in the literature, but it is unclear how similar they are to the possibilities from many-field inflation. In this work we study stochastic backgrounds from more-than-two field inflation for the first time, focusing on the scalar-induced background produced during the radiation era by a brief turn in three-field space. We find an analytic expression for the enhancement in the power spectrum as a function of the turn rate and the torsion, and show that unique signatures of three-field dynamics are possible in the primordial power spectrum and gravitational wave spectrum. We confirm our analytic results with a suite of numerical simulations and find good agreement in the shape and amplitude of the power spectra. We also comment on the detection prospects in LISA and other future detectors. We do not expect the moderately large growth of the inflationary perturbations necessary for detection to cause a breakdown of perturbation theory, but this must be verified on a case-by-case basis for specific microphysical models to make a definitive claim.

Gravitational echoes of lepton number symmetry breaking with light and ultralight Majorons

We formulate a version of the low-scale Majoron model equipped with an inverse seesaw mechanism featuring lepton-number preserving dimension-6 operators in the scalar potential. Contrary to its dimension-4 counterpart, we find that the model can simultaneously provide light and ultralight Majorons, neutrino masses and their mixing, while featuring strong first-order cosmological phase transitions associated to the spontaneous breaking of the lepton number and the electroweak symmetries in the early Universe. We show by a detailed numerical analysis under which circumstances the model can be probed via the primordial gravitational wave spectrum potentially observable at LISA and other planned facilities. We discuss which implications result for collider physics observables, such as scalar trilinear couplings, the scalar mixing angle and the mass of a new CP-even Higgs boson.

Primordial gravitational waves by chaotic potential with a sharp step

We calculate the primordial gravitational wave spectrum observed today, Ω0gw(f) produced by a chaotic inflationary model featuring a step in its potential. Considering an inflaton field, slowly rolling down the potential, we analyze the scalar and tensor power spectra for the step potential model and found oscillatory density fluctuations within a specific range of wavenumbers around the feature. Localized small anomalies are observed in the tensor power spectrum also. We estimate the observational parameters, including the scalar spectral index (ns), tensor tilt (nt) and tensor-to-scalar ratio (r), which are found to be consistent with Planck satellite results. Additionally, by employing the relation between Ω0gw(f) and r, we determine the effective equation of state parameter wˆ(f) at the end of inflation. Evolution of wˆ(f) from 0.2 to 0.33, followed by constancy is obtained in the ntˆ(f)−wˆ(f) plot. This evolution of wˆ(f) is attributed to the reheating process, which is crucial for transitioning from the inflationary phase to the subsequent radiation-dominated era.

Revisiting the cosmological phase transitions on the inflationary gravitational waves with BKP18

The effects of the electroweak and the quark-gluon plasma phase transitions are considered in the course of evolution of the universe and the resulting spectrum of primordial gravitational waves normalized with the BICEP/Keck and Planck joint data is obtained. The QGP index n=0.203 leads to a step reduction of ∼17.6% in the amplitude and a step of ∼35% in the energy density spectrum for frequency >1.36×10−8Hz. On the other hand, the EW index w=0.0147 leads to a step of ∼1.47% in the amplitude and a step of ∼2.9% in the energy density spectrum for frequency >10−5Hz. The combined effect of phase transitions on the inflationary gravitational waves leads to about ∼19% reduction in the amplitude and an overall reduction of ∼38% in the energy density as compared to the spectrum without considering these phase transitions. The resulting spectrum for R2 inflation model is found to be well within the BBN bound and its potential detectability is tested with the power-law integrated sensitivity curves of the future LISA, DECIGO, BBO, SKA and IPTA experiments.

Enhanced Gravitational Waves from Inflaton Oscillons.

In broad classes of inflationary models the period of accelerated expansion is followed by fragmentation of the inflaton scalar field into localized, long-lived, and massive oscillon excitations. We demonstrate that matter dominance of oscillons, followed by their rapid decay, significantly enhances the primordial gravitational wave (GW) spectrum. These oscillon-induced GWs, sourced by second-order perturbations, are distinct and could be orders of magnitude lower in frequency than the previously considered GWs associated with oscillon formation. We show that detectable oscillon-induced GW signatures establish direct tests independent from cosmic microwave background radiation for regions of parameter space of monodromy, and logarithmic and pure natural (plateau) potential classes of inflationary models, among others. We demonstrate that oscillon-induced GWs in a model based on pure natural inflation could be directly observable with the Einstein Telescope, Cosmic Explorer, and DECIGO. These signatures offer a new route for probing the underlying inflationary physics.

A peak in the power spectrum of primordial gravitational waves induced by primordial dark magnetic fields

Dark gauge fields have been discussed as candidates for dark matter recently. If they existed, primordial dark magnetic fields during inflation would have existed. It is believed that primordial gravitational waves (PGWs) arise out of quantum fluctuations during inflation. We study the graviton-dark photon conversion process in the presence of background primordial dark magnetic fields and find that the process induces the tachyonic instability of the PGWs. As a consequence, a peak appears in the power spectrum of PGWs. It turns out that the peak height depends on the direction of observation. The peak frequency could be in the range from 10-5 to 103 Hertz for GUT scale inflation. Hence, the observation of PGWs could provide a new window for probing primordial dark magnetic fields.

Gravitational reheating

Our present understanding of the reheating phase is incomplete due to a lack of observations. Apart from its cosmological implications, the reheating should play a vital role in particle physics and inflation model building. Conventionally, reheating dynamics are modeled by invoking arbitrary coupling among the inflaton and daughter fields. Such an approach lacks robust cosmological predictions, due to its arbitrary couplings, and is difficult to verify through observation. In this paper, we propose a minimal reheating scenario, where the inflaton is coupled with all the daughter fields only gravitationally. Besides being successful in reheating the Universe, the scenario offers a strong cosmological prediction of the primordial gravitational wave spectrum and discards a large number of possible models of dark matter and inflation that are otherwise consistent with Planck.

E^+e^- annihilation on the stochastic background of primordial gravitational waves with BKP18

The evolution of inflationary primordial gravitational waves with the expansion of the universe is studied while taking into account the e^+e^- annihilation which leads to step correction in the spectrum of primordial gravitational waves which is sim 10% in the amplitude and sim 25% in the energy density. The amplitudes and energy densities are studied for the alpha -attractor inflation models which are in agreement with the recent BICEP/Keck and Planck 2018 joint result. The energy densities are well within the big bang nucleosynthesis bound, but the spectra for these models are very much below the detection range of the currently operating and upcoming detectors.

Quantum gravitational signatures in next-generation gravitational wave detectors

A recent study established a correspondence between the Generalized Uncertainty Principle (GUP) and Modified theories of gravity, particularly Stelle gravity. We investigate the consequences of this correspondence for inflation and cosmological observables by evaluating the power spectrum of the scalar and tensor perturbations using two distinct methods. First, we employ PLANCK observations to determine the GUP parameter γ0. Then, we use the value of γ0 to investigate the implications of quantum gravity on the power spectrum of primordial gravitational waves and their possible detectability in the next-generation detectors, like Einstein Telescope and Cosmic explorer.

Waterfall stiff period can generate observable primordial gravitational waves

A toy-model is studied, which considers two flat directions meeting at an enhanced symmetry point such that they realise the usual hybrid inflation mechanism. The kinetic term of the waterfall field features a pole at its Planckian vacuum expectation value (VEV), as with α-attractors. Consequently, after the phase transition which terminates hybrid inflation, the waterfall field never rolls to its VEV. Instead, it drives a stiff period, where the barotropic parameter of the Universe w ≈ 1/2 results in a peak in the spectrum of primordial gravitational waves, which will be observable by the forthcoming LISA mission as well as by Advanced LIGO.

Gravitational wave and CMB probes of axion kination

Rotations of an axion field in field space provide a natural origin for an era of kination domination, where the energy density is dominated by the kinetic term of the axion field, preceded by an early era of matter domination. Remarkably, no entropy is produced at the end of matter domination and hence these eras of matter and kination domination may occur even after Big Bang Nucleosynthesis. We derive constraints on these eras from both the cosmic microwave background and Big Bang Nucleosynthesis. We investigate how this cosmological scenario affects the spectrum of possible primordial gravitational waves and find that the spectrum features a triangular peak. We discuss how future observations of gravitational waves can probe the viable parameter space, including regions that produce axion dark matter by the kinetic misalignment mechanism or the baryon asymmetry by axiogenesis. For QCD axion dark matter produced by the kinetic misalignment mechanism, a modification to the inflationary gravitational wave spectrum occurs above 0.01 Hz and, for high values of the energy scale of inflation, the prospects for discovery are good. We briefly comment on implications for structure formation of the universe.

Quantum corrections to the primordial tensor spectrum: open EFTs & Markovian decoupling of UV modes

Perturbative quantum corrections to primordial power spectra are important for testing the robustness and the regime of validity of inflation as an effective field theory. Although this has been done extensively for the density power spectrum (and, to some extent, for the tensor spectrum) using loop corrections, we do so in an open quantum system approach to the problem. Specifically, we calculate the first-order corrections to the primordial gravitational wave spectrum due to (cubic) tensor interactions alone. We show that our results match expectations from standard loop corrections only in the strict Markovian limit, and therefore, establish a systematic way to relax this approximation in the future, as is generally necessary for gravitational systems.

Effects of a Geometrically Realized Early Dark Energy Era on the Spectrum of Primordial Gravitational Waves

In this work, we investigate the effects of a geometrically generated early dark energy era on the energy spectrum of the primordial gravitational waves. The early dark energy era, which we choose to have a constant equation of state parameter w, is synergistically generated by an appropriate f(R) gravity in the presence of matter and radiation perfect fluids. As we demonstrate, the predicted signal for the energy spectrum of the f(R) primordial gravitational waves is amplified and can be detectable, for various reheating temperatures, especially for large reheating temperatures. The signal amplitude depends on the duration of the early dark energy era and on the value of the dark energy equation of state parameter, with the latter affecting more crucially the amplification. Specifically, the amplification occurs when the equation of state parameter approaches the de Sitter value w=−1. Regarding the duration of the early dark energy era, we find that the largest amplification occurs when the early dark energy era commences at temperature T=0.85 eV until T=7.8 eV. Moreover, we study a similar scenario in which amplification occurs, where the early dark energy era commences at T=0.29 eV and lasts until the temperature is increased by ΔT∼1.7 eV. The discovery of primordial gravitational waves will reveal if several symmetries in the Universe exist or not so this work is important toward revealing the primordial gravitational waves.

Generating enhanced primordial GWs during inflation with intermittent violation of NEC and diminishment of GW propagating speed

We investigate both the null energy condition (NEC) violating scenario and the cT-diminishing scenario for generating enhanced power spectrum of primordial gravitational waves (GWs) during inflation, where cT is the propagating speed of primordial GWs. Both of these two scenarios can be realized stably with theories beyond Horndeski, hence can be uniformly implemented within the framework of the effective field theory. We calculate the power spectrum of primordial GWs by assuming that the inflationary Universe undergoes three phases, where the violation of NEC or the diminishment of cT occurs in the intermediate phase. A template of the spectrum is given for the NEC-violating scenario. We also discuss the underlying relation and discrepancy between these two scenarios with a disformal transformation.

Spectrum of Primordial Gravitational Waves in Modified Gravities: A Short Overview

In this work, we shall exhaustively study the effects of modified gravity on the energy spectrum of the primordial gravitational waves background. S. Weinberg has also produced significant works related to the primordial gravitational waves, with the most important one being the effects of neutrinos on primordial gravitational waves. With this short review, our main aim is to gather all the necessary information for studying the effects of modified gravity on primordial gravitational waves in a concrete and quantitative way and in a single paper. After reviewing all the necessary techniques for extracting the general relativistic energy spectrum, and how to obtain, in a WKB way, the modified gravity damping or amplifying factor, we concentrate on specific forms of modified gravity of interest. The most important parameter involved for the calculation of the effects of modified gravity on the energy spectrum is the parameter aM, which we calculate for the cases of f(R,ϕ) gravity, Chern–Simons-corrected f(R,ϕ) gravity, Einstein–Gauss–Bonnet-corrected f(R,ϕ) gravity, and higher derivative extended Einstein–Gauss–Bonnet-corrected f(R,ϕ) gravity. The exact form of aM is presented explicitly for the first time in the literature. With regard to Einstein–Gauss–Bonnet-corrected f(R,ϕ) gravity, and higher derivative extended Einstein–Gauss–Bonnet-corrected f(R,ϕ) gravity theories, we focus on the case in which the gravitational wave propagating speed is equal to that of light in a vacuum. We provide expressions for aM expressed in terms of the cosmic time and in terms of the redshift, which can be used directly for the numerical calculation of the effect of modified gravity on the primordial gravitational wave energy spectrum.

Amplification of Primordial Gravitational Waves by a Geometrically Driven non‐canonical Reheating Era

AbstractIn order to describe inflation in general relativity, scalar fields must inevitably be used, with all the setbacks of that description. On the other hand, gravity and other modified gravity theories seem to provide a unified description of early and late‐time dynamics without resorting to scalar or phantom theories. The question is, can modified gravity affect directly the mysterious radiation domination era? Addressing this question is the focus in this work, and we shall consider the case for which in the early stages of the radiation domination era, namely during the reheating era, the background equation of state parameter is different from . As we show, in the context of gravity, an abnormal reheating era can affect the primordial gravitational wave energy spectrum today. Since future interferometers will exactly probe this era, which consists of subhorizon modes that reentered the horizon during the early stages of the radiation domination era, the focus in this work is how a short abnormal reheating era that deviates from the standard perfect fluid pattern with , and generated by higher order curvature terms, can affect the primordial gravitational wave energy spectrum. Using a WKB approach, we calculate the effect of an gravity generated abnormal reheating era, and as we show the primordial gravitational wave spectrum is significantly amplified, a result which is in contrast to the general relativistic case, where the effect is minor.