Primordial Gravitational Wave Background Research Articles

Backreaction of axion-SU(2) dynamics during inflation

We consider the effects of backreaction on axion-SU(2) dynamics during inflation. We use the linear evolution equations for the gauge field modes and compute their backreaction on the background quantities numerically using the Hartree approximation. We show that the spectator chromo-natural inflation attractor is unstable when back-reaction becomes important. Working within the constraints of the linear mode equations, we find a new dynamical attractor solution for the axion field and the vacuum expectation value of the gauge field, where the latter has an opposite sign with respect to the chromo-natural inflation solution. Our findings are of particular interest to the phenomenology of axion-SU(2) inflation, as they demonstrate the instability of the usual trajectory due to large backreaction effects. The viable parameter space of the model becomes significantly altered, provided future non-Abelian lattice simulations confirm the existence of the new dynamical attractor. In addition, the backreaction effects lead to characteristic oscillatory features in the primordial gravitational wave background that are potentially detectable with upcoming gravitational wave detectors.

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.

Primordial gravitational waves in the nano-Hertz regime and PTA data — towards solving the GW inverse problem

In recent years, several pulsar timing array collaborations have reported first hints for a stochastic gravitational wave background at nano-Hertz frequencies. Here we elaborate on the possibility that this signal comes from new physics that leads to the generation of a primordial stochastic gravitational wave background. We propose a set of simple but concrete models that can serve as benchmarks for gravitational waves sourced by cosmological phase transitions, domain wall networks, cosmic strings, axion dynamics, or large scalar fluctuations. These models are then confronted with pulsar timing data and with cosmological constraints. With only a limited number of free parameters per model, we are able to identify viable regions of parameter space and also make predictions for future astrophysical and laboratory tests that can help with model identification and discrimination.

Updated constraints on amplitude and tilt of the tensor primordial spectrum

We have taken a comprehensive approach to update the limits on the tensor-to-scalar ratio (r) and the tensor spectral index (nt ), using 10 datasets from the BICEP/Keck Array 2015 and 2018, Planck releases 3 and 4, and LIGO-Virgo-KAGRA Collaboration. By fitting the complete ΛCDM+r+nt model with two different approaches for the tensor sector, we have not only established which method is the most reliable, but have also achieved the strongest constraint on the tensor-to-scalar ratio in current literature: r < 0.028 and -1.37 < nt < 0.42 at 95% confidence level. Furthermore, our examination of the common signal detected by the NANOGrav Collaboration further confirms that a simple power-law cannot reconcile the constraints from different datasets if the NANOGrav detection is due to a primordial inflationary gravitational wave background, as previously shown in the literature.

Detecting cosmological gravitational wave background after removal of compact binary coalescences in future gravitational wave detectors

The improved sensitivity of third generation gravitational wave detectors opens the possibility of detecting the primordial cosmological stochastic gravitational wave background (SGWB). Detection of the cosmological SGWB is facing a novel challenge: it will likely be masked by the foreground generated by a large number of coalescences of compact binary systems consisting of black holes and/or neutron stars. In this paper, we investigate the possibility of reducing this foreground by removing (notching) the individually resolved compact binary signals in time-frequency space. We establish that such an approach could be used to reach the SGWB sensitivity floor defined by the unresolved part of the compact binaries foreground, which we find to be between ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{GW}}\ensuremath{\sim}(9.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}--8.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11})$ for a frequency independent energy density spectrum and depending on the rate of coalescing binary neutron star systems. Since third-generation gravitational wave detectors will not be able to resolve all compact binaries, the unresolvable component of the compact binaries foreground may limit the SGWB searches with these detectors.

Impact of LIGO-Virgo black hole binaries on gravitational wave background searches

We study the impact of the black hole binary population currently probed by LIGO-Virgo on future searches for the primordial gravitational wave background. We estimate the foreground generated by the binaries using the observed event rate and a simple modeling of the black hole population. We subtract individually resolvable binaries from the foreground and utilize Fisher analysis to derive sensitivity curves for power-law signals including these astrophysical foregrounds. Even with optimistic assumptions, we find that the reach of future experiments will be severely reduced.

How does SU(N) -natural inflation isotropize the Universe?

We study the homogeneous and anisotropic dynamics of pseudoscalar inflation coupled to an $\mathrm{SU}(N)$ gauge field. To see how the initially anisotropic universe is isotropized in such an inflation model, we derive the equations to obtain axisymmetric $\mathrm{SU}(N)$ gauge field configurations in Bianchi type-I geometry and discuss a method to identify their isotropic subsets which are the candidates of their late-time attractor. Each isotropic solution is characterized by the corresponding SU(2) subalgebra of the $\mathrm{SU}(N)$ algebra. It is shown numerically that the isotropic universe is a universal late-time attractor in the case of the SU(3) gauge field. Interestingly, we find that a transition between the two distinct gauge-field configurations characterized by different SU(2) subalgebras can occur during inflation. We clarify the conditions for this to occur. This transition could leave an observable imprint on the cosmic microwave background and the primordial gravitational wave background.

Kinetically stabilized inflation

In this work, we propose a string-inspired two fields inflation model to address the fine-tuning problem that the standard inflation model suffers. The fast-rolling tachyon mathcal{T} originated from the D-brane and anti-D-brane pair annihilation locks the inflaton φ slowly rolling on a Higgs-like potential Vleft(varphi right)=-{m}_{varphi}^2{varphi}^2+lambda {varphi}^4 and drives a kinetically stabilized (KS) inflation. Our numerical simulation confirms such a solution is a dynamic attractor. In particular, for λ < 0.8 × 10−3, the e-folding number contributed by the KS inflation phase can be larger than 62 to solve the horizon and flatness problems of Big Bang theory. Notably, this KS inflation generates a nearly scale-invariant primordial curvature perturbations spectrum consistent with current cosmic microwave background (CMB) observations. It predicts a low tensor-to-scalar ratio, which the current primordial gravitational wave background (the B-modes in CMB) searches favor.

Constraining cosmic inflation with observations: Prospects for 2030

ABSTRACT The ability to test and constrain theories of cosmic inflation will advance substantially over the next decade. Key data sources include cosmic microwave background (CMB) measurements and observations of the distribution of matter at low-redshift from optical, near-infrared, and 21-cm intensity surveys. A positive detection of a CMB B-mode consistent with a primordial stochastic gravitational wave background (SGWB) is widely viewed as a smoking gun for an inflationary phase. Still, a null result does not exclude inflation. However, in a significant class of inflationary scenarios, a low SGWB amplitude is correlated with a more significant running, αs, in the primordial density perturbations than is seen with the simplest inflationary potentials. With this motivation, we forecast the precision with which the spectral index ns and αs can be constrained by currently envisaged observations, including CMB (Simons Observatory, CMB-S4 and LiteBIRD), optical/near infra-red (DESI and SPHEREx), and 21-cm intensity mapping (Tianlai and CHIME) surveys. We identify optimal combinations of data sets for constraining the running and show that they may yield additional and informative constraints on the overall inflationary parameter space if the SGWB remains undetected.

Primordial stochastic gravitational wave background anisotropies: in-in formalization and applications

Primordial non-Gaussianities of the scalar(tensor)-tensor-tensor type supporting a non-trivial squeezed component are known to induce anisotropies in the stochastic gravitational wave background. We derive the explicit form of such anisotropies by making use, for the first time in this context, of the in-in formalism for cosmological correlation functions. After illustrating the general method and using it for the minimal single-field slow-roll case, we apply it to multi-field models, providing both a tree-level and a one-loop example. First, we make contact with previous results on anisotropies due to the presence of an extra spin-2 field during inflation. Secondly, we calculate the 1-loop scalar-tensor-tensor three-point function in the context of so-called supersolid inflation. The corresponding gravitational wave anisotropy is induced atop a gravitational signal that may be sufficiently large for detection.

Testing super heavy dark matter from primordial black holes with gravitational waves

Ultra-light primordial black holes with masses M BH < 109 g evaporate before big-bang nucleosynthesis producing all matter fields, including dark matter, in particular super-heavy dark matter: M DM ≳ 1010 GeV. If the dark matter gets its mass via U(1) symmetry-breaking, the phase transition that gives a mass to the dark matter also produces cosmic strings which radiate gravitational waves. Because the symmetry-breaking scale ΛCS is of the same order as M DM, the gravitational waves radiated by the cosmic strings have a large enough amplitude to be detectable across all frequencies accessible with current and planned experimental facilities. Moreover, an epoch of early primordial black hole domination introduces a unique spectral break in the gravitational wave spectrum whose frequency is related to the super-heavy dark matter mass. Hence, the features of a stochastic background of primordial gravitational waves could indicate that super-heavy dark matter originated from primordial black holes. In this perspective, the recent finding of a stochastic common-spectrum process across many pulsars by two nano-frequency pulsar timing arrays would fix the dark matter mass to be 3 × 1013 GeV ≲ M DM ≲ 1014 GeV. The (non-)detection of a spectral break at 0.2 Hz ≲ f * ≲ 0.4 Hz would (exclude) substantiate this interpretation of the signal.

New physics from the polarized light of the cosmic microwave background

Cosmology requires new physics beyond the Standard Model of elementary particles and fields. What is the fundamental physics behind dark matter and dark energy? What generated the initial fluctuations in the early Universe? Polarised light of the cosmic microwave background (CMB) may hold the key to answers. In this article, we discuss two new developments in this research area. First, if the physics behind dark matter and dark energy violates parity symmetry, their coupling to photons rotates the plane of linear polarisation as the CMB photons travel more than 13 billion years. This effect is known as `cosmic birefringence': space filled with dark matter and dark energy behaves as if it were a birefringent material, like a crystal. A tantalising hint for such a signal has been found with the statistical significance of $3\sigma$. Next, the period of accelerated expansion in the very early Universe, called `cosmic inflation', produced a stochastic background of primordial gravitational waves (GW). What generated GW? The leading idea is vacuum fluctuations in spacetime, but matter fields could also produce a significant amplitude of primordial GW. Finding its origin using CMB polarisation opens a new window into the physics behind inflation. These new scientific targets may influence how data from future CMB experiments are collected, calibrated, and analysed.

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.

Optimization of Design Parameters for Gravitational Wave Detector DECIGO Including Fundamental Noises

The DECi-hertz Interferometer Gravitational-Wave Observatory (DECIGO) is a space gravitational wave (GW) detector. DECIGO was originally designed to be sensitive enough to observe primordial GW background (PGW). However, due to the lowered upper limit of the PGW by the Planck observation, further improvement of the target sensitivity of DECIGO is required. In the previous studies, DECIGO’s parameters were optimized to maximize the signal-to-noise ratio (SNR) of the PGW to quantum noise including the effect of diffraction loss. To simulate the SNR more realistically, we optimize DECIGO’s parameters considering the GWs from double white dwarfs (DWDs) and the thermal noise of test masses. We consider two cases of the cutoff frequency of GWs from DWDs. In addition, we consider two kinds of thermal noise: thermal noise in a residual gas and internal thermal noise. To investigate how the mirror geometry affects the sensitivity, we calculate it by changing the mirror mass, keeping the mirror thickness, and vice versa. As a result, we obtained the optimums for the parameters that maximize the SNR that depends on the mirror radius. This result shows that a thick mirror with a large radius gives a good SNR and enables us to optimize the design of DECIGO based on the feasibility study of the mirror size in the future.

Imprint of early dark energy in stochastic gravitational wave background

Early dark energy that relieves Hubble tension leaves a fingerprint in the primordial stochastic gravitational wave background that originates from cosmic string network. The signal is not only detectable with future planned gravitational wave experiments, but also distinguishable from other astrophysical and cosmological signals in the gravitational wave frequency spectrum. We find that the cosmic string gravitational wave spectrum can probe other new physics that are generated in post-big bang nucleosynthesis, which extends GW cosmic archaeology search region.

Pre-inflationary bounce effects on primordial gravitational waves of f(R) gravity

In this work we shall study a possible pre-inflationary scenario for our Universe and how this might be realized by f(R) gravity. Specifically, we shall introduce a scenario in which the Universe in the pre-inflationary era contracts until it reaches a minimum magnitude, and subsequently expands, slowly entering a slow-roll quasi-de Sitter inflationary era. This pre-inflationary bounce avoids the cosmic singularity, and for the eras before and after the quasi-de Sitter inflationary stage, approximately satisfies the string theory motivated scale factor duality a(t)=a−1(−t). We investigate which approximate forms of f(R) can realize such a non-singular pre-inflationary scenario, the quasi-de Sitter patch of which is described by an R2 gravity, thus the exit from inflation is guaranteed. Furthermore, since in string theory pre-Big Bang scenarios lead to an overall amplification of the gravitational wave energy spectrum, we examine in detail this perspective for the f(R) gravity generating this pre-inflationary non-singular bounce. As we show, in the f(R) gravity case, the energy spectrum of the primordial gravitational waves background is also amplified, however the drawback is that the amplification is too small to be detected by future high frequency interferometers. Thus we conclude that, as in the case of single scalar field theories, f(R) gravity cannot produce detectable stochastic gravitational waves and a synergistic theory of scalars and higher order curvature terms might be needed.

Clarifying transfer function approximations for the large-scale gravitational wave background in ΛCDM

ABSTRACTThe primordial gravitational wave background (GWB) offers an exciting future avenue of discovery for new physics. Its information content encodes multiple eras in the early Universe’s history, corresponding to many orders of magnitude in frequency and physical scale to be measured today. By numerically solving for the GW transfer functions we provide simple yet accurate formulas describing the average power of the large-scale energy spectrum of the GWB for arbitrary primordial tensor power spectra. In doing so, we can pedagogically explain and clarify previous GWB literature, highlight the important cosmological parameters of various GWB features, and reveal multiple ways in which cancelling conceptual errors can give deceptively accurate results. The scales considered here are particularly important for CMB probes of the GWB, via B-modes and spectral distortions. In particular, we carefully study the effects of both neutrino damping, and the precise nature of the transition between the radiation-dominated (RD) and matter-dominated (MD) eras. A byproduct of numerically solving the problem is the ability to study the robustness of common approximations in the literature. Specifically, we show that a numerical treatment is especially important around the RD–MD transition, and for a brief moment of history where neutrino damping occurs during MD. In passing, we also discuss the effects of late acceleration caused by dark energy – showing that this can be neglected in most practical GWB applications – and the effects of changing relativistic degrees of freedom on the GWB at very small scales.

Measuring the primordial gravitational wave background in the presence of other stochastic signals

Standard methodologies for the extraction of the stochastic gravitational wave background (SGWB) from auto- or cross-correlation of interferometric signals often involve the use of a filter function.The standard optimal filter maximizes the signal-to-noise ratio (SNR) between the total SGWB and the noise.We derive expressions for the optimal filter and SNR in the presence of a target SGWB plus other unwanted components. We also generalize the methodology to the case of template-free reconstruction.The formalism allows to easily perform analyses and forecasts that marginalize over foreground signals, such as the typical ΩGW∝ f2/3 background arising from binary coalescence.We demonstrate the methodology with the LISA mission and discuss possible extensions and domains of application.

Characterization of extragalactic point-sources on E- and B-mode maps of the CMB polarization

Although interesting in themselves, extragalactic sources emitting in the microwave range (mainly radio-loud active galactic nuclei and dusty galaxies) are also considered a contaminant from the point of view of Cosmic Microwave Background (CMB) experiments. These sources appear as unresolved point-like objects in CMB measurements because of the limited resolution of CMB experiments. Amongst other issues, point-like sources are known to obstruct the reconstruction of the lensing potential, and can hinder the detection of the Primordial Gravitational Wave Background for low values of r. Therefore, extragalactic point-source detection and subtraction is a fundamental part of the component separation process necessary to achieve some of the science goals set for the next generation of CMB experiments. As a previous step to their removal, in this work we present a new filter based on steerable wavelets that allows the characterization of the emission of these extragalactic sources. Instead of the usual approach of working in polarization maps of the Stokes' Q and U parameters, the proposed filter operates on E- and B-mode polarization maps. In this way, it benefits from the lower intensity that, both, the CMB, and the galactic foreground emission, present in B-modes to improve its performance. To demonstrate its potential, we have applied the filter to simulations of the future PICO satellite, and we predict that, for the regions of fainter galactic foreground emission in the 30 GHz and 155 GHz bands of PICO, our filter will be able to characterize sources down to a minimum polarization intensity of, respectively, 125 pK and 14 pK. Adopting a Π=0.02 polarization degree, these values correspond to 169 mJy and 288 mJy intensities.

Simulations of a bubble wall interacting with an electroweak plasma

We perform large-scale real-time simulations of a bubble wall sweeping through an out-of-equilibrium plasma. The scenario we have in mind is the electroweak phase transition, which may be first order in extensions of the Standard Model, and produce such bubbles. The process may be responsible for baryogenesis and can generate a background of primordial cosmological gravitational waves. We study thermodynamic features of the plasma near the advancing wall, the generation of Chern-Simons number/Higgs winding number and consider the potential for CP-violation at the wall generating a baryon asymmetry. A number of technical details necessary for a proper numerical implementation are developed.