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DOE OSTI2021

Towards testing the theory of gravity with DESI: summary statistics, model predictions and future simulation requirements

Shortly after its discovery, General Relativity (GR) was applied to predict the behavior of our Universe on the largest scales, and later became the foundation of modern cosmology. Its validity has been verified on a range of scales and environments from the Solar system to merging black holes. However, experimental confirmations of GR on cosmological scales have so far lacked the accuracy one would hope for — its applications on those scales being largely based on extrapolation and its validity there sometimes questioned in the shadow of the discovery of the unexpected cosmic acceleration. Future astronomical instruments surveying the distribution and evolution of galaxies over substantial portions of the observable Universe, such as the Dark Energy Spectroscopic Instrument (DESI), will be able to measure the fingerprints of gravity and their statistical power will allow strong constraints on alternatives to GR. In this paper, based on a set of N-body simulations and mock galaxy catalogs, we study the predictions of a number of traditional and novel summary statistics beyond linear redshift distortions in two well-studied modified gravity models — chameleon f(R) gravity and a braneworld model — and the potential of testing these deviations from GR using DESI. These summary statistics employ a wide array of statistical properties of the galaxy and the underlying dark matter field, including two-point and higher-order statistics, environmental dependence, redshift space distortions and weak lensing. We find that they hold promising power for testing GR to unprecedented precision. The major future challenge is to make realistic, simulation-based mock galaxy catalogs for both GR and alternative models to fully exploit the statistic power of the DESI survey (by matching the volumes and galaxy number densities of the mocks to those in the real survey) and to better understand the impact of key systematic effects. Using these, we identify future simulation and analysis needs for gravity tests using DESI.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Misinterpreting modified gravity as dark energy: a quantitative study

Standard cosmological data analyses typically constrain simple phenomenological dark-energy parameters, for example the present-day value of the equation of state parameter, w 0 , and its variation with scale factor, w a . However, results from such an analysis cannot easily indicate the presence of modified gravity. Even if general relativity does not hold, experimental data could still be fit sufficiently well by a phenomenological w 0 w a CDM, unmodified-gravity model. Hence, it would be very useful to know if there are generic signatures of modified gravity in standard analyses. Here we present, for the first time to our knowledge, a quantitative mapping showing how modified gravity models look when (mis)interpreted within the standard unmodified-gravity analysis. Scanning through a broad space of modified-gravity (Horndeski) models, and assuming a near-future survey consisting of CMB, BAO, and SNIa observations, we report values of the best-fit set of cosmological parameters including (w 0 , w a ) that would be inferred if modified gravity were at work. We find that modified gravity models that can masquerade as standard gravity lead to very specific biases in standard-parameter spaces. Here, we also comment on implications for measurements of the amplitude of mass fluctuations described by the parameter S 8 .

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Dynamical instability of collapsed dark matter halos

A self-interacting dark matter halo can experience gravothermal collapse, resulting in a central core with an ultrahigh density. It can further contract and collapse into a black hole, a mechanism proposed to explain the origin of supermassive black holes. We study dynamical instability of the core in general relativity. Here we use a truncated Maxwell-Boltzmann distribution to model the dark matter distribution and solve the Tolman-Oppenheimer-Volkoff equation. For given model parameters, we obtain a series of equilibrium configurations and examine their dynamical instability based on considerations of total energy, binding energy, fractional binding energy, and adiabatic index. Our numerical results indicate that the core can collapse into a black hole when the fractional binding energy reaches 0.035 with a central gravitational redshift of 0.5. We further show for the instability to occur in the classical regime, the boundary temperature of the core should be at least 10% of the mass of dark matter particles; for a 10 9 M ⊙ seed black hole, the particle mass needs to be larger than a few keV. These results can be used to constrain different collapse models, in particular, those with dissipative dark matter interactions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searches

The Einstein field equations of general relativity constrain the local curvature at every point in spacetime, but say nothing about the global topology of the Universe. Cosmic microwave background anisotropies have proven to be the most powerful probe of non-trivial topology since, within ΛCDM, these anisotropies have well-characterized statistical properties, the signal is principally from a thin spherical shell centered on the observer (the last scattering surface), and space-based observations nearly cover the full sky. The most generic signature of cosmic topology in the microwave background is pairs of circles with matching temperature and polarization patterns. No such circle pairs have been seen above noise in the WMAP or Planck temperature data, implying that the shortest non-contractible loop around the Universe through our location is longer than 98.5% of the comoving diameter of the last scattering surface. We translate this generic constraint into limits on the parameters that characterize manifolds with each of the nine possible non-trivial orientable Euclidean topologies, and provide a code which computes these constraints. In all but the simplest cases, the shortest non-contractible loop in the space can avoid us, and be shorter than the diameter of the last scattering surface by a factor ranging from 2 to at least 6. Further, this result implies that a broader range of manifolds is observationally allowed than widely appreciated. Probing these manifolds will require more subtle statistical signatures than matched circles, such as off-diagonal correlations of harmonic coefficients.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

A test of gravity with Pulsar Timing Arrays

Abstract A successful measurement of the Stochastic Gravitational Wave Background (SGWB) in Pulsar Timing Arrays (PTAs) would open up a new window through which to test the predictions of General Relativity (GR). We consider how these measurements might reveal deviations from GR by studying the overlap reduction function — the quantity that in GR is approximated by the Hellings-Downs curve — in some sample modifications of gravity, focusing on the generic prediction of a modified dispersion relation for gravitational waves. We find a distinct signature of such modifications to GR — a shift in the minimum angle of the angular distribution — and demonstrate that this shift is quantitatively sensitive to any change in the phase velocity. In a given modification of gravity, this result can be used, in some regions of parameter space, to distinguish the effect of a modified dispersion relation from that due to the presence of extra polarization modes.

Astronomy & Astrophysics↗
DOE OSTI2025

DESI2024: Dark Energy Spectroscopic Instrument (DESI) survey, presentation of Year 1 results

The series of papers included in this special issue represent the first cosmological measurements from the Dark Energy Spectroscopic Instrument (DESI). These papers present the validation of the DESI clustering catalogs, the methodology for the cosmology measurements, and the full cosmology implications. These measurements were derived from a catalog of approximately 6.4 million extragalactic sources in a redshift range of 0.1 < z < 4.2. Owing to advances in fiber positioner technology and to a larger telescope, this sample was acquired in only one year of observation, yet is more than double the size of the galaxy and quasar samples from the first four phases of the Sloan Digital Sky Survey (SDSS) that spanned 20 years. With these new galaxy and quasar catalogs, the DESI collaboration completed percent-level constraints on the cosmic expansion history and the growth of structure. In turn, these new measurements provided a new platform from which to test the equation of state of dark energy, the summed mass of the three neutrino mass eigenstates, global curvature, and General Relativity. By surpassing the precision of the previous generation spectroscopic survey, the results in this special issue mark the transition in the field of cosmology to Stage-IV dark energy science.

baryon acoustic oscillations↗
DOE OSTI2025

DESI 2024 V: Full-Shape galaxy clustering from galaxies and quasars

We present the measurements and cosmological implications of the galaxy two-point clustering using over 4.7 million unique galaxy and quasar redshifts in the range 0.1 < z < 2.1 divided into six redshift bins over a ∼ 7,500 square degree footprint, from the first year of observations with the Dark Energy Spectroscopic Instrument (DESI Data Release 1). By fitting the full power spectrum, we extend previous DESI DR1 baryon acoustic oscillation (BAO) measurements to include redshift-space distortions and signals from the matter-radiation equality scale. For the first time, this Full-Shape analysis is blinded at the catalogue-level to avoid confirmation bias and the systematic errors are accounted for at the two-point clustering level, which automatically propagates them into any cosmological parameter. When analyzing the data in terms of compressed model-agnostic variables, we obtain a combined precision of 4.7% on the amplitude of the redshift space distortion (RSD) signal reaching a similar precision with just one year of DESI data than with twenty years of observation from the previous generation survey. We also analyze the data to directly constrain the cosmological parameters within the ΛCDM model using perturbation theory and combine this information with the reconstructed DESI DR1 galaxy BAO. Using a Big Bang Nucleosynthesis Gaussian prior on the baryon density parameter, ω b , and a weak Gaussian prior on the spectral index, n s , we constrain the matter density is Ω m = 0.296±0.010 and the Hubble constant H 0 = (68.63 ± 0.79)[km s -1 Mpc -1 ]. Additionally, we measure the amplitude of clustering σ 8 = 0.841±0.034. The DESI DR1 galaxy clustering results are in agreement with the ΛCDM model based on general relativity with parameters consistent with those from Planck. The cosmological interpretation of these results in combination with DESI DR1 Ly-α forest data and external datasets are presented in the companion paper [1].

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Modified gravity constraints from the full shape modeling of clustering measurements from DESI 2024

We present cosmological constraints on deviations from general relativity (GR) from the first-year of clustering observations from the Dark Energy Spectroscopic Instrument (DESI) in combination with other available datasets including the CMB data from Planck with CMB-lensing from Planck and ACT, BBN constraints on the physical baryon density, the galaxy weak lensing and clustering from DESY3 and supernova data from DESY5. We first consider the μ(a,k)–Σ(a,k) modified gravity (MG) parameterization (as well as η(a,k)) in a ΛCDM and a w 0 w a CDM cosmological backgrounds. Using a functional form for time-only evolution gives μ 0 = 0.11 +0.44 -0.54 from DESI(FS+BAO)+BBN and a wide prior on n s . Using DESI(FS+BAO)+CMB+DESY3+DESY5-SN, we obtain μ 0 = 0.05 ± 0.22 and Σ 0 = 0.008 ± 0.045 and similarly μ 0 = 0.02 +0.19 -0.24 and η 0 = 0.09 +0.36 -0.60 , in an ΛCDM background. In w 0 w a CDM we obtain μ 0 = -0.24 +0.32 -0.28 and Σ 0 = 0.006 ± 0.043, consistent with GR, and we still find a preference of the data for a dynamical dark energy with w 0 > -1 and w a < 0. Using functional dependencies in both time and scale gives μ 0 and Σ 0 with a same level of precision as above but other scale MG parameters remain hard to constrain. We then move to binned parameterizations in a ΛCDM background starting with two bins in redshift and obtain, μ 1 = 1.02 ± 0.13, μ 2 = 1.04 ± 0.11, Σ 1 = 1.021 ± 0.029 and Σ 2 = 1.022 +0.027 -0.023 , all consistent with the unity value of GR in the binning formalism. We then extend the analysis to combine two bins in redshift and two in scale giving 8 MG parameters that we find all consistent with GR. We note that we find here that the tension reported in previous studies about Σ 0 being inconsistent with GR when using Planck PR3 data goes away when we use the recent LoLLiPoP+HiLLiPoP likelihoods. As noted in previous studies, this seems to indicate that the tension is indeed related to the CMB lensing anomaly in PR3 which is also resolved when using the recent likelihoods. We then constrain the class of Horndeski theory in the effective field theory of dark energy approach. We consider both EFT-basis and α-basis in the analysis. Assuming a power law parameterization for the EFT function Ω, which controls non-minimal coupling, we obtain Ω 0 = 0.012 +0.001 -0.012 and s 0 = 0.996 +0.54 -0.20 from the combination of DESI(FS+BAO)+DESY5SN+CMB in a ΛCDM background, which are consistent with GR. Similar results are obtained when using the α-basis and assuming no-braiding (α B = 0) giving c M < 1.14 at 95% CL in a ΛCDM background, also in agreement with GR. However, we see a mild yet consistent indication for c B > 0 when α B is allowed to vary which will require further study to determine whether this is due to systematics or new physics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Joint analysis of 6dFGS and SDSS peculiar velocities for the growth rate of cosmic structure and tests of gravity

ABSTRACT Measurement of peculiar velocities by combining redshifts and distance indicators is a powerful way to measure the growth rate of a cosmic structure and test theories of gravity at low redshift. Here we constrain the growth rate of the structure by comparing observed Fundamental Plane peculiar velocities for 15 894 galaxies from the 6dF Galaxy Survey (6dFGS) and Sloan Digital Sky Survey (SDSS) with predicted velocities and densities from the 2M++ redshift survey. We measure the velocity scale parameter $\beta \equiv {\Omega _{\rm m}^\gamma }/b = 0.372^{+0.034}_{-0.050}$ and $0.314^{+0.031}_{-0.047}$ for 6dFGS and SDSS, respectively, where Ωm is the mass density parameter, γ is the growth index, and b is the bias parameter normalized to the characteristic luminosity of galaxies, L*. Combining 6dFGS and SDSS, we obtain β = 0.341 ± 0.024, implying that the amplitude of the product of the growth rate and the mass fluctuation amplitude is fσ8 = 0.338 ± 0.027 at an effective redshift z = 0.035. Adopting Ωm = 0.315 ± 0.007, as favoured by Planck and using γ = 6/11 for General Relativity and γ = 11/16 for DGP gravity, we get $S_8(z=0) = \sigma _8 \sqrt{\Omega _{\rm m}/0.3} =0.637 \pm 0.054$ and 0.741 ± 0.062 for GR and DGP, respectively. This measurement agrees with other low-redshift probes of large-scale structure but deviates by more than 3σ from the latest Planck CMB measurement. Our results favour values of the growth index γ > 6/11 or a Hubble constant H0 > 70 km s−1 Mpc−1 or a fluctuation amplitude σ8 < 0.8 or some combination of these. Imminent redshift surveys such as Taipan, DESI, WALLABY, and SKA1-MID will help to resolve this tension by measuring the growth rate of cosmic structure to 1 per cent in the redshift range 0 < z < 1.

Said, Khaled↗
DOE OSTI2021

Singling out modified gravity parameters and data sets reveals a dichotomy between Planck and lensing

ABSTRACT An important route to testing general relativity (GR) at cosmological scales is usually done by constraining modified gravity (MG) parameters added to the Einstein perturbed equations. Most studies have analysed so far constraints on pairs of MG parameters, but here, we explore constraints on one parameter at a time while fixing the other at its GR value. This allows us to analyse various models while benefiting from a stronger constraining power from the data. We also explore which specific data sets are in tension with GR. We find that models with (μ = 1, η) and (μ, η = 1) exhibit a 3.9σ and 3.8σ departure from GR when using Planck18 + Supernovae type Ia (SNe) + Baryon acoustic oscillation (BAO), while (μ, η) shows a tension of 3.4σ. We find no tension with GR for models with the MG parameter Σ fixed to its GR value. Using a Bayesian model selection analysis, we find that some one-parameter MG models are moderately favoured over ΛCDM when using all data set combinations except Planck cosmic microwave background lensing and dark energy survey data. Namely, Planck18 shows a moderate tension with GR that only increases when adding any combination of redshift space distortion, SNe, or BAO. However, adding lensing diminishes or removes these tensions, which can be attributed to the ability of lensing in constraining the MG parameter Σ. The two overall groups of data sets are found to have a dichotomy when performing consistency tests with GR, which may be due to systematic effects, lack of constraining power, or modelling. These findings warrant further investigation using more precise data from ongoing and future surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Gravitomagnetic vorticity generation in black hole accretion discs: a potential spatial constraint on plasma flow stability

We calculate the vorticity generation rate in the accretion disc near a slowly rotating black hole in the low-velocity, weak-field limit of general relativity. Specifically, we find that the frame-dragging effect due to the black hole’s rotation – manifested through the gravitomagnetic field – can generate vorticity in a moving plasma in the accretion disc. The mechanism remains operational as long as the accretion disc has non-negligible vertical height and is independent of the exact thermodynamical profile of the disc. The enstrophy density generation rate, as a measure of turbulence and dissipation, is presented, which indicates that the frame-dragging effect can disrupt the stability of the disc away from the z = 0 plane.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Testing horndeski gravity with S2 star orbit

ABSTRACT We have explored a completely new and alternative way to restrict the parameter space of Horndeski theory of gravity. Using its Newtonian limit, it is possible to test the theory at a regime where, given its complexity and the small magnitude of the expected effects, it is poorly probed. At Newtonian level, it gives rise to a generalized Yukawa-like Newtonian potential which we have tested using S2 star orbit data. Our model adds five parameters to the General Relativity model, and the analysis constrains two of them with unprecedented precision to these energy scales, while it only gives an exclusion region for the remaining parameters. We have shown the potential of weak-field tests to constrain Horndeski gravity opening, as a matter of fact, which is a new avenue that deserves to be further, and deeply, explored in the near future.

Della Monica, R. (ORCID:0000000238429297)↗
DOE OSTI2023

Magnetic frame-dragging correction to the electromagnetic solution of a compact neutron star

ABSTRACT Neutron stars are usually modelled as spherical, rotating perfect conductors with a predominant intrinsic dipolar magnetic field anchored to their stellar crust. Due to their compactness, General Relativity corrections must be accounted for in Maxwell’s equations, leading to modified interior and exterior electromagnetic solutions. We present analytical solutions for slowly rotating magnetized neutron stars, taking into account the magnetic frame-dragging correction. For typical compactness values, i.e. Rs ∼ 0.5 [R*], we show that the new terms lead to a per cent order correction in the magnetic field orientation and strength compared to the case, with no magnetic frame-dragging correction. Also, we obtain a self-consistent redistribution of the surface azimuthal current. We verify the validity of the derived solution through two-dimensional particle-in-cell simulations of an isolated neutron star. Defining the azimuthal electric and magnetic field amplitudes during the transient phase as observables, we prove that the magnetic frame-dragging correction reduces the transient wave amplitude, as expected from the analytical solution. We show that simulations are more accurate and stable, when we include all first-order terms. The increased accuracy at lower spatiotemporal resolutions translates into a reduction in simulation runtimes.

Torres, R. (ORCID:0000000291820228)↗
DOE OSTI2023

The r -modes of slowly rotating, stratified neutron stars

ABSTRACT The only r-modes that exist in a globally barotropic, rotating, Newtonian star are the fundamental l = |m| solutions, where l and m are the indices of the spherical harmonic $Y_l^m$ that describe the mode’s angular dependence. This is in stark contrast to a stellar model that is non-barotropic throughout its interior, which hosts all the l ≥ |m| perturbations including radial overtones. In reality, neutron stars are stratified with locally barotropic regions. Therefore, we explore how stratification alters a star’s ability to support r-modes. We consider the globally stratified case and examine the behaviour of the modes as the star gets close to barotropicity. In this limit, we find that all but the fundamental l = |m| perturbations change character and become generic inertial modes. Restricting the analysis to l = |m| perturbations, we develop the r-mode equations in order to consider stellar models that exhibit local barotropicity. Our results for such models show that the r-mode overtones diverge and join the inertial modes. In order to see which r-modes persist and retain their character in realistic neutron stars, these calculations will need to be brought into full general relativity.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Exploring modified gravity: constraints on the μ and Σ parametrization with WMAP , ACT, and SPT

ABSTRACT The cosmic acceleration problem remains one of the most significant challenges in cosmology. One of the proposed solutions to this problem is the modification of gravity on large scales. In this paper, we explore the well-known μ–Σ parametrization scenarios and confront them with observational data, including the cosmic microwave background (CMB) radiation from the Wilkinson Microwave Anisotropy Probe (WMAP), Atacama Cosmology Telescope (ACT), and South Pole Telescope (SPT), as well as large-scale structure data from the Sloan Digital Sky Survey (SDSS; baryon acoustic oscillation + redshift-space distortion) and Pantheon supernova (SN) catalogue. We employ a Bayesian framework to constrain the model parameters and discuss the implications of our results on the viability of modified gravity theories. Our analysis reveals the strengths and limitations of the μ–Σ parametrization and provides valuable insights into the nature of gravity on cosmological scales. From the joint analysis of the ACT + WMAP + SDSS + SN, we find μ0 − 1 = 0.02 ± 0.19 and Σ0 − 1 = 0.021 ± 0.068 at 68 per cent confidence level (CL). In light of the SPT + WMAP + SDSS + SN, we find μ0 − 1 = 0.07 ± 0.18 and $\Sigma _0 -1 = -0.009^{+0.078}_{-0.11}$ at 68 per cent CL. In all the analyses carried out, we do not find any deviations from the theory of general relativity. Our results represent an observational update on the well-known μ–Σ parametrization in view of current CMB data, independent of and competitive with the constraints obtained with the Planck data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Reducing model error using optimized galaxy selection: weak lensing cluster mass estimation

Galaxy clusters are one of the most powerful probes to study extensions of General Relativity and the Standard Cosmological Model. Upcoming surveys like the Vera Rubin Observatory’s Legacy Survey of Space and Time are expected to revolutionise the field, by enabling the analysis of cluster samples of unprecedented size and quality. To reach this era of high-precision cluster cosmology, the mitigation of sources of systematic error is crucial. A particularly important challenge is bias in cluster mass measurements induced by the mismodelling of photometric redshift estimates of source galaxies. This work proposes a method to optimise the source sample selection in cluster weak lensing analyses drawn from wide-field survey lensing catalogs to reduce the bias on reconstructed cluster masses. We use a combinatorial optimisation scheme and methods from variational inference to select galaxies in latent space to produce a probabilistic galaxy source sample catalog for highly accurate cluster mass estimation. We show that our method reduces the critical surface mass density Σ crit relative modelling bias on the 60-70% level, while maintaining up to 90% of galaxies. We highlight that our methodology has applications beyond cluster mass estimation as an approach to jointly combine galaxy selection and model inference under sources of systematics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Probing cosmic velocities with the pairwise kinematic Sunyaev-Zel’dovich signal in DESI Bright Galaxy Sample DR1 and ACT DR6

We present a measurement of the pairwise kinematic Sunyaev-Zel’dovich (kSZ) signal using the Dark Energy Spectroscopic Instrument (DESI) Bright Galaxy Sample (BGS) Data Release 1 (DR1) galaxy sample overlapping with the Atacama Cosmology Telescope (ACT) CMB temperature map. Our analysis makes use of 1.6 million galaxies with stellar masses log⁡ 𝑀 ⋆ /𝑀 ⊙ >10, and we explore measurements across a range of aperture sizes (2.1′ <𝜃 ap <3.5′) and stellar mass selections. This statistic directly probes the velocity field of the large-scale structure, a unique observable of cosmic dynamics and modified gravity. In particular, at low redshifts, this quantity is especially interesting, as deviations from General Relativity are expected to be largest. Notably, our result represents the highest-significance low-redshift (𝑧 ∼ 0.3) detection of the kSZ pairwise effect yet. In our most optimal configuration (𝜃 ap =3.3′, log⁡ 𝑀 ⋆ >11), we achieve a 5⁢𝜎 detection. Assuming that an estimate of the optical depth and galaxy bias of the sample exists via e.g., external observables, this measurement constrains the fundamental cosmological combination 𝐻 0 ⁡𝑓⁡𝜎$^2_8$. A key challenge is the degeneracy with the galaxy optical depth. We address this by combining CMB lensing, which allows us to infer the halo mass and galaxy population properties, with hydrodynamical simulation estimates of the mean optical depth, $\bar{𝜏}$ . We stress that this is a proof-of-concept analysis; with BGS DR2 data we expect to improve the statistical precision by roughly a factor of two, paving the way toward robust tests of modified gravity with kSZ-informed velocity-field measurements at low redshift.

Hadzhiyska, Boryana [Institute of Astronomy; Kavli↗
DOE OSTI2020

Impact of transforming to conformal Fermi coordinates on quasisingle field non-Gaussianity

In general relativity, predictions for observable quantities can be expressed in a coordinate independent way. Nonetheless it may be inconvenient to do so. Using a particular frame may be the easiest way to connect theoretical predictions to measurable quantities. For the cosmological curvature bispectrum such frame is described by the conformal Fermi coordinates. In single field inflation it was shown that going to this frame cancels the squeezed limit of the density perturbation bispectrum calculated in global coordinates. Furthermore, we explore this issue in quasisingle field inflation when the curvaton mass and the curvaton-inflaton mixing are small. In this case, the contribution to the bispectrum from the coordinate transformation to conformal Fermi coordinates is of the same order as that from the inflaton-curvaton interaction term but does not cancel it.

79 ASTRONOMY AND ASTROPHYSICS↗