Amplitude Of Primordial Power Spectrum Research Articles

Probing scalar induced gravitational waves with PTA and LISA: the importance of third order correction

We revisit the calculation of third order scalar induced gravitational waves (SIGWs) and extend it from a monochromatic primordial power spectrum to a more general log-normal one. We investigate the impact of third order SIGWs on signal-to-noise ratio (SNR) of Laser Interferometer Space Antenna (LISA) and pulsar timing array (PTA) observations, and find that third order SIGWs significantly contribute to the total energy density spectrum of gravitational waves (GW) in high-frequency region. For a primordial power spectrum amplitude of Aζ = 10-2 ∼ 10-1, the effects of third order SIGWs lead to a 40% to 400% increase in the SNR for LISA. Additionally, our PTA data analysis reveals that third order SIGWs diminish both the amplitude Aζ and the peak frequency f * of the primordial power spectrum.

Primordial black holes and gravitational waves in hybrid inflation with chaotic potentials

We study the formation of primordial black hole (PBH) dark matter and the generation of scalar induced secondary gravitational waves (SIGWs) in a non-supersymmetric model of hybrid inflation with chaotic (polynomial-like) potential, including one-loop radiative corrections. A radiatively corrected version of these models is entirely consistent with Planck's data. By adding non-canonical kinetic energy term in the lagrangian, the inflation experiences a period of ultra-slow-roll, and the amplitude of primordial power spectrum is enhanced to O(10−2). The enhanced power spectra of primordial curvature perturbations can have both sharp and broad peaks. A wide mass range of PBHs is realized in our model with the frequencies of scalar induced gravitational waves ranged from nHz to kHz. We present several benchmark points where the PBH mass generated during inflation is around (1−100)M⊙, (10−9−10−7)M⊙ and (10−16−10−11)M⊙. The PBHs can make up most of the dark matter with masses around (10−16−10−11)M⊙ and (1−100)M⊙, and their associated SIGWs can be probed by the upcoming ground and space-based gravitational wave (GW) observatories. The evidence of stochastic process recently reported by NANOGrav may be interpreted as SIGWs associated with the formation of PBHs. These SIGWs may also be tested by future interferometer-type GW observations of SKA, DECIGO, LISA, BBO, TaiJi, TianQin, CE and ET.

Primordial black holes and secondary gravitational waves from string inspired general no-scale supergravity

The formation of primordial black hole (PBH) dark matter and the generation of scalar induced secondary gravitational waves (SIGWs) have been studied in the generic no-scale supergravity inflationary models. By adding an exponential term to the K\"ahler potential, the inflaton experiences a period of ultraslow-roll and the amplitude of primordial power spectrum at small scales is enhanced to $\mathcal{O}({10}^{\ensuremath{-}2})$. The enhanced power spectra of primordial curvature perturbations can have both sharp and broad peaks. A wide mass range of PBHs can be produced in our model, and the frequencies of the accompanied SIGWs are ranged form nanohertz to kilohertz. We show four benchmark points where the generated PBH masses are around $\mathcal{O}({10}^{\ensuremath{-}16}\text{ }\text{ }{M}_{\ensuremath{\bigodot}})$, $\mathcal{O}({10}^{\ensuremath{-}12}\text{ }\text{ }{M}_{\ensuremath{\bigodot}})$, $\mathcal{O}({10}^{\ensuremath{-}2}\text{ }\text{ }{M}_{\ensuremath{\bigodot}})$ and $\mathcal{O}({10}^{2}\text{ }\text{ }{M}_{\ensuremath{\bigodot}})$. The PBHs with masses around $\mathcal{O}({10}^{\ensuremath{-}16}\text{ }\text{ }{M}_{\ensuremath{\bigodot}})$ and $\mathcal{O}({10}^{\ensuremath{-}12}\text{ }\text{ }{M}_{\ensuremath{\bigodot}})$ can make up almost all the dark matter, and the accompanied SIGWs can be probed by the upcoming space-based gravitational wave observatory. Also, the SIGWs accompanied with the formation of stellar mass PBHs can be used to interpret the stochastic GW background in the nanohertz band, detected by the North American Nanohertz Observatory for Gravitational Waves, and can be tested by future interferometric gravitational wave observatory.

Constraining the Neutrino Mass with the Drifting Coefficient of the Field Cluster Mass Function

Abstract A new diagnostics to break the degeneracy between the total neutrino mass (M ν ) and the primordial power spectrum amplitude (σ 8) using the drifting coefficient of the field cluster mass function is presented. Analyzing the data from the Cosmological Massive Neutrino Simulations, we first determine the numerical mass functions of the field clusters at various redshifts. Then, we compare the numerical results with the analytical model characterized by a single parameter called the drifting coefficient, which measures the drifts of the collapse density threshold, δ c, from the Einstein–de Sitter spherical value, δ sc, at a given mass scale. It is found that the analytic model for the field cluster mass function is found to work excellently even in the presence of massive neutrinos, and that its drifting coefficient evolves differently in the cosmologies with different values of M ν . At low redshifts (z ≲ 0.3) the more massive neutrinos drift δ c further from δ sc, while the opposite trend is found at higher redshifts (z ≳ 0.3). Speculating that this distinct redshift-dependent effect of massive neutrinos on the drifting coefficient of the field cluster mass function might help break the σ 8–M ν degeneracy, we also show that the sensitivity of this new diagnostics to M ν is high enough to discriminate the case of M ν = 0.1 eV from that of massless neutrinos.

Precision modelling of the matter power spectrum in a Planck-like Universe

We use a suite of high-resolution $N$-body simulations and state-of-the-art perturbation theory to improve the code halofit, which predicts the nonlinear matter power spectrum. We restrict attention to parameters in the vicinity of the Planck Collaboration's best fit. On large-scales ($k\lesssim 0.07 h/{\rm Mpc}$), our model evaluates the 2-loop calculation from the Multi-point Propagator Theory of Bernardeau et al.(2012). On smaller scales ($k \gtrsim 0.7 h/{\rm Mpc}$), we transition to a smoothing-spline-fit model, that characterises the differences between the Takahashi et al. (2012) recalibration of halofit2012 and our simulations. We use an additional suite of simulations to explore the response of the power spectrum to variations in the cosmological parameters. In particular, we examine: the time evolution of the dark energy equation of state ($w_0$, $w_a$); the matter density $\Omega_m$; the physical densities of CDM and baryons $(\omega_c,\omega_b)$; and the primordial power spectrum amplitude $A_s$, spectral index $n_s$, and its running $\alpha$. We construct correction functions, which improve halofit's dependence on cosmological parameters. Our newly calibrated model reproduces all of our data with $\lesssim1\%$ precision. Including various systematic errors, such as choice of $N$-body code, resolution, and through inspection of the scaled second order derivatives, we estimate the accuracy to be $\lesssim3\%$ over the hyper-cube: $w_0\in\{-1.05,-0.95\}$, $w_a\in\{-0.4,0.4\}$, $\Omega_{\rm m,0}\in\{0.21,0.4\}$, $\omega_{\rm c}\in\{0.1,0.13\}$, $\omega_{\rm b}\in\{2.0,2.4\}$, $n_{\rm s}\in\{0.85,1.05\}$, $A_s\in\{1.72\times 10^{-9},2.58\times 10^{-9}\}$, $\alpha\in\{-0.2,0.2\}$ up to $k=9.0 h/{\rm Mpc}$ and out to $z=3$. Outside of this range the model reverts to halofit2012.

MassiveNuS: cosmological massive neutrino simulations

The non-zero mass of neutrinos suppresses the growth of cosmic structure on small scales. Since the level of suppression depends on the sum of the masses of the three active neutrino species, the evolution of large-scale structure is a promising tool to constrain the total mass of neutrinos and possibly shed light on the mass hierarchy. In this work, we investigate these effects via a large suite of N-body simulations that include massive neutrinos using an analytic linear-response approximation: the Cosmological Massive Neutrino Simulations (MassiveNuS). The simulations include the effects of radiation on the background expansion, as well as the clustering of neutrinos in response to the nonlinear dark matter evolution. We allow three cosmological parameters to vary: the neutrino mass sum Mν in the range of 0–0.6 eV, the total matter density Ωm, and the primordial power spectrum amplitude As. The rms density fluctuation in spheres of 8 comoving Mpc/h (σ8) is a derived parameter as a result. Our data products include N-body snapshots, halo catalogues, merger trees, ray-traced galaxy lensing convergence maps for four source redshift planes between zs=1–2.5, and ray-traced cosmic microwave background lensing convergence maps. We describe the simulation procedures and code validation in this paper. The data are publicly available at http://columbialensing.org.

An analytical approach to the CMB polarization in a spatially closed background

Abstract The scalar mode polarization of the cosmic microwave background is derived in a spatially closed universe from the Boltzmann equation using the line of sight integral method. The EE and TE multipole coefficients have been extracted analytically by considering some tolerable approximations such as considering the evolution of perturbation hydrodynamically and sudden transition from opacity to transparency at the time of last scattering. As the major advantage of analytic expressions, C E E , l S and C T E , l S explicitly show the dependencies on baryon density Ω B , matter density Ω M , curvature Ω K , primordial spectral index n s , primordial power spectrum amplitude A s , Optical depth τ r e i o n , recombination width σ t and recombination time t L . Using a realistic set of cosmological parameters taken from a fit to data from Planck, the closed universe EE and TE power spectrums in the scalar mode are compared with numerical results from the CAMB code and also latest observational data. The analytic results agree with the numerical ones on the big and moderate scales. The peak positions are in good agreement with the numerical result on these scales while the peak heights agree with that to within 20 % due to the approximations have been considered for these derivations. Also, several interesting properties of CMB polarization are revealed by the analytic spectra.

Response approach to the squeezed-limit bispectrum: application to the correlation of quasar and Lyman-α forest power spectrum

The squeezed-limit bispectrum, which is generated by nonlinear gravitational evolution as well as inflationary physics, measures the correlation of three wavenumbers, in the configuration where one wavenumber is much smaller than the other two. Since the squeezed-limit bispectrum encodes the impact of a large-scale fluctuation on the small-scale power spectrum, it can be understood as how the small-scale power spectrum ``responds'' to the large-scale fluctuation. Viewed in this way, the squeezed-limit bispectrum can be calculated using the response approach even in the cases which do not submit to perturbative treatment. To illustrate this point, we apply this approach to the cross-correlation between the large-scale quasar density field and small-scale Lyman-α forest flux power spectrum. In particular, using separate universe simulations which implement changes in the large-scale density, velocity gradient, and primordial power spectrum amplitude, we measure how the Lyman-α forest flux power spectrum responds to the local, long-wavelength quasar overdensity, and equivalently their squeezed-limit bispectrum. We perform a Fisher forecast for the ability of future experiments to constrain local non-Gaussianity using the bispectrum of quasars and the Lyman-α forest. Combining with quasar and Lyman-α forest power spectra to constrain the biases, we find that for DESI the expected 1−σ constraint is err[fNL]∼60. Ability for DESI to measure fNL through this channel is limited primarily by the aliasing and instrumental noise of the Lyman-α forest flux power spectrum. The combination of response approach and separate universe simulations provides a novel technique to explore the constraints from the squeezed-limit bispectrum between different observables.

What is the optimal way to measure the galaxy power spectrum?

Measurements of the galaxy power spectrum contain a wealth of information about the Universe. Its optimal extraction is vital if we are to truly understand the micro-physical nature of dark matter and dark energy. In Smith & Marian (2015) we generalized the power spectrum methodology of Feldman et al. (1994) to take into account the key tenets of galaxy formation: galaxies form and reside exclusively in dark matter haloes; a given dark matter halo may host galaxies of various luminosities; galaxies inherit the large-scale bias associated with their host halo. In this paradigm we derived the optimal weighting and reconstruction scheme for maximizing the signal-to-noise on a given band power estimate. For a future all-sky flux-limited galaxy redshift survey of depth b_J ~22, we now demonstrate that the optimal weighting scheme does indeed provide improved S/N at the level of ~20% when compared to Feldman et al. (1994) and ~60% relative to Percival et al. (2003), for scales of order k~0.5 Mpc/h. Using a Fisher matrix approach, we show that the cosmological information yield is also increased relative to these alternate methods -- especially the primordial power spectrum amplitude and dark energy equation of state.

Constraints on the primordial power spectrum of small scales using the neutrino signals from the dark matter decay

Many inflation theories predict that the primordial power spectrum is scale invariant. The amplitude of the power spectrum can be constrained by different observations such as the cosmic microwave background (CMB), Lyman-α, large-scale structures and primordial black holes (PBHs). Although the constraints from the CMB are robust, the corresponding scales are very large (10-4 < k < 1 Mpc -1). For small scales (k > 1 Mpc -1), the research on the PBHs provides much weaker limits. Recently, ultracompact dark matter minihalos (UCMHs) was proposed and it was found that they could be used to constraint the small-scale primordial power spectrum. The limits obtained by the research on the UCMHs are much better than that of PBHs. Most of previous works focus on the dark matter annihilation within the UCMHs, but if the dark matter particles do not annihilate the decay is another important issue. In previous work [Y.-P. Yang, G.-L. Yang and H.-S. Zong, Europhys. Lett.101, 69001 (2013)], we investigated the gamma-ray flux from the UCMHs due to the dark matter decay. In addition to these flux, the neutrinos are usually produced going with the gamma-ray photons especially for the lepton channels. In this work, we studied the neutrino flux from the UCMHs due to the dark matter decay. Finally, we got the constraints on the amplitude of primordial power spectrum of small scales.