Primordial Power Spectrum Research Articles

Non-linear reconstruction of features in the primordial power spectrum from large-scale structure

ABSTRACT Potential features in the primordial power spectrum have been searched for in galaxy surveys in recent years since these features can assist in understanding the nature of inflation. The null detection to date suggests that any such features should be fairly weak, and next-generation galaxy surveys, with their unprecedented sizes and precisions, are in a position to place stronger constraints than before. However, even if such primordial features once existed in the early Universe, they would have been significantly damped in the non-linear regime at low redshift due to structure formation, which makes them difficult to be directly detected in real observations. A potential way to tackle this challenge for probing the features is to undo the cosmological evolution, i.e. using reconstruction to obtain an approximate linear density field. By employing a set of N-body simulations, here we show that a recently proposed non-linear reconstruction algorithm can effectively retrieve damped oscillatory features from halo catalogues and improve the accuracy of the measurement of feature parameters (assuming that such primordial features do exist). We do a Fisher analysis to forecast how non-linear reconstruction affects the constraining power, and find that it can lead to significantly more robust constraints on the feature amplitude for a DESI-like survey. Comparing non-linear reconstruction with other ways of improving constraints, such as increasing the survey volume and range of scales, this shows that it is possible to achieve what the latter do, but at a lower cost.

Rescuing palindromic universes with improved recombination modeling

We explore the linearly quantized primordial power spectra associated with palindromic universes. Extending the results of Lasenby et al. [Phys. Rev. D 105, 083514 (2022)] and Bartlett et al. [Phys. Rev. D 105, 083515 (2022)], we improve the modeling of recombination and include higher orders in the photonic Boltzmann hierarchy. In so doing, we find that the predicted power spectra become largely consistent with observational data. The improved recombination modeling involves developing further techniques for dealing with the future conformal boundary, by integrating the associated perturbation equations both forwards and backwards in conformal time. The resulting wave vector quantization gives a lowest allowed wave number ${k}_{0}=9.93\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$ and linear spacing $\mathrm{\ensuremath{\Delta}}k=1.63\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$, providing fits consistent with observational data equivalent in quality to the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model.

Non-Gaussianity in inflationary scenarios for primordial black holes

Working in an idealised framework in which a series of phases of evolution defined by the second slow-roll parameter η are matched together, we calculate the reduced bispectrum, f NL, for models of inflation with a large peak in their primordial power spectra. We find f NL is typically approximately constant over scales at which the peak is located, and provide an analytic approximation for this value. This allows us to identify the conditions under which f NL is large enough to have a significant impact on the resulting production of primordial black holes (PBHs) and scalar induced gravitational waves (SIGWs). Together with analytic formulae for the gradient of the rise and fall in the power spectrum, this provides a toolkit for designing or quickly analysing inflationary models that produce PBHs and SIGWs.

Bottom-up reconstruction of viable GW170817 compatible Einstein–Gauss–Bonnet theories

In this work we shall use a bottom-up approach for obtaining viable inflationary Einstein–Gauss–Bonnet models which are also compatible with the GW170817 event. Specifically, we shall use a recently developed theoretical framework in which we shall specify only the tensor-to-scalar ratio, in terms of the e-foldings number. Starting from the tensor-to-scalar ratio, we shall reconstruct from it the Einstein–Gauss–Bonnet theory which can yield such a tensor-to-scalar ratio, finding the scalar potential and the Gauss–Bonnet coupling scalar function as functions of the e-foldings number. Accordingly, the calculation of the spectral index of the primordial scalar perturbations, and of the tensor spectral index easily is greatly simplified and these observational indices can easily be found. After presenting the general formalism for the bottom-up reconstruction, we exemplify our findings by presenting several Einstein–Gauss–Bonnet models of interest which yield a viable inflationary phenomenology. These models have also an interesting common characteristic, which is a blue tilted tensor spectral index. We also investigate the predicted energy spectrum of the primordial gravitational waves for these Einstein–Gauss–Bonnet models, and as we show, all the models yield a detectable primordial wave energy power spectrum.

Peaks and primordial black holes: the effect of non-Gaussianity

In light of recent developments in the field, we re-evaluate the effect of local-type non-Gaussianity on the primordial black hole (PBH) abundance (and consequently, upon constraints on the primordial power spectrum arising from PBHs). We apply peaks theory to the full, non-linear compaction, finding that, whilst the effect of non-Gaussianity is qualitatively similar to previous findings, the effect is much less significant. It is found the non-Gaussianity parameters f NL local and g NL local typically need to be approximately 1 or 2 orders of magntiude larger respectively to have a similar to that previously found. The effect will be to weaken the dependance of PBH constraints on the primordial power spectrum on the non-Gaussianity parameters, as well as to dramatically weaken constraints on the non-Gaussianity parameters (and/or PBH abundance) arising from the non-observation of dark matter isocurvature modes. We also consider the correlation between the curvature perturbation ζ and the compaction C, finding that, whilst PBHs may form at rare peaks in C these do not necessarily correspond to rare peaks in ζ — casting some doubt on many of the existing calculations of the PBH abundance.

The third order scalar induced gravitational waves

Since the gravitational waves were detected by LIGO and Virgo, it has been promising that lots of information about the primordial Universe could be learned by further observations on stochastic gravitational waves background. The studies on gravitational waves induced by primordial curvature perturbations are of great interest. The aim of this paper is to investigate the third order induced gravitational waves. Based on the theory of cosmological perturbations, the first order scalar induces the second order scalar, vector and tensor perturbations. At the next iteration, the first order scalar, the second order scalar, vector and tensor perturbations all induce the third order tensor perturbations. We present the two point function 〈h λ,(3) h λ',(3)〉 and corresponding energy density spectrum of the third order gravitational waves for a monochromatic primordial power spectrum. The shape of the energy density spectrum of the third order gravitational waves is different from that of the second order scalar induced gravitational waves. And it is found that the third order gravitational waves sourced by the second order scalar perturbations dominate the two point function 〈h λ,(3) h λ',(3)〉 and corresponding energy density spectrum of third order scalar induced gravitational waves.

Anisotropy of phase transition gravitational wave and its implication for primordial seeds of the Universe

We quantitatively study how the primordial density fluctuations are imprinted on the anisotropy of the phase transition gravitational wave (PTGW). Generated long before recombination and free from Silk damping, the anisotropic PTGW might reveal the density perturbation seeded from inflation or alternatives. We find new behaviors of the PTGW anisotropy power spectrum. The PTGW anisotropy is stronger than the anisotropy of the cosmic microwave background temperature at all scales, and the high-$\ell$ multiples are enhanced about 1 order due to the early integrated Sachs-Wolfe effect. Furthermore, differences in primordial power spectra at small scales manifest themselves more significantly on the angular power spectrum of PTGW anisotropy compared to that of the cosmic microwave background. These properties might provide a novel clue to understanding the primordial density perturbation of our early Universe and thereby complete our understanding of inflation theory. Taking nanohertz PTGW from dark matter models as a typical example, we obtain amplitudes of PTGW anisotropy which are about 4 or 3 orders weaker than the isotropic PTGW energy spectra.

Improved cosmological fits with quantized primordial power spectra

We observationally examine cosmological models based on primordial power spectra with quantized wavevectors. Introducing a linearly quantized power spectrum with $k_0=3.225\times10^{-4}\mathrm{Mpc}^{-1}$ and spacing $\Delta k = 2.257 \times 10^{-4} \mathrm{Mpc}^{-1}$ provides a better fit to the Planck 2018 observations than the concordance baseline, with $\Delta \chi^2 = -8.55$. Extending the results of Lasenby et al [1], we show that the requirement for perturbations to remain finite beyond the future conformal boundary in a universe containing dark matter and a cosmological constant results in a linearly quantized primordial power spectrum. It is found that the infrared cutoffs for this future conformal boundary quantized cosmology do not provide cosmic microwave background power spectra compatible with observations, but future theories may predict more observationally consistent quantized spectra.

Probing the primordial Universe with 21 cm line from cosmic dawn/epoch of reionization

Abstract In the most distant reaches of the Universe, the 21 cm hyperfine transition in neutral hydrogen provides one of the only available tracers of large-scale structure. A number of instruments have been working or are planned to measure the 21 cm line signals, and in particular, the Experiment to Detect the Global EoR Signature (EDGES) has recently reported the first detection of an absorption signal, which corresponds to the 21 cm line global signal at the epoch of reionization (EoR). The future large radio telescope, the Square Kilometre Array (SKA) will be able to deliver the high-precision measurement of the 21 cm line emission/absorption signals. In this paper, we review the current status for the 21 cm line global and fluctuation signals from EoR to the dark ages, and then summarize the recent studies of how we probe the primordial Universe particularly motivated by the recent EDGES result and future observations by SKA. We focus on two applications for constraining cosmology with the EDGES result: constraints on the primordial magnetic fields and those on the primordial power spectrum. We also discuss the potential of future SKA for probing the inflationary Universe, by discussing expected constraints on the primordial power spectrum, its adiabaticity, and primordial non-Gaussianities from future observations of 21 cm fluctuations.

Missing large-angle correlations versus even-odd point-parity imbalance in the cosmic microwave background

Context.The existence of a maximum correlation angle (θmax ≳ 60°) in the two-point angular temperature correlations of cosmic microwave background (CMB) radiation, measured by WMAP andPlanck, stands in sharp contrast to the prediction of standard inflationary cosmology, in which the correlations should extend across the full sky (i.e., 180°). The introduction of a hard lower cutoff (kmin) in the primordial power spectrum, however, leads naturally to the existence ofθmax. Among other cosmological anomalies detected in these data, an apparent dominance of odd-over-even parity multipoles has been seen in the angular power spectrum of the CMB. This feature, however, may simply be due to observational contamination in certain regions of the sky.Aims.In attempting to provide a more detailed assessment of whether this odd-over-even asymmetry is intrinsic to the CMB, we therefore proceed in this paper, first, to examine whether this odd-even parity imbalance also manifests itself in the angular correlation function and, second, to examine in detail the interplay between the presence ofθmaxand this observed anomaly.Methods.We employed several parity statistics and recalculated the angular correlation function for different values of the cutoffkminin order to optimize the fit to the differentPlanck2018 data.Results.We find a phenomenological connection between these features in the data, concluding that both must be considered together in order to optimize the theoretical fit to thePlanck2018 data.Conclusions.This outcome is independent of whether the parity imbalance is intrinsic to the CMB, but if it is, the odd-over-even asymmetry would clearly point to the emergence of new physics.

Cosmological implications of generalized holonomy corrections

Most of the phenomenology of loop quantum gravity in the cosmological sector is based on the so-called holonomy correction to the Hamiltonian constraint. It straightforwardly modifies the Friedmann equations. In this work, we investigate the influence of corrections generalizing the one usually used in loop quantum cosmology. We find that a long enough inflation phase can be generated by purely quantum geometrical effects but we also underline the limitations of this scenario. In addition, we study the effects of generalized holonomy corrections on an inflationary phase generated by a massive scalar field. At the level of perturbations, we investigate in details the consequences on the primordial scalar power spectrum.

The primordial matter power spectrum on sub-galactic scales

ABSTRACTThe primordial matter power spectrum quantifies fluctuations in the distribution of dark matter immediately following inflation. Over cosmic time, overdense regions of the primordial density field grow and collapse into dark matter haloes, whose abundance and density profiles retain memory of the initial conditions. By analysing the image magnifications in 11 strongly lensed and quadruply imaged quasars, we infer the abundance and concentrations of low-mass haloes, and cast the measurement in terms of the amplitude of the primordial matter power spectrum. We anchor the power spectrum on large scales, isolating the effect of small-scale deviations from the Lambda cold dark matter (ΛCDM) prediction. Assuming an analytic model for the power spectrum and accounting for several sources of potential systematic uncertainty, including three different models for the halo mass function, we obtain correlated inferences of $\log _{10}\left(P / P_{\Lambda \rm {CDM}}\right)$, the power spectrum amplitude relative to the predictions of the concordance cosmological model, of $0.0_{-0.4}^{+0.5}$, $0.1_{-0.6}^{+0.7}$, and $0.2_{-0.9}^{+1.0}$ at k = 10, 25, and 50 $\rm {Mpc^{-1}}$ at $68 {{\ \rm per\ cent}}$ confidence, consistent with CDM and single-field slow-roll inflation.

Optimising inflationary features the Bayesian way

Modern cosmological data demand modern data analysis techniques. We introduce BayOp, a new likelihood sampling and maximisation method which is based on the Bayesian Optimisation algorithm and learns a function instead of randomly sampling from it. We apply BayOp to analyse Planck data for traces of inflationary features models with global periodic modulations of the primordial power spectrum. While we do not find any new evidence for features, we demonstrate that BayOp provides an extremely efficient way of sampling likelihoods over low-to-moderate-dimensional parameter spaces, even for very complex likelihood landscapes.

Inflation and primordial fluctuations inF(T)gravity’s rainbow

We study slow-roll inflation and the generation of primordial fluctuations in $F(T)$ gravity's rainbow. We obtain the second order action for scalar and tensor perturbations and then calculate the primordial power spectrum for them. Thus, after calculating the inflationary observables up to first order in slow-roll approximation, namely the scalar spectral index ${n}_{s}$ and the tensor-to scalar ratio $r$, we confront the predictions of the model with the current PLANCK and BICEP/Keck data.

Model-independent Estimators for the Statistical Anisotropy of the Cosmic Microwave Background

We construct estimators for testing the statistical anisotropy of the cosmic microwave background arising due to a quadrupolescale-independent anisotropy in the primordial power spectrum. The estimators do not require the knowledge of basic cosmological parameters. We determine the sensitivity of the constructed estimators to the magnitude of the statistical anisotropy and perform test simulations that confirm our theoretical estimates.

Amplification of primordial perturbations from the rise or fall of the inflaton

The next generation of cosmic microwave background, gravitational wave, and large scale structure, experiments will provide an unprecedented opportunity to probe the primordial power spectrum on small scales. An exciting possibility for what lurks on small scales is a sharp rise in the primordial power spectrum: this can lead to the formation of primordial black holes, providing a dark matter candidate or the black holes observed by the LIGO-Virgo collaboration. In this work we develop a mechanism for the amplification of the small-scale primordial power spectrum, in the context of single-field inflation with a step-like feature in the inflaton potential.Specifically, we consider both the upward and the downward step in the potential. We also discuss the possibility of the strong coupling between perturbations because the rapid changes of the potential derivatives with the time-dependent field value, caused by the step-like feature, could make the coupling stronger. As a result, we find that the perturbations can remain weakly coupled yet sufficiently enhanced if the step realizes the rapid changes of the potential derivatives in some fraction of an e-fold, \U0001d4aa(\U0001d4abℛ 1/2) ≲ ΔN < 1, where \U0001d4abℛ is the power spectrum of the curvature perturbation at that time.We also discuss the PBH formation rate from the inflaton trapping at the local minimum, which can occur in the potential with an upward step.

Quasi-matter Bounce Cosmology in Light of Planck

Abstract We study quasi-matter bounce cosmology in light of Planck cosmic microwave background angular anisotropy measurements along with the BICEP2/Keck Array data. We propose a new primordial scalar power spectrum by considering a linear approximation of the equation of state w ≅ w 0 + κ(η − η 0) for quasi-matter field in the contracting phase of the universe. Using this new primordial scalar power spectrum, we constrain the zeroth-order approximation of the equation of state w 0 = −0.00340 ± 0.00044 and first-order correction 10 4 ζ = − 1.67 − 0.83 + 1.50 at the 1σ confidence level by Planck temperature and polarization in combination with the BICEP2/Keck Array data in which ζ = 12κ/k * with pivot scale k *. The spectral index of scalar perturbations is determined to be n Bs = 0.9623 ± 0.0055, which lies 7σ away from the scale-invariant primordial spectrum. We find scale dependency for n s at the 1σ confidence level and a tighter constraint on the running of the spectral index compared to ΛCDM+α s cosmology. The running of the spectral index in quasi-matter bounce cosmology is α Bs = π ζ/2c s = −0.0021 ± 0.0016, which is nonzero at the 1.3σ level, whereas in ΛCDM+α s it is nonzero at the 0.8σ level for Planck temperature and polarization data. The sound speed of density fluctuations of the quasi-matter field at the crossing time is c s = 0.097 − 0.023 + 0.037 , which is not a very small value in the contracting phase.

Consistency of Planck Data With Power-law Primordial Scalar Power Spectrum

Abstract In this work we explore the possibility of variations in the primordial scalar power spectrum around the power-law shape, as predicted by single-field slow-roll inflationary scenarios. We search for a trace of these fluctuations in a semiblind, model-independent way in observations of the cosmic microwave background (CMB) sky. In particular, we use two sets of perturbation patterns, specific patterns with typical features such as oscillations, bumps, and transitions, as well as perturbation modes, constructed from eigenanalysis of the forecasted or measured covariance of perturbation parameters. These modes, in principle, span the parameter space of all possible perturbations to the primordial spectrum and, when rank ordered, the ones with the highest detectability would suffice to explore the constrainable features around the power-law spectrum in a data-driven (and not theoretically biased) manner. With Planck measurements of CMB anisotropies, the amplitudes of all perturbation patterns considered in this work are found to be consistent with zero. This finding confirms, in the absence of theoretical biases, the consistency of the Planck data with the assumption of a power-law inflationary pattern for the primordial spectrum.

Compressed Python likelihood for large scale temperature and polarization from Planck

We present Planck-low-py, a binned low-$\ensuremath{\ell}$ temperature and $E$-mode polarization likelihood, as an option to facilitate ease of use of the Planck 2018 large scale data in joint-probe analysis and forecasting. It is written in python and compresses the $\ensuremath{\ell}&lt;30$ temperature and polarization angular power spectra information from Planck into two log-normal bins in temperature and seven in polarization. These angular scales constrain the optical depth to reionization and provide a lever arm to constrain the tilt of the primordial power spectrum. Using Planck-low-py, we show that cosmological constraints on $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model parameters, and on parameters including running and isocurvature, agree with those derived with the full Commander and SimAll likelihoods from the Planck legacy release.

Accurate model for the primordial black hole mass distribution from a peak in the power spectrum

We examine the shape of the primordial black hole mass distribution arising from a peak in the primordial power spectrum. In light of improvements to the modeling, we revisit the claim that the effects of critical collapse produce a distribution that is not described by the commonly assumed lognormal, showing that this conclusion remains valid, particularly for narrow peaks where the shape of the mass distribution is insensitive to the peak properties and critical collapse determines a minimum width. We propose some alternative models that may better describe the shape, both for the narrow peak case and for much broader peaks where the effect of the peak shape is significant. We highlight the skew-lognormal and a generalized model motivated by the physics of critical collapse as the best of these possible alternatives. These models can be used as an accurate and fast approximation to the numerically calculated mass distribution, allowing for efficient implementation in an MCMC analysis. We advocate the use of one of these two models instead of the lognormal with sufficiently accurate data, such as future LIGO--Virgo observations, or when considering strongly mass dependent constraints on the PBH abundance.